CN117236450A - Quantum entanglement resource scheduling method and device and electronic equipment - Google Patents

Quantum entanglement resource scheduling method and device and electronic equipment Download PDF

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CN117236450A
CN117236450A CN202311196888.6A CN202311196888A CN117236450A CN 117236450 A CN117236450 A CN 117236450A CN 202311196888 A CN202311196888 A CN 202311196888A CN 117236450 A CN117236450 A CN 117236450A
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方堃
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Beijing Baidu Netcom Science and Technology Co Ltd
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Beijing Baidu Netcom Science and Technology Co Ltd
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Abstract

The disclosure provides a quantum entanglement resource scheduling method and device and electronic equipment, relates to the technical field of quantum computing, and particularly relates to the technical field of quantum entanglement. The specific implementation scheme is as follows: receiving a quantum application request of a quantum network; based on the quantum application request, triggering nodes in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene; determining a first relation based on the input state information and the target error, wherein the first relation is a maximum optimized function relation of the optimal conversion rate of the quantum entanglement purification scene and the dimension of the output state information under a first preset condition, the first preset condition is that the conversion error from the input state information to the maximum entanglement state is smaller than or equal to the target error, and the conversion error is measured based on the distance between the Schmitt vectors of the quantum states under the quantum entanglement purification scene; determining a value of optimal conversion based on the first relationship; and carrying out resource scheduling on the quantum application service based on the quantum application request and the value of the optimal conversion rate.

Description

Quantum entanglement resource scheduling method and device and electronic equipment
Technical Field
The disclosure relates to the technical field of quantum computing, in particular to the technical field of quantum entanglement, and specifically relates to a quantum entanglement resource scheduling method, a quantum entanglement resource scheduling device and electronic equipment.
Background
The quantum network may be used to perform quantum application services, for example, the quantum communication system may deploy quantum key distribution application services to enable secure information transfer using quantum entanglement states, and for example, the quantum network may deploy communication application services to effectively allocate entanglement resources to various nodes of the quantum network for communication.
Quantum entanglement is a very specific and unique phenomenon in quantum mechanics, where two or more quantum systems enter a closely related complex state. In this state, the quantum states of the individual systems cannot be defined individually, but rather need to be considered in combination with all other systems as a whole.
Quantum entanglement of different structures may be applied in different scenarios. In most usage scenarios, the most desirable quantum entanglement is the bell state (i.e., the largest entanglement of dimension 2). Therefore, in order to ensure the practical effect of quantum entanglement in the relevant applications, a given quantum entanglement state needs to be converted into a bell state required for the application by a certain operation, which is called quantum entanglement purification, before actually being put into use.
When entanglement resources are scheduled for quantum application requests in a quantum network, direct scheduling is usually performed on the basis of entanglement resources obtained in a quantum entanglement purification scene of the quantum network.
Disclosure of Invention
The disclosure provides a quantum entanglement resource scheduling method and device and electronic equipment.
According to a first aspect of the present disclosure, there is provided a quantum entanglement resource scheduling method, comprising:
receiving a quantum application request of a quantum network, wherein the quantum application request is used for scheduling entanglement resources to execute quantum application services;
based on the quantum application request, triggering nodes in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene;
determining a first relation based on the input state information and the target error, wherein the first relation is a maximum optimized function relation of the optimal conversion rate of the quantum entanglement purification scene and the dimension of the output state information under a first preset condition, the first preset condition is that the conversion error from the input state information to the maximum entanglement state is smaller than or equal to the target error, and the conversion error is measured based on the distance between the Schmitt vectors of the quantum states in the quantum entanglement purification scene;
determining a value of the optimal conversion rate based on the first relationship;
and scheduling resources of the quantum application service based on the quantum application request and the value of the optimal conversion rate.
According to a second aspect of the present disclosure, there is provided a quantum entanglement resource scheduling device comprising:
the receiving module is used for receiving a quantum application request of the quantum network, wherein the quantum application request is used for scheduling entanglement resources to execute quantum application services;
the acquisition module is used for triggering nodes in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene based on the quantum application request;
the first determining module is used for determining a first relation based on the input state information and the target error, wherein the first relation is a maximum optimized functional relation between the optimal conversion rate of the quantum entanglement purification scene and the dimension of the output state information under a first preset condition, the first preset condition is that the conversion error from the input state information to the maximum entanglement state is smaller than or equal to the target error, and the conversion error is measured based on the distance between the Schmitt vectors of the quantum states under the quantum entanglement purification scene;
a second determining module configured to determine a value of the optimal conversion rate based on the first relationship;
and the resource scheduling module is used for scheduling the resource of the quantum application service based on the quantum application request and the value of the optimal conversion rate.
According to a third aspect of the present disclosure, there is provided an electronic device comprising:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform any one of the methods of the first aspect.
According to a fourth aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform any of the methods of the first aspect.
According to a fifth aspect of the present disclosure, there is provided a computer program product comprising a computer program which, when executed by a processor, implements any of the methods of the first aspect.
According to the technology disclosed by the invention, the problem that the flexibility of the quantum network to the resource scheduling of the quantum application service is relatively poor in the related technology is solved, and the flexibility and the accuracy of the quantum network to the resource scheduling of the quantum application service can be improved.
It should be understood that the description in this section is not intended to identify key or critical features of the embodiments of the disclosure, nor is it intended to be used to limit the scope of the disclosure. Other features of the present disclosure will become apparent from the following specification.
Drawings
The drawings are for a better understanding of the present solution and are not to be construed as limiting the present disclosure. Wherein:
fig. 1 is a flow diagram of a quantum entanglement resource scheduling method according to a first embodiment of the present disclosure;
FIG. 2 is a schematic representation of quantum state copy number versus average conversion for quantum entanglement purification;
fig. 3 is a schematic structural view of a quantum entanglement resource scheduling device according to a second embodiment of the present disclosure;
fig. 4 is a schematic block diagram of an example electronic device used to implement embodiments of the present disclosure.
Detailed Description
Exemplary embodiments of the present disclosure are described below in conjunction with the accompanying drawings, which include various details of the embodiments of the present disclosure to facilitate understanding, and should be considered as merely exemplary. Accordingly, one of ordinary skill in the art will recognize that various changes and modifications of the embodiments described herein can be made without departing from the scope and spirit of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
First embodiment
As shown in fig. 1, the present disclosure provides a quantum entanglement resource scheduling method, including the steps of:
step S101: a quantum application request of a quantum network is received, the quantum application request being for scheduling entangled resources for execution of a quantum application service.
In this embodiment, the quantum entanglement resource scheduling method relates to the technical field of quantum computing, in particular to the technical field of quantum entanglement, and can be widely applied to the scheduling scene of quantum network entangled resources of quantum application service. The quantum entanglement resource scheduling method of the embodiment of the disclosure can be executed by the quantum entanglement resource scheduling device of the embodiment of the disclosure. The quantum entanglement resource scheduling device of the embodiment of the disclosure can be configured in any electronic equipment to execute the quantum entanglement resource scheduling method of the embodiment of the disclosure.
The quantum network may be a quantum key distribution network, a quantum communication network, or a network for performing quantum computation in a quantum computer, which is not particularly limited herein.
The quantum network may be functionally divided into multiple layers, which may include an upper quantum application service layer and a lower service support layer, which may receive quantum application requests sent by the upper quantum application service layer to schedule entanglement resources for execution of quantum application services.
Optionally, the quantum application service includes any one of:
quantum key distribution application services;
A communication application service;
distributed quantum computing application services.
In one scenario, the quantum key distribution application service and the communication application service can schedule entangled resources obtained by quantum entanglement purification by a service support layer of the bottom layer to realize safe information transmission. In another scenario, the distributed quantum computing application service may schedule entangled resources obtained by quantum entanglement purification by the underlying service support layer to perform complex algorithms, such as distributed quantum computing.
The quantum application request may carry a service identification, an entangled resource number, entangled resource characteristics, and the like. For example, the entangled resource features carried in the quantum application request indicate the maximum entangled state, i.e. the quantum application service needs to use the maximum entangled state to realize the corresponding service.
Step S102: based on the quantum application request, triggering nodes in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene.
Quantum entanglement is a very specific and unique phenomenon in quantum mechanics, where two or more quantum systems enter a closely related complex state. In this state, the quantum states of the individual systems cannot be defined individually, but rather need to be considered in combination with all other systems as a whole.
A common example is two entangled particles whose spin states may be indeterminate, but interrelated. Even though the two particles are far apart, their spin states remain entangled. For example, if one of the particles is measured with its spin up, then wherever the other particle is, its spin is measured, with the result being necessarily down. In particular, this correlation is independent of the physical distance of the entangled particles. This situation is beyond the understanding of classical physics because, from the point of view of classical physics, two objects that are far apart are unlikely to have such a "transient" interaction. This phenomenon can be approximated by the term "ghost-like superspeed". However, this is an essential feature of the quantum world and has been confirmed by a large number of experiments.
Quantum entanglement is important not only in theory but also in practical applications such as quantum computing, quantum cryptography, and quantum communication. In the field of quantum computing, quantum entanglement is considered as a key factor in achieving large-scale quantum computing. With entangled qubits, quantum computers can process a large amount of information, exceeding the processing power of classical computers.
Secondly, quantum entanglement plays a vital role in quantum cryptography, particularly in quantum key distribution protocols, a secure cryptographic key is created for both parties of communication by quantum entanglement, and any attempt to steal the key breaks the entangled state and is detected. In addition, due to the "ghost-like overstepping effect" of entangled particles, changing the state of one particle can instantaneously affect another particle entangled therewith, which makes long-distance quantum communication and quantum clock synchronization possible, no matter how far the distance between the two particles is. In quantum invisible transport states, "transport" of one quantum state from one place to another can be accomplished by utilizing quantum entanglement.
The quantum entanglement can also be applied to the fields of quantum precision measurement and the like, and higher precision and sensitivity are provided compared with the traditional technology. The nature of quantum entanglement allows communication and computation beyond the limits of classical theory, opening new possibilities for technological development.
Quantum entanglement of different structures may be applied in different scenarios. In most usage scenarios, the most desirable quantum entanglement is the bell state (i.e., the largest entanglement of dimension 2). Therefore, in order to ensure the practical effect of quantum entanglement in the relevant applications, a certain operation is required to convert a given quantum entanglement state into a bell state required for the application, before actually being put into use. This operation is then known as quantum entanglement purification.
In step S102, when the quantum application request is acquired, based on the entanglement resource feature and the entanglement resource number carried by the quantum application request, the node in the quantum network may be triggered to prepare input state information in the quantum entanglement purification scene, so as to acquire the input state information to prepare for quantum entanglement purification operation.
The more entanglement resources, the more input state information can be obtained, so that more entanglement resources can be generated for scheduling. However, the input state information is related to the noise environment and hardware devices of the nodes in the quantum network, and the amount of input state information that the nodes in the quantum network prepare is typically limited under the limitations of the corresponding noise environment and hardware devices. Nodes may refer to quantum devices, or may refer to modules in a quantum computer, and are not specifically limited herein.
The input state information refers to a quantum state input in a quantum entanglement purification process, the quantum state is obtained by tensor product on the basis of n initial quantum states, the initial quantum states are quantum states on two quantum systems, the dimensions of the two quantum systems can be identical, the dimension of one quantum system can be d, and n is the copy number of the input state information. For the quantum state |ψ on any AB quantum system > AB The input state information can be expressed as
Ideally, the quantum state obtained by quantum entanglement purification is required to be a perfect bell state, and the conversion rate is very low due to the fact that the conversion requirement is often too strict, so that the error between the quantum state obtained by quantum entanglement purification and the bell state is usually required to meet a given error threshold in practical application. The error threshold is a target error, and when the error between the quantum state obtained by quantum entanglement purification and the bell state is smaller than or equal to the error threshold, the error between the quantum state obtained by quantum entanglement purification and the bell state meets the error threshold.
The target error can be preset, the quantum application request can carry the target error, and the target error can be obtained from the quantum application request correspondingly.
Step S103: and determining a first relation based on the input state information and the target error, wherein the first relation is a maximum optimized function relation of the optimal conversion rate of the quantum entanglement purification scene and the dimension of the output state information under a first preset condition, the first preset condition is that the conversion error from the input state information to the maximum entanglement state is smaller than or equal to the target error, and the conversion error is measured based on the distance between the Schmitt vectors of the quantum states under the quantum entanglement purification scene.
The basic idea of quantum entanglement purification is to convert one or more pairs of initial quantum entanglement states into as many bell states as possible through a series of local quantum operations and classical communication (Local Operations and Classical Communication, LOCC), and to ensure that the difference between the converted quantum states and the ideal bell states is less than a given error threshold epsilon.
If through a certain LOCC operation scheme, n pairs of initial quantum entanglement states can be converted into m pairs of bell states within the error range, the conversion rate of the scheme is called m/n. For example, if 10 pairs of initial quantum entanglement states are required to obtain a pair of bell states, then the conversion rate of this quantum entanglement purification process is 1/10 or 0.1. Thus, higher conversion indicates higher efficiency of the entanglement purification process, and less entanglement resources are consumed to produce an equivalent number of bell states.
The quantum entanglement purification conversion rate is used as a key parameter for measuring entanglement purification protocol efficiency, and the calculation of the quantum entanglement purification conversion rate has a vital meaning. First, because the quantum resources (e.g., initial quantum entanglement) available in actual quantum information handling systems are often limited, understanding and calculation of entanglement purification conversion can help manage these resources more effectively for optimal system performance.
Second, comparing the conversion rates of different entangled purification protocols can guide the selection of the most efficient protocol under specific conditions or optimize the existing protocol to increase its efficiency. Furthermore, since entanglement is susceptible to errors and noise, entanglement purification is a means of reducing these effects, the conversion rate of which can reflect the purification effect, indicating whether further error correction is required.
In addition, the optimal conversion rate of entanglement purification can be used as a benchmark for measuring the performance of the quantum information processing system. Comparing the theoretically expected conversion with the actual measured conversion, it is possible to evaluate whether the system performance is expected or whether potential room for improvement is revealed. The optimal conversion rate can be calculated, and the corresponding optimal entanglement purification protocol can be found, so that the efficiency of quantum entanglement purification operation is maximized, and the quantum entanglement purification method has very important practical value.
In specific product requirements and application scenes, the application of calculating the quantum entanglement purification conversion rate is particularly important.
1. In designing and constructing quantum computers, high quality entangled states need to be generated and manipulated to perform complex quantum algorithms. In this process, quantum entanglement purification conversion provides an important efficiency indicator. For example, if the conversion rate of some entanglement purification protocol is found to be low, it may be necessary to find a more efficient protocol or to improve existing entanglement generation and purification techniques. Furthermore, comparing the theoretical expected and actually measured conversions can help to evaluate the actual performance of the quantum computer and to determine the technical problems that may exist.
2. In quantum communication systems, such as quantum key distribution protocols, entangled states are often used to enable secure information transfer. However, loss and noise during transmission may reduce the quality of the entangled state, resulting in reduced security of information transmission. In this case, entanglement purification is very important. By calculating the conversion rate, it is possible to know how much original entanglement resources are needed to guarantee a secure information transmission under given system conditions.
3. In building a quantum network, entangled resources need to be efficiently allocated to the various nodes of the network. Knowing the conversion of entanglement purification, these resources can be better planned and managed, for example, to determine which nodes need more entanglement resources, or how to adjust the topology of the network to optimize resource utilization.
In summary, calculating the conversion rate of quantum entanglement purification plays a key role in various quantum information products and applications, and has important significance for promoting the progress of quantum information technology. Since different schemes have different quantum entanglement purification conversions, how to find a scheme with an optimal conversion rate and calculate a corresponding optimal conversion rate is a widely focused issue in the industry.
The objective of this embodiment is to determine the optimal conversion rate under any given finite resource quantum entanglement state and error threshold, and schedule the resource for the quantum application service based on the quantum application request and the value of the optimal conversion rate. Thus, entangled resources which can be obtained by quantum entanglement purification can be simulated through the value of the optimal conversion rate, and the flexibility and the accuracy of the quantum network for resource scheduling of quantum application services are correspondingly improved. Furthermore, the optimal conversion rate can be used for optimizing the conversion efficiency in the quantum entanglement purification process so as to optimize the quantum entanglement purification protocol of the quantum network.
In step S103, there are various conversion error modes for defining quantum states, and different error defining modes are applicable to different usage scenarios, and the corresponding calculation difficulties are also completely different. The conversion error can be understood as defining that the quantum state after conversion is in a pure state (i.e. a maximum entangled state) under ideal conditions, and the error between the quantum state and the output state information obtained by quantum entanglement purification is smaller than or equal to the target error.
Under the definition of the conversion error, the optimal conversion rate of quantum entanglement purification is represented as the following formula (1).
The above formula (1) is the first relationship determined,for the first preset condition ε is the target error, ++>For transformation error, ++>The maximum dimension achievable for the output state information may be equivalent to the optimal conversion, which may be defined by +.>Calculated, n is the copy number of the input state information, m is more than or equal to 2, m is a positive integer,/>Is the maximum entanglement between quantum systems A and B, equivalent to log 2 m is the dimension of the output state information of quantum entanglement purification.
Conversion errors can be measured by the distance between schmitt vectors of quantum states in a quantum entanglement purification scenario. Optionally, the conversion error is measured based on a trace norm of the schmitt vector of the quantum state in the quantum entanglement purification scene, which may be a 1-norm of the schmitt vector of the quantum state in the quantum entanglement purification scene, and the multiple may be any multiple, for example, the conversion error may be 1/2 of the 1-norm of the schmitt vector of the quantum state in the quantum entanglement purification scene.
Alternatively, the conversion error is expressed as:
wherein T (|beta)>→|λ>) For the conversion error, |λ>Is the maximum entangled state, |beta>For input state information in quantum entanglement purification scene, p λ Schmitt vector p, which is the maximum entangled state β The method comprises the steps that a Schmitt vector r of input state information in a quantum entanglement purification scene is a Schmitt vector r of output state information in the quantum entanglement purification scene, prob (d) represents a set of probability distribution vectors with all dimensions d, and d is a quantum system dimension of the input state information.
I.e.May be 1/2 of the 1-norm of the schmitt vector of the quantum state in the quantum entanglement purification scene, and the conversion error may be represented as shown in the following formula (2).
||x|| 1 Is the 1-norm of the vector x, λ is |φ m >May beMaximum entanglement between quantum systems A and B, β beingThe input state information in the quantum entanglement purification scene can be obtained, and the quantum state can be the quantum state of the quantum systems A and B.
It should be noted that, for any of the quantum systems a and B, the quantum state |ψ in one copy is> AB It is in the presence of Schmidt decompositionWherein |i> A ,|i> B The basis vectors on the quantum systems A and B are respectively, d is the dimension of the quantum system A, the system dimensions of the quantum systems A and B are the same, and p i Descending order (p) 1 ≥p 2 ≥...≥p d ). Is called p ψ =(p 1 ,p 2 ,...,p d ) Is quantum state |psi> AB Is a schmitt vector of (c).
For any vector p, note p (K) Is the sum of the first K largest elements of vector p, i.eFor any two vectors of length d, r > p is noted β Meaning that for any K.epsilon. {1, 2.,. D }, the sum of the first K largest elements of vector r is greater than or equal to vector p β The sum of the first K largest elements of (c). Wherein r > p β Is the condition that the optimization function in the above formula (2) needs to satisfy, and +.>Is an optimization function.
Step S104: based on the first relationship, a value of the optimal conversion is determined.
The optimal conversion rate value is used for optimizing the conversion efficiency in the quantum entanglement purification process or scheduling entanglement resources in the quantum entanglement purification process.
Under the condition of providing input state information and target errors, the dimension of the output state information can be solved under a first preset condition through related calculation software, so that the value of the optimization function in the first relation is at the maximum value, and the maximum value is the value of the optimal conversion rate of quantum entanglement purification.
On the premise of obtaining the value of the optimal conversion rate, related applications such as quantum key distribution protocol application, quantum network construction application, debugging application of quantum entanglement purification algorithm, distributed quantum computing application and the like can be carried out based on the value of the optimal conversion rate, and in the applications, the conversion efficiency in the quantum entanglement purification process can be optimized based on the optimal conversion rate, and entanglement resources in the quantum entanglement purification process can be scheduled.
Step S105: and scheduling resources of the quantum application service based on the quantum application request and the value of the optimal conversion rate.
The maximum number of entanglement resources which can be obtained through purification can be simulated based on the value of the optimal conversion rate under the corresponding input state information, the quantum application request also carries the quantity of entanglement resources which need to be scheduled, and when the maximum number of entanglement resources which can be obtained through purification is greater than or equal to the quantity of entanglement resources in the quantum application request, quantum entanglement purification operation can be executed in response to the quantum application request, entanglement resources are correspondingly obtained, and quantum application service is performed to an upper layer.
In the case where the maximum number of entanglement resources available for purification is smaller than the number of entanglement resources in the quantum application request, the quantum application request may be directly rejected without performing the quantum entanglement purification operation.
In this embodiment, a quantum application request of a quantum network is received; based on a quantum application request, triggering a node in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene; based on the input state information and the target error, constructing an optimization function to determine the optimal conversion rate of the quantum entanglement purification scene; and then, carrying out resource scheduling on the quantum application service based on the quantum application request and the value of the optimal conversion rate. Therefore, the entanglement resources available for quantum entanglement purification can be simulated through the value of the optimal conversion rate, and the flexibility and accuracy of the quantum network for resource scheduling of quantum application services are correspondingly improved.
And the conversion error from the input state information to the maximum entangled state is measured based on the distance between the Schmitt vectors of the quantum states in the quantum entangled purifying scene, the maximum optimized function relation between the optimal conversion rate of the quantum entangled purification and the dimension of the output state information under the first preset condition is constructed based on the input state information and the target error of the quantum entangled purification, and then the maximum optimized function relation is solved to obtain the value of the optimal conversion rate. The method is suitable for determining the optimal conversion rate under the conditions of any given limited resource quantum entanglement state and error threshold, so that the flexibility of determining the optimal conversion rate of quantum entanglement purification can be improved, the requirements of practical application scenes are met, and the conversion efficiency in the quantum entanglement purification process and entanglement resources in the quantum entanglement purification process can be optimized more accurately.
Optionally, the step S105 specifically includes:
determining entanglement resources which can be obtained by purification in a quantum entanglement purification scene of the quantum network based on the value of the optimal conversion rate;
and carrying out resource scheduling on the quantum application service under the condition that the purified entangled resource is larger than or equal to the entangled resource requested by the quantum application request.
The entanglement resources which can be obtained by purification in the quantum entanglement purification scene of the quantum network can be determined based on the value of the optimal conversion rate and the input state information prepared by the nodes of the quantum network. And then comparing the purified entanglement resources determined based on the value of the optimal conversion rate with entanglement resources requested by the quantum application request, and carrying out resource scheduling on the quantum application service based on the comparison result.
In case that the available entanglement resources determined based on the value of the optimal conversion rate are greater than or equal to entanglement resources requested by the quantum application request, at this time, there are enough entanglement resources for scheduling, and thus, the corresponding entanglement resources can be scheduled to an upper layer for the quantum application service.
In this way, resource scheduling for quantum application services can be achieved based on the value of optimal conversion.
Optionally, the method further comprises:
and refusing to respond to the quantum application request under the condition that the available entanglement resource is smaller than the entanglement resource requested by the quantum application request.
Thus, by simulating the entanglement resources available for quantum entanglement purification based on the value of the optimal conversion rate, the quantum entanglement purification operation is not required to be performed in the case that the entanglement resources are smaller than those requested by the quantum application request, and the response to the quantum application request can be directly refused, so that unnecessary operations are reduced.
Optionally, the method further comprises:
and under the condition that the purified entanglement resources are smaller than entanglement resources requested by the quantum application request, based on the value of the optimal conversion rate, adjusting input state information in a quantum entanglement purification scene of the quantum network so as to improve the purified entanglement resources in the quantum entanglement purification scene.
Under the condition that the available entangled resources are smaller than the entangled resources requested by the quantum application request, the input state information with the minimum required amount can be determined based on the value of the optimal conversion rate and the entangled resources in the quantum application request, so that safe information transmission is ensured. The input state information under the quantum entanglement purification scene of the quantum network is adjusted, for example, the quantity of the input state information under the quantum entanglement purification scene of the quantum network is increased, so that quantum entanglement purification is carried out, more entanglement resources can be obtained for resource scheduling, and the flexibility and accuracy of quantum entanglement resource scheduling can be further improved.
In the above formula (1), the quantum stateIs of the dimension |AB| n As n grows exponentially, directly solving for the calculation +.>The complexity of (c) also increases exponentially with n, so the complexity of solving the optimal conversion can be reduced by converting the first relationship.
Optionally, the step S104 specifically includes:
performing schmitt decomposition on the input state information to convert the first relation into a second relation and a third relation, wherein the second relation is a minimum optimized functional relation between the optimal conversion rate and first information, the first information comprises a first target norm of a first schmitt vector of the input state information, a target error and a first variable, the first target norm is a sum of first K maximum elements of the first schmitt vector, the third relation is a minimum optimized functional relation between a lower boundary of a target value range of the first variable and a second variable under a second preset condition, the second preset condition is that the second target norm of the first schmitt vector is larger than the target error, and the second target norm is a sum of first Y maximum elements of the first schmitt vector; k is the first variable, K is a positive integer, Y is the second variable, and Y is a positive integer.
Determining a target value range of the first variable based on the third relation and second information, wherein the second information is the copy number and quantum system dimension of the input state information;
and determining the value of the optimal conversion rate based on the second relation and the target value range of the first variable.
In this embodiment, the input state information in the above formula (1) may be subjected to schmitt decomposition to convert the first relationship into a second relationship and a third relationship, that is, the above formula (1) is converted into the second relationship and the third relationship, the second relationship may be represented by the following formula (3), and the third relationship may be represented by the following formula (4).
Wherein, in the above formulas (3) and (4),for the lower valued function, i.e. the maximum integer not greater than x,/>First schmitt vector +.>I is the lower bound in the target range of values of the first variable,for the second preset condition,/o>First schmitt vector +.>Is a second target norm of (c).
As can be seen from the above formulas (3) and (4), for calculationCan calculate +.>And->And solving the minimum optimization function in the third relation under the second preset condition to obtain the target value range of the first variable.
Optionally, the determining, based on the third relationship and the second information, the target value range of the first variable includes:
determining a lower bound value of the target value range based on the third relationship;
and determining an upper limit value of the target value range based on the second information.
Namely, solving the minimum optimization function in the third relation under the second preset condition to obtain the lower bound value in the target value range of the first variable, and obtaining the minimum value by d n And calculating the upper limit value of the target value range, so that the target value range of the first variable can be obtained.
Further, calculateBased on->And solving the second relation, wherein the aim is to enable the value of the optimization function in the second relation to be at the minimum value in the target value range of the first variable, and the minimum value is the value corresponding to the optimal conversion rate of the quantum entanglement purification.
In this way, by converting the first relationship into the second relationship and the third relationship to determine the optimal conversion rate, the complexity of solving the optimal conversion rate can be reduced.
Optionally, the determining, based on the third relationship, a lower bound value of the target value range includes:
acquiring the first schmitt vector;
sequentially acquiring a second target norm of the first Schmitt vector according to the sequence from small to large of the second variable; outputting a value of the second variable if the second target norm is greater than the target error;
wherein the value of the second variable is the lower bound value of the target value range.
The first schmitt vector may be obtained in various manners, for example, the input state information is subjected to schmitt decomposition, and the first schmitt vector may be obtained. For another example, the schmitt decomposition is performed on the quantum state in one copy of the input state information to obtain a second schmitt vector of the quantum state, and the first schmitt vector is determined based on the second schmitt vector by using symmetry of the quantum state of the input state information and the schmitt vector of the input state information.
Under the condition that a first Schmitt vector is acquired, sequentially acquiring a second target norm of the first Schmitt vector according to the sequence from the smaller second variable to the larger second variable; and under the condition that the second target norm is obtained, judging whether the second target norm is larger than the target error, namely judging whether a second preset condition is met, and if so, outputting the value of the second variable, wherein the value is the lower bound value of the target value range of the first variable.
Therefore, the solution of the optimization function in the third relation can be realized, the target value range of the first variable is obtained, and the solution of the optimization function in the second relation is further solved, so that the value of the optimal conversion rate of quantum entanglement purification is obtained.
In the determination of the first Schmitt vector, due to the quantum stateIs larger in dimension and as n grows exponentially, the corresponding direct calculation of the quantum state +.>The first schmitt vector of the input state information is relatively high in complexity, so that the first schmitt vector can be determined based on the second schmitt vector of the quantum state under one copy of the input state information by utilizing the quantum state symmetry of the input state information, and the complexity in the determination process of the first schmitt vector is reduced. Optionally, the acquiring the first schmitt vector includes:
acquiring a second Schmitt vector of a quantum state under one copy in the input state information;
based on the quantum system dimension of the input state information, carrying out distribution processing on the copy number of the input state information to obtain W pieces of distribution information, wherein one piece of distribution information comprises a distribution result and the repetition number of the distribution result;
based on the W pieces of distribution information, performing polynomial combination on the first elements in the second Schmitt vectors to obtain W pieces of second elements corresponding to W pieces of distribution results one by one and the repetition times of each second element, wherein the repetition times of the second elements are the repetition times of the distribution results corresponding to the second elements;
Arranging the W second elements in descending order to obtain a target vector;
the first schmitt vector is obtained by arranging the target vector according to the repetition times of each second element.
Optionally, sequentially acquiring a second target norm of the first schmitt vector according to the order of the second variable from small to large; outputting a value of the second variable if the second target norm is greater than the target error, comprising:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
outputting a value of the second variable if the first sum is greater than the target error;
wherein the value of the second variable isN is the second label, P is the first sum, s i And epsilon is the target error for a second element corresponding to the first index i in the target vector.
The specific process of efficiently calculating the first Schmitt vector and efficiently solving the lower bound value of the target value range of the first variable is as follows:
input: second schmitt vector p ψ =(p 1 ,p 2 ,...,p d ) The positive integer n is more than or equal to 1, and the target error epsilon [0,1 ]];
And (3) outputting:
step 1: and carrying out distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information. Specifically, consider n 1 +n 2 +...+n d =n, and integer n i Not less than 0, then corresponds to n 1 ,n 2 ,...,n d The value modes of (a) are commonSeed, and each case corresponds to a repetition number +.>
Step 2: based on the W distribution information, performing polynomial combination on the first element in the second Schmitt vector to calculateA different polynomial +.>Obtaining W second elements corresponding to W distribution results one by one and the repetition times of each second element;
step 3: the W second elements are arranged in descending order to obtain a target vector(s) 1 ,s 2 ,...,s W ) And record the second element s i Corresponding repetition number v i The first schmitt vector can be obtained by arranging the target vector according to the repetition number of each second element, so that the first schmitt vector can be determined based on the second schmitt vector of the quantum state under one copy of the input state information by utilizing the quantum state symmetry of the input state information;
Step 4: let n=0, p=0, where N and P are intermediate variables for recording the first sign of the second element in the target vector, the second sign of the corresponding element in the first schmitt vector, and the first addition of the third element in the first schmitt vector during the round-robin from small to large. Wherein the second label refers to the maximum label of the elements corresponding to the first label in the first schmitt vector, if the first label is 1, and the repetition number of the second element corresponding to the first label 1 is 10, the elements corresponding to the first label in the first schmitt vector are the elements with labels 1 to 10, the maximum label is 10, the second label is 10, and the first summation is the summation of the elements with labels 1 to 10 in the first schmitt vector;
step 5: for each i e {1,2,., W } loops:
step 5.1: let n=n+v i ,P=P+v i s i
Step 5.2: if ε < P, returnAs an output.
The output is the value of the second variable Y, and the value of the optimization function under the value in the third relation is at the minimum.
In the step 5, W cycles are needed at most, that is, W is a polynomial degree about n, so that the solution of the minimum optimization function in the third relationship can be performed under the second preset condition with high efficiency, and the lower boundary value in the target value range of the first variable is obtained.
Optionally, the determining the value of the optimal conversion rate based on the second relation and the target value range of the first variable includes:
and under the condition that the lower bound in the target value range of the first variable is equal to the upper bound, determining the value of the first variable under the minimum optimization function value in the second relation as the upper bound in the target value range, and obtaining the value of the optimal conversion rate.
The optimization function in the second relationship may be represented by the following equation (5).
When the target value range of the first variable is only one value, the value is the value of the first variable with the minimum optimization function value of the optimization function, and the value of the optimal conversion rate is (log 2 f(d n ) I.e. the value of output optimum conversion is/>
In this way, a determination of the value that efficiently achieves optimal conversion can be achieved.
Optionally, the determining the value of the optimal conversion rate based on the second relation and the target value range of the first variable includes:
under the condition that the lower bound in the target value range of the first variable is not equal to the upper bound, acquiring a first target norm of the first Schmitt vector to obtain a gradient function of an optimization function in the second relation, wherein the gradient function is a function of the first information;
And determining the value of the first variable of the optimization function under the minimum optimization function value based on the gradient function and the target value range of the first variable, and obtaining the value of the optimal conversion rate.
The gradient function of the optimization function can be represented by the following formula (6).
As can be seen from equation (6) above, which relates to the first target norm, the gradient function can be obtained by calculating the first target norm.
And then, based on the gradient function, solving an extreme point of the optimization function in the target value range of the first variable, namely determining a variable value when the gradient function value is zero, wherein the extreme point is the value of the first variable of the optimization function under the minimum optimization function value, and obtaining the value of the optimal conversion rate. In this way, a determination of an optimal conversion rate for quantum entanglement purification can be achieved.
The first target norm may be directly obtained based on a first schmitt vector of the input state information, or may be obtained based on a second schmitt vector of the quantum state under one copy of the input state information. Optionally, the obtaining the first target norm of the first schmitt vector includes:
obtaining a target vector, wherein the target vector is obtained by arranging W second elements according to a descending order, the W second elements are obtained by performing polynomial combination on first elements in a quantum state second Schmitt vector under one copy of input state information based on W distribution information, one distribution information comprises a distribution result and the repetition number of the distribution result, the W distribution information is obtained by performing distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information, the first Schmitt vector is obtained by arranging the target vector according to the repetition number of each second element, and the repetition number of the second elements is the repetition number of the distribution result corresponding to the second elements;
A first target norm of the first schmitt vector is determined based on the target vector and a number of repetitions of a second element in the target vector.
The quantum state symmetry of the input state information may be utilized to determine a first schmitt vector based on a second schmitt vector of quantum states in one copy of the input state information to reduce complexity in the first schmitt vector determination process.
A first target norm of the first schmitt vector is then determined based on the target vector and a number of repetitions of a second element in the target vector. Therefore, the first target norm of the first Schmitt vector of the input state information can be efficiently solved, and the solving complexity of the optimal conversion rate is reduced.
Optionally, the determining the first target norm of the first schmitt vector based on the target vector and the number of repetitions of the second element in the target vector includes:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
Outputting a first target norm of the first schmitt vector if the first variable is less than the second label;
wherein the first target norm is s i * (K-N) +P, N being the second label, P being the first sum, s i And the second element corresponding to the first index i in the target vector.
Which efficiently calculates a first target normThe specific process of (2) is as follows:
input: second schmitt vector p ψ =(p 1 ,p 2 ,...,p d ) The positive integer n is more than or equal to 1, and m is more than or equal to 1;
and (3) outputting:
step 1: and carrying out distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information. Specifically, consider n 1 +n 2 +...+n d =n, and integer n i Not less than 0, then corresponds to n 1 ,n 2 ,...,n d The value modes of (a) are commonSeed, and each case corresponds to a repetition number +.>
Step 2: based on the W distribution information, performing polynomial combination on the first element in the second Schmitt vector to calculateA different polynomial +.>Obtaining W second elements corresponding to W distribution results one by one and the repetition times of each second element;
step 3: the W second elements are arranged in descending order to obtain a target vector(s) 1 ,s 2 ,...,s W ) And record the second element s i Corresponding repetition number v i The first schmitt vector can be obtained by arranging the target vector according to the repetition number of each second element, so that the first schmitt vector can be determined based on the second schmitt vector of the quantum state under one copy of the input state information by utilizing the quantum state symmetry of the input state information;
step 4: let n=0, p=0, where N and P are intermediate variables for recording the first sign of the second element in the target vector, the second sign of the corresponding element in the first schmitt vector, and the first addition of the third element in the first schmitt vector during the round-robin from small to large. Wherein the second label refers to the maximum label of the element corresponding to the first label in the first schmitt vector;
step 5: for each i e {1,2,., W } loops:
step 5.1: let n=n+v i ,P=P+v i s i
Step 5.2: if K < N, return s i * (K-N) +P as output.
The output is the first target norm.
The algorithm described above requires at most W cycles in step 5, W being the polynomial degree for n. If the memory space of the new polynomial is allowed, the loop degree can be reduced to a logarithmic number with respect to n by a dichotomy search. Optionally, the determining the first target norm of the first schmitt vector based on the target vector and the number of repetitions of the second element in the target vector includes:
Determining W second labels of elements corresponding to the W first labels in the first Schmitt vector based on W first labels of the W second elements in the target vector and the repetition times of the second elements in the target vector;
performing dichotomy search on the first variable, and outputting a first target norm of the first Schmitt vector when the first variable is located in a target interval;
wherein the target interval is an interval determined by two adjacent second labels corresponding to the binary values in the binary search in the W second labels, and the first target norm is s c+1 *(K-N c )+P c C is the scoring value, s c+1 N being the second element corresponding to the first index c+1 in the target vector c A second index, P, corresponding to the element corresponding to the first index c in the first Schmitt vector c And a second summation of a fourth element in the first schmitt vector, wherein the fourth element comprises an element corresponding to the first mark c and an element before the element corresponding to the first mark c.
The specific process of searching and efficiently solving the first target norm by adopting the dichotomy is as follows:
input: second schmitt vector p ψ =(p 1 ,p 2 ,...,p d ) The positive integer n is more than or equal to 1, and m is more than or equal to 1;
and (3) outputting:
step 1: and carrying out distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information. Specifically, consider n 1 +n 2 +...+n d =n, and integer n i Not less than 0, then corresponds to n 1 ,n 2 ,...,n d The value modes of (a) are commonSeed, and each case corresponds to a repetition number +.>
Step 2: based on the W distribution information, performing polynomial combination on the first element in the second Schmitt vector to calculateA different polynomial +.>Obtaining W second elements corresponding to W distribution results one by one and the repetition times of each second element;
step 3: the W second elements are arranged in descending order to obtain a target vector(s) 1 ,s 2 ,...,s W ) And record the second element s i Corresponding repetition number v i The first schmitt vector can be obtained by arranging the target vector according to the repetition number of each second element, so that the first schmitt vector can be determined based on the second schmitt vector of the quantum state under one copy of the input state information by utilizing the quantum state symmetry of the input state information;
step 4: let N 0 =0,P 0 =0, where N 0 And P 0 Is an intermediate variable, and is used for recording the second label of the element corresponding to the first label in the first schmitt vector and the first addition of the third element in the first schmitt vector in the cycle process from small to large of the first label of the second element in the target vector. Wherein the second label refers to the maximum label of the element corresponding to the first label in the first schmitt vector;
Step 5: for any j e {1,2,., W }, calculateAnd->
Step 6: let the lower bound a=0 and the upper bound b=w of the dichotomy search;
step 7: the following loop is performed until the output is returned:
step 7.1: let two-component
Step 7.2: if N c ≤K≤N c+1 Return s c+1 *(K-N c )+P c As an output, the output is the first target norm;
step 7.3: if K < N c Let b=c;
step 7.4: if K > N c+1 Let a=c+1.
Optionally, the determining the value of the first variable of the optimization function under the minimum optimization function value based on the gradient function and the target value range of the first variable, to obtain the value of the optimal conversion rate includes:
under the condition that a first objective gradient function value is greater than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle lower boundary of the objective value range, and obtaining the value of the optimal conversion rate, wherein the first objective gradient function value is the value of the gradient function when the value of the first variable is the middle lower boundary of the objective value range;
under the condition that a second objective gradient function value is smaller than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle upper boundary of the objective value range to obtain the value of the optimal conversion rate, wherein the second objective gradient function value is the value d of the first variable n -1 a value of a gradient function, d being a quantum system dimension of the input state information, n being a copy number of the input state information;
under the condition that the first target gradient function value is smaller than zero and the second target gradient function value is larger than zero, performing dichotomy search based on the lower bound of the target value range and the first target value, and determining the optimization under the condition that the upper bound of the dichotomy search interval is smaller than or equal to the second target valueThe value of the first variable of the function under the minimum optimization function value is the upper bound of the dichotomy search interval, the value of the optimal conversion rate is obtained, and the first target value is d n -1, the second target value is the lower bound of the dichotomy search interval plus 1;
in the dichotomy search, when the third objective gradient function value is greater than or equal to zero, the upper bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and when the third objective gradient function value is less than zero, the lower bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and the third objective gradient function value is a value of the gradient function when the value of the first variable is the dichotomy value in the dichotomy search.
The specific process for efficiently calculating the optimal conversion rate is as follows:
input: second schmitt vector p ψ =(p 1 ,p 2 ,...,p d ) The positive integer n is more than or equal to 1, and the target error epsilon [0,1 ]];
And (3) outputting:
step 1: calculating the middle and lower bounds of the target value range of the first variableDenoted as l;
step 2: if l=d n Return toAs an output;
step 3: calculating a gradient function value (i.e., a first objective gradient function value) when the value of the first variable is l, denoted as g (l);
step 4: g (l) is more than or equal to 0, returnsAs an output;
step 5: calculating the value of the first variable as d n Gradient function value at-1 (i.eA second objective gradient function value) representing g (d n -1);
Step 6: if g (d) n -1) is less than or equal to 0, return toAs an output;
step 7: if g (l) is less than 0, and g (d) n -1) > 0, let the lower bound a=l and the upper bound b=d of the dichotomy search n -1;
Step 8: if the cycle condition b > a+1 is satisfied, the following cycle is performed:
step 8.1: let two-component
Step 8.2: if the third objective gradient function value g (c) is more than or equal to 0, let b=c; otherwise, let a=c;
step 9: if the circulation condition is not satisfied, returnAs an output.
Will outputDividing by the copy number n of the input state information to obtain the value of the optimal conversion rate of the quantum entanglement purification, so that the optimal conversion rate of the quantum entanglement purification can be obtained by high-efficiency solving.
The determination scheme of the optimal conversion rate of quantum entanglement purification of the embodiment can be suitable for the situation of any given limited resource quantum entanglement state and any given error threshold value, and meets the requirements of practical application scenes. In particular, the computational complexity involved grows polynomial with the copy number of the initial quantum states, which is very efficient in practical use scenarios. In addition, when the error threshold is taken to be zero or the initial quantum state copy number is taken to be sufficiently large, determination of optimal conversion rate of quantum entanglement purification under ideal conditions can also be covered. Therefore, the use scene is greatly expanded while ensuring high-efficiency calculation, and the method meets the actual application requirements better.
The actual effects of the present embodiment are shown below with a specific example. Consider the initial quantum stateThe Schmitt vector is p ψ = (0.9, 0.1), error threshold epsilon=0.1, quantum state copy number n takes on a value of 1 to 500.
FIG. 2 is a graph showing the relationship between the quantum state copy number and the average conversion rate of quantum entanglement purification, as shown in FIG. 2, the horizontal axis represents the quantum state copy number, and the vertical axis represents the average conversion rate, namelyThe horizontal line 201 represents the progressive value of the curve 202 as n approaches infinity, which can be given by shannon entropy of the p vector, obtained using a 16G memory and a plain notebook operation of the Intel Core i7 TH GEN processor, with a practical calculation time of approximately 5 minutes. In contrast, directly solving the optimal conversion for quantum entanglement purification based on equation (1) above requires calculating and storing a length of 2 500 Far beyond the computational power of existing supercomputers. Therefore, the efficient calculation mode of the optimal conversion rate of quantum entanglement purification has important practical value.
Second embodiment
As shown in fig. 3, the present disclosure provides a quantum entanglement resource scheduling device 300, comprising:
a receiving module 301, configured to receive a quantum application request of a quantum network, where the quantum application request is used to schedule entangled resources to execute a quantum application service;
the obtaining module 302 is configured to trigger, based on the quantum application request, a node in the quantum network to obtain input state information and a target error in a quantum entanglement purification scene;
a first determining module 303, configured to determine a first relationship based on the input state information and the target error, where the first relationship is a maximum optimized functional relationship between an optimal conversion rate of the quantum entanglement purification scene and a dimension of the output state information under a first preset condition, and the first preset condition is that a conversion error from the input state information to the maximum entanglement state is less than or equal to the target error, and the conversion error is measured based on a distance between schmitt vectors of the quantum states under the quantum entanglement purification scene;
A second determining module 304, configured to determine a value of the optimal conversion rate based on the first relationship;
and a resource scheduling module 305, configured to perform resource scheduling on the quantum application service based on the quantum application request and the value of the optimal conversion rate.
Optionally, the resource scheduling module 305 is specifically configured to:
determining entanglement resources which can be obtained by purification in a quantum entanglement purification scene of the quantum network based on the value of the optimal conversion rate;
and carrying out resource scheduling on the quantum application service under the condition that the purified entangled resource is larger than or equal to the entangled resource requested by the quantum application request.
Optionally, the apparatus further comprises:
and the refusal response module is used for refusing to respond to the quantum application request under the condition that the available entanglement resource is smaller than the entanglement resource requested by the quantum application request.
Optionally, the apparatus further includes:
and the adjusting module is used for adjusting the input state information in the quantum entanglement purification scene of the quantum network based on the value of the optimal conversion rate under the condition that the entanglement resources obtained by purification are smaller than entanglement resources requested by the quantum application request so as to improve the entanglement resources obtained by purification in the quantum entanglement purification scene.
Optionally, the apparatus further includes:
the quantum application service includes any one of the following:
quantum key distribution application services;
a communication application service;
distributed quantum computing application services.
Optionally, the second determining module 304 includes:
the conversion submodule is used for carrying out schmitt decomposition on the input state information so as to convert the first relation into a second relation and a third relation, wherein the second relation is a minimum optimized functional relation between the optimal conversion rate and first information, the first information comprises a first target norm of a first schmitt vector of the input state information, a target error and a first variable, the first target norm is the sum of first K maximum elements of the first schmitt vector, the third relation is a minimum optimized functional relation between the lower bound of a target value range of the first variable and a second variable under a second preset condition, the second preset condition is that the second target norm of the first schmitt vector is larger than the target error, the second target norm is the sum of first Y maximum elements of the first schmitt vector, K is a positive integer, and Y is a positive integer;
The first determining submodule is used for determining a target value range of the first variable based on the third relation and second information, and the second information is the copy number and the quantum system dimension of the input state information;
and the second determining submodule is used for determining the value of the optimal conversion rate based on the second relation and the target value range of the first variable.
Optionally, the first determining sub-module includes:
a first determining unit, configured to determine a lower bound value of the target value range based on the third relationship;
and the second determining unit is used for determining an upper limit value of the target value range based on the second information.
Optionally, the first determining unit is specifically configured to:
acquiring the first schmitt vector;
sequentially acquiring a second target norm of the first Schmitt vector according to the sequence from small to large of the second variable; outputting a value of the second variable if the second target norm is greater than the target error;
wherein the value of the second variable is the lower bound value of the target value range.
Optionally, the first determining unit is specifically configured to:
acquiring a second Schmitt vector of a quantum state under one copy in the input state information;
Based on the quantum system dimension of the input state information, carrying out distribution processing on the copy number of the input state information to obtain W pieces of distribution information, wherein one piece of distribution information comprises a distribution result and the repetition number of the distribution result;
based on the W pieces of distribution information, performing polynomial combination on the first elements in the second Schmitt vectors to obtain W pieces of second elements corresponding to W pieces of distribution results one by one and the repetition times of each second element, wherein the repetition times of the second elements are the repetition times of the distribution results corresponding to the second elements;
arranging the W second elements in descending order to obtain a target vector;
the first schmitt vector is obtained by arranging the target vector according to the repetition times of each second element.
Optionally, the first determining unit is specifically configured to:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
Outputting a value of the second variable if the first sum is greater than the target error;
wherein the value of the second variable isN is the second label, P is the first sum, s i And epsilon is the target error for a second element corresponding to the first index i in the target vector.
Optionally, the second determining submodule includes:
and the third determining unit is used for determining that the value of the first variable under the minimum optimization function value in the second relation is the upper bound in the target value range under the condition that the lower bound is equal to the upper bound in the target value range of the first variable, so as to obtain the value of the optimal conversion rate.
Optionally, the second determining submodule includes:
the obtaining unit is used for obtaining a first target norm of the first schmitt vector under the condition that the lower bound is not equal to the upper bound in the target value range of the first variable to obtain a gradient function of an optimization function in the second relation, wherein the gradient function is a function of the first information;
and a fourth determining unit, configured to determine, based on the gradient function and the target value range of the first variable, a value of the first variable of the optimization function under a minimum optimization function value, and obtain the value of the optimal conversion rate.
Optionally, the acquiring unit is specifically configured to:
obtaining a target vector, wherein the target vector is obtained by arranging W second elements according to a descending order, the W second elements are obtained by performing polynomial combination on first elements in a quantum state second Schmitt vector under one copy of input state information based on W distribution information, one distribution information comprises a distribution result and the repetition number of the distribution result, the W distribution information is obtained by performing distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information, the first Schmitt vector is obtained by arranging the target vector according to the repetition number of each second element, and the repetition number of the second elements is the repetition number of the distribution result corresponding to the second elements;
a first target norm of the first schmitt vector is determined based on the target vector and a number of repetitions of a second element in the target vector.
Optionally, the acquiring unit is specifically configured to:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
Outputting a first target norm of the first schmitt vector if the first variable is less than the second label;
wherein the first target norm is s i * (K-N) +P, N being the second label, P being the first sum, s i And the second element corresponding to the first index i in the target vector.
Optionally, the acquiring unit is specifically configured to:
determining W second labels of elements corresponding to the W first labels in the first Schmitt vector based on W first labels of the W second elements in the target vector and the repetition times of the second elements in the target vector;
performing dichotomy search on the first variable, and outputting a first target norm of the first Schmitt vector when the first variable is located in a target interval;
wherein the target interval is an interval determined by two adjacent second labels corresponding to the binary values in the binary search in the W second labels, and the first target norm is s c+1 *(K-N c )+P c C is the scoring value, s c+1 N being the second element corresponding to the first index c+1 in the target vector c A second index, P, corresponding to the element corresponding to the first index c in the first Schmitt vector c For the fourth element in the first schmitt vectorThe fourth element includes the element corresponding to the first reference c and the element preceding the element corresponding to the first reference c.
Optionally, the fourth determining unit is specifically configured to:
under the condition that a first objective gradient function value is greater than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle lower boundary of the objective value range, and obtaining the value of the optimal conversion rate, wherein the first objective gradient function value is the value of the gradient function when the value of the first variable is the middle lower boundary of the objective value range;
under the condition that a second objective gradient function value is smaller than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle upper boundary of the objective value range to obtain the value of the optimal conversion rate, wherein the second objective gradient function value is the value d of the first variable n -1 a value of a gradient function, d being a quantum system dimension of the input state information, n being a copy number of the input state information;
under the condition that the first target gradient function value is smaller than zero and the second target gradient function value is larger than zero, performing dichotomy search based on the lower bound of the target value range and a first target value, and under the condition that the upper bound of the dichotomy search interval is smaller than or equal to a second target value, determining that the value of a first variable of the optimization function under the minimum optimization function value is the upper bound of the dichotomy search interval, and obtaining the value of the optimal conversion rate, wherein the first target value is d n -1, the second target value is the lower bound of the dichotomy search interval plus 1;
in the dichotomy search, when the third objective gradient function value is greater than or equal to zero, the upper bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and when the third objective gradient function value is less than zero, the lower bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and the third objective gradient function value is a value of the gradient function when the value of the first variable is the dichotomy value in the dichotomy search.
Optionally, the conversion error is measured based on a trace norm of a schmitt vector of quantum states in the quantum entanglement purification scenario.
Alternatively, the conversion error is expressed as:
wherein T (|beta)>→|λ>) For the conversion error, |λ>Is the maximum entangled state, |beta>For input state information in quantum entanglement purification scene, p λ Schmitt vector p, which is the maximum entangled state β The method comprises the steps that a Schmitt vector r of input state information in a quantum entanglement purification scene is a Schmitt vector r of output state information in the quantum entanglement purification scene, prob (d) represents a set of probability distribution vectors with all dimensions d, and d is a quantum system dimension of the input state information.
The quantum entanglement resource scheduling device 300 provided by the present disclosure can realize each process realized by the quantum entanglement resource scheduling method embodiment, and can achieve the same beneficial effects, and for avoiding repetition, a detailed description is omitted here.
In the technical scheme of the disclosure, the related processes of collecting, storing, using, processing, transmitting, providing, disclosing and the like of the personal information of the user accord with the regulations of related laws and regulations, and the public order colloquial is not violated.
According to embodiments of the present disclosure, the present disclosure also provides an electronic device, a readable storage medium and a computer program product.
FIG. 4 illustrates a schematic block diagram of an example electronic device that may be used to implement embodiments of the present disclosure. Electronic devices are intended to represent various forms of digital computers, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other appropriate computers. The electronic device may also represent various forms of mobile devices, such as personal digital processing, cellular telephones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the disclosure described and/or claimed herein.
As shown in fig. 4, the apparatus 400 includes a computing unit 401 that can perform various suitable actions and processes according to a computer program stored in a Read Only Memory (ROM) 402 or a computer program loaded from a storage unit 408 into a Random Access Memory (RAM) 403. In RAM 403, various programs and data required for the operation of device 400 may also be stored. The computing unit 401, ROM 402, and RAM 403 are connected to each other by a bus 404. An input/output (I/O) interface 405 is also connected to bus 404.
Various components in device 400 are connected to I/O interface 405, including: an input unit 406 such as a keyboard, a mouse, etc.; an output unit 407 such as various types of displays, speakers, and the like; a storage unit 408, such as a magnetic disk, optical disk, etc.; and a communication unit 409 such as a network card, modem, wireless communication transceiver, etc. The communication unit 409 allows the device 400 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunication networks.
The computing unit 401 may be a variety of general purpose and/or special purpose processing components having processing and computing capabilities. Some examples of computing unit 401 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various specialized Artificial Intelligence (AI) computing chips, various computing units running machine learning model algorithms, a Digital Signal Processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 401 performs the various methods and processes described above, such as the quantum entanglement resource scheduling method. For example, in some embodiments, the quantum entanglement resource scheduling method may be implemented as a computer software program tangibly embodied on a machine-readable medium, such as the storage unit 408. In some embodiments, part or all of the computer program may be loaded and/or installed onto the device 400 via the ROM 402 and/or the communication unit 409. When the computer program is loaded into RAM 403 and executed by computing unit 401, one or more steps of the quantum entanglement resource scheduling method described above may be performed. Alternatively, in other embodiments, the computing unit 401 may be configured to perform the quantum entanglement resource scheduling method in any other suitable way (e.g. by means of firmware).
Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuit systems, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), systems On Chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs, the one or more computer programs may be executed and/or interpreted on a programmable system including at least one programmable processor, which may be a special purpose or general-purpose programmable processor, that may receive data and instructions from, and transmit data and instructions to, a storage system, at least one input device, and at least one output device.
Program code for carrying out methods of the present disclosure may be written in any combination of one or more programming languages. These program code may be provided to a processor or controller of a general purpose computer, special purpose computer, or other programmable data processing apparatus such that the program code, when executed by the processor or controller, causes the functions/operations specified in the flowchart and/or block diagram to be implemented. The program code may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.
In the context of this disclosure, a machine-readable medium may be a tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. The machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. The machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
To provide for interaction with a user, the systems and techniques described here can be implemented on a computer having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and pointing device (e.g., a mouse or trackball) by which a user can provide input to the computer. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.
The systems and techniques described here can be implemented in a computing system that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such background, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), and the internet.
The computer system may include a client and a server. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server may be a cloud server, a server of a distributed system, or a server incorporating a blockchain.
It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps recited in the present disclosure may be performed in parallel, sequentially, or in a different order, provided that the desired results of the disclosed aspects are achieved, and are not limited herein.
The above detailed description should not be taken as limiting the scope of the present disclosure. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present disclosure are intended to be included within the scope of the present disclosure.

Claims (39)

1. A quantum entanglement resource scheduling method, comprising:
receiving a quantum application request of a quantum network, wherein the quantum application request is used for scheduling entanglement resources to execute quantum application services;
based on the quantum application request, triggering nodes in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene;
determining a first relation based on the input state information and the target error, wherein the first relation is a maximum optimized function relation of the optimal conversion rate of the quantum entanglement purification scene and the dimension of the output state information under a first preset condition, the first preset condition is that the conversion error from the input state information to the maximum entanglement state is smaller than or equal to the target error, and the conversion error is measured based on the distance between the Schmitt vectors of the quantum states in the quantum entanglement purification scene;
Determining a value of the optimal conversion rate based on the first relationship;
and scheduling resources of the quantum application service based on the quantum application request and the value of the optimal conversion rate.
2. The method of claim 1, wherein the scheduling the quantum application service for resources based on the quantum application request and the value of the optimal conversion rate comprises:
determining entanglement resources which can be obtained by purification in a quantum entanglement purification scene of the quantum network based on the value of the optimal conversion rate;
and carrying out resource scheduling on the quantum application service under the condition that the purified entangled resource is larger than or equal to the entangled resource requested by the quantum application request.
3. The method of claim 2, further comprising:
and refusing to respond to the quantum application request under the condition that the available entanglement resource is smaller than the entanglement resource requested by the quantum application request.
4. The method of claim 2, further comprising:
and under the condition that the purified entanglement resources are smaller than entanglement resources requested by the quantum application request, based on the value of the optimal conversion rate, adjusting input state information in a quantum entanglement purification scene of the quantum network so as to improve the purified entanglement resources in the quantum entanglement purification scene.
5. The method of claim 1, wherein the quantum application service comprises any one of:
quantum key distribution application services;
a communication application service;
distributed quantum computing application services.
6. The method of claim 1, wherein the determining the value of the optimal conversion based on the first relationship comprises:
performing schmitt decomposition on the input state information to convert the first relation into a second relation and a third relation, wherein the second relation is a minimum optimized functional relation between the optimal conversion rate and first information, the first information comprises a first target norm of a first schmitt vector of the input state information, a target error and a first variable, the first target norm is a sum of first K maximum elements of the first schmitt vector, the third relation is a minimum optimized functional relation between a lower boundary of a target value range of the first variable and a second variable under a second preset condition, the second preset condition is that the second target norm of the first schmitt vector is larger than the target error, the second target norm is a sum of first Y maximum elements of the first schmitt vector, K is a positive integer, Y is the second variable, and Y is a positive integer;
Determining a target value range of the first variable based on the third relation and second information, wherein the second information is the copy number and quantum system dimension of the input state information;
and determining the value of the optimal conversion rate based on the second relation and the target value range of the first variable.
7. The method of claim 6, wherein the determining the target range of values for the first variable based on the third relationship and second information comprises:
determining a lower bound value of the target value range based on the third relationship;
and determining an upper limit value of the target value range based on the second information.
8. The method of claim 7, wherein the determining a lower bound of the target range of values based on the third relationship comprises:
acquiring the first schmitt vector;
sequentially acquiring a second target norm of the first Schmitt vector according to the sequence from small to large of the second variable; outputting a value of the second variable if the second target norm is greater than the target error;
wherein the value of the second variable is the lower bound value of the target value range.
9. The method of claim 8, wherein the obtaining the first schmitt vector comprises:
acquiring a second Schmitt vector of a quantum state under one copy in the input state information;
based on the quantum system dimension of the input state information, carrying out distribution processing on the copy number of the input state information to obtain W pieces of distribution information, wherein one piece of distribution information comprises a distribution result and the repetition number of the distribution result;
based on the W pieces of distribution information, performing polynomial combination on the first elements in the second Schmitt vectors to obtain W pieces of second elements corresponding to W pieces of distribution results one by one and the repetition times of each second element, wherein the repetition times of the second elements are the repetition times of the distribution results corresponding to the second elements;
arranging the W second elements in descending order to obtain a target vector;
the first schmitt vector is obtained by arranging the target vector according to the repetition times of each second element.
10. The method of claim 9, wherein the sequentially obtaining the second target norms of the first schmitt vectors in order of decreasing second variables; outputting a value of the second variable if the second target norm is greater than the target error, comprising:
Sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
outputting a value of the second variable if the first sum is greater than the target error;
wherein the value of the second variable isN is the second label, P is the first sum, s i And epsilon is the target error for a second element corresponding to the first index i in the target vector.
11. The method of claim 6, wherein the determining the value of the optimal conversion based on the second relationship and the target range of values for the first variable comprises:
and under the condition that the lower bound in the target value range of the first variable is equal to the upper bound, determining the value of the first variable under the minimum optimization function value in the second relation as the upper bound in the target value range, and obtaining the value of the optimal conversion rate.
12. The method of claim 6, wherein the determining the value of the optimal conversion based on the second relationship and the target range of values for the first variable comprises:
under the condition that the lower bound in the target value range of the first variable is not equal to the upper bound, acquiring a first target norm of the first Schmitt vector to obtain a gradient function of an optimization function in the second relation, wherein the gradient function is a function of the first information;
and determining the value of the first variable of the optimization function under the minimum optimization function value based on the gradient function and the target value range of the first variable, and obtaining the value of the optimal conversion rate.
13. The method of claim 12, wherein the obtaining the first target norm of the first schmitt vector comprises:
obtaining a target vector, wherein the target vector is obtained by arranging W second elements according to a descending order, the W second elements are obtained by performing polynomial combination on first elements in a quantum state second Schmitt vector under one copy of input state information based on W distribution information, one distribution information comprises a distribution result and the repetition number of the distribution result, the W distribution information is obtained by performing distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information, the first Schmitt vector is obtained by arranging the target vector according to the repetition number of each second element, and the repetition number of the second elements is the repetition number of the distribution result corresponding to the second elements;
A first target norm of the first schmitt vector is determined based on the target vector and a number of repetitions of a second element in the target vector.
14. The method of claim 13, wherein the determining the first target norm of the first schmitt vector based on the target vector and a number of repetitions of the second element in the target vector comprises:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
outputting a first target norm of the first schmitt vector if the first variable is less than the second label;
wherein the first target norm is s i * (K-N) +P, N being the second label, P being the first sum, s i Is saidAnd a second element corresponding to the first index i in the target vector.
15. The method of claim 13, wherein the determining the first target norm of the first schmitt vector based on the target vector and a number of repetitions of the second element in the target vector comprises:
Determining W second labels of elements corresponding to the W first labels in the first Schmitt vector based on W first labels of the W second elements in the target vector and the repetition times of the second elements in the target vector;
performing dichotomy search on the first variable, and outputting a first target norm of the first Schmitt vector when the first variable is located in a target interval;
wherein the target interval is an interval determined by two adjacent second labels corresponding to the binary values in the binary search in the W second labels, and the first target norm is s c+1 *(K-N c )+P c C is the scoring value, s c+1 N being the second element corresponding to the first index c+1 in the target vector c A second index, P, corresponding to the element corresponding to the first index c in the first Schmitt vector c And a second summation of a fourth element in the first schmitt vector, wherein the fourth element comprises an element corresponding to the first mark c and an element before the element corresponding to the first mark c.
16. The method of claim 12, wherein the determining the value of the first variable of the optimization function at the minimum optimization function value based on the gradient function and the target range of values of the first variable, results in the value of the optimal conversion rate, comprising:
Under the condition that a first objective gradient function value is greater than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle lower boundary of the objective value range, and obtaining the value of the optimal conversion rate, wherein the first objective gradient function value is the value of the gradient function when the value of the first variable is the middle lower boundary of the objective value range;
under the condition that a second objective gradient function value is smaller than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle upper boundary of the objective value range to obtain the value of the optimal conversion rate, wherein the second objective gradient function value is the value d of the first variable n -1 a value of a gradient function, d being a quantum system dimension of the input state information, n being a copy number of the input state information;
under the condition that the first target gradient function value is smaller than zero and the second target gradient function value is larger than zero, performing dichotomy search based on the lower bound of the target value range and a first target value, and under the condition that the upper bound of the dichotomy search interval is smaller than or equal to a second target value, determining that the value of a first variable of the optimization function under the minimum optimization function value is the upper bound of the dichotomy search interval, and obtaining the value of the optimal conversion rate, wherein the first target value is d n -1, the second target value is the lower bound of the dichotomy search interval plus 1;
in the dichotomy search, when the third objective gradient function value is greater than or equal to zero, the upper bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and when the third objective gradient function value is less than zero, the lower bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and the third objective gradient function value is a value of the gradient function when the value of the first variable is the dichotomy value in the dichotomy search.
17. The method of claim 1, wherein the conversion error is measured based on a trace norm of a schmitt vector of quantum states in the quantum entanglement purification scene.
18. The method of claim 17, wherein the conversion error is represented as:
wherein T (|beta)>→|λ>) For the conversion error, |λ>Is the maximum entangled state, |beta>For input state information in quantum entanglement purification scene, p λ Schmitt vector p, which is the maximum entangled state β The method comprises the steps that a Schmitt vector r of input state information in a quantum entanglement purification scene is a Schmitt vector r of output state information in the quantum entanglement purification scene, prob (d) represents a set of probability distribution vectors with all dimensions d, and d is a quantum system dimension of the input state information.
19. A quantum entanglement resource scheduling device, comprising:
the receiving module is used for receiving a quantum application request of the quantum network, wherein the quantum application request is used for scheduling entanglement resources to execute quantum application services;
the acquisition module is used for triggering nodes in the quantum network to acquire input state information and target errors in a quantum entanglement purification scene based on the quantum application request;
the first determining module is used for determining a first relation based on the input state information and the target error, wherein the first relation is a maximum optimized functional relation between the optimal conversion rate of the quantum entanglement purification scene and the dimension of the output state information under a first preset condition, the first preset condition is that the conversion error from the input state information to the maximum entanglement state is smaller than or equal to the target error, and the conversion error is measured based on the distance between the Schmitt vectors of the quantum states under the quantum entanglement purification scene;
a second determining module configured to determine a value of the optimal conversion rate based on the first relationship;
and the resource scheduling module is used for scheduling the resource of the quantum application service based on the quantum application request and the value of the optimal conversion rate.
20. The apparatus of claim 19, wherein the resource scheduling module is specifically configured to:
determining entanglement resources which can be obtained by purification in a quantum entanglement purification scene of the quantum network based on the value of the optimal conversion rate;
and carrying out resource scheduling on the quantum application service under the condition that the purified entangled resource is larger than or equal to the entangled resource requested by the quantum application request.
21. The apparatus of claim 20, further comprising:
and the refusal response module is used for refusing to respond to the quantum application request under the condition that the available entanglement resource is smaller than the entanglement resource requested by the quantum application request.
22. The apparatus of claim 20, further comprising:
and the adjusting module is used for adjusting the input state information in the quantum entanglement purification scene of the quantum network based on the value of the optimal conversion rate under the condition that the entanglement resources obtained by purification are smaller than entanglement resources requested by the quantum application request so as to improve the entanglement resources obtained by purification in the quantum entanglement purification scene.
23. The apparatus of claim 19, further comprising:
The quantum application service includes any one of the following:
quantum key distribution application services;
a communication application service;
distributed quantum computing application services.
24. The apparatus of claim 19, wherein the second determination module comprises:
the conversion submodule is used for carrying out schmitt decomposition on the input state information so as to convert the first relation into a second relation and a third relation, wherein the second relation is a minimum optimized functional relation between the optimal conversion rate and first information, the first information comprises a first target norm of a first schmitt vector of the input state information, a target error and a first variable, the first target norm is the sum of first K maximum elements of the first schmitt vector, the third relation is a minimum optimized functional relation between the lower bound of a target value range of the first variable and a second variable under a second preset condition, the second preset condition is that the second target norm of the first schmitt vector is larger than the target error, the second target norm is the sum of first Y maximum elements of the first schmitt vector, K is a positive integer, and Y is a positive integer;
The first determining submodule is used for determining a target value range of the first variable based on the third relation and second information, and the second information is the copy number and the quantum system dimension of the input state information;
and the second determining submodule is used for determining the value of the optimal conversion rate based on the second relation and the target value range of the first variable.
25. The apparatus of claim 24, wherein the first determination submodule comprises:
a first determining unit, configured to determine a lower bound value of the target value range based on the third relationship;
and the second determining unit is used for determining an upper limit value of the target value range based on the second information.
26. The apparatus of claim 25, wherein the first determining unit is specifically configured to:
acquiring the first schmitt vector;
sequentially acquiring a second target norm of the first Schmitt vector according to the sequence from small to large of the second variable; outputting a value of the second variable if the second target norm is greater than the target error;
wherein the value of the second variable is the lower bound value of the target value range.
27. The apparatus of claim 26, wherein the first determining unit is specifically configured to:
acquiring a second Schmitt vector of a quantum state under one copy in the input state information;
based on the quantum system dimension of the input state information, carrying out distribution processing on the copy number of the input state information to obtain W pieces of distribution information, wherein one piece of distribution information comprises a distribution result and the repetition number of the distribution result;
based on the W pieces of distribution information, performing polynomial combination on the first elements in the second Schmitt vectors to obtain W pieces of second elements corresponding to W pieces of distribution results one by one and the repetition times of each second element, wherein the repetition times of the second elements are the repetition times of the distribution results corresponding to the second elements;
arranging the W second elements in descending order to obtain a target vector;
the first schmitt vector is obtained by arranging the target vector according to the repetition times of each second element.
28. The apparatus of claim 27, wherein the first determining unit is specifically configured to:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
Outputting a value of the second variable if the first sum is greater than the target error;
wherein the value of the second variable isN is the firstTwo reference numerals, P is the first sum, s i And epsilon is the target error for a second element corresponding to the first index i in the target vector.
29. The apparatus of claim 24, wherein the second determination submodule comprises:
and the third determining unit is used for determining that the value of the first variable under the minimum optimization function value in the second relation is the upper bound in the target value range under the condition that the lower bound is equal to the upper bound in the target value range of the first variable, so as to obtain the value of the optimal conversion rate.
30. The apparatus of claim 24, wherein the second determination submodule comprises:
the obtaining unit is used for obtaining a first target norm of the first schmitt vector under the condition that the lower bound is not equal to the upper bound in the target value range of the first variable to obtain a gradient function of an optimization function in the second relation, wherein the gradient function is a function of the first information;
and a fourth determining unit, configured to determine, based on the gradient function and the target value range of the first variable, a value of the first variable of the optimization function under a minimum optimization function value, and obtain the value of the optimal conversion rate.
31. The apparatus of claim 30, wherein the obtaining unit is specifically configured to:
obtaining a target vector, wherein the target vector is obtained by arranging W second elements according to a descending order, the W second elements are obtained by performing polynomial combination on first elements in a quantum state second Schmitt vector under one copy of input state information based on W distribution information, one distribution information comprises a distribution result and the repetition number of the distribution result, the W distribution information is obtained by performing distribution processing on the copy number of the input state information based on the quantum system dimension of the input state information, the first Schmitt vector is obtained by arranging the target vector according to the repetition number of each second element, and the repetition number of the second elements is the repetition number of the distribution result corresponding to the second elements;
a first target norm of the first schmitt vector is determined based on the target vector and a number of repetitions of a second element in the target vector.
32. The apparatus of claim 31, wherein the obtaining unit is specifically configured to:
sequentially determining a second label of an element corresponding to the first label in the first schmitt vector and a first addition of a third element in the first schmitt vector according to the sequence from small to large of the first label of the second element in the target vector based on the repetition times of the second element, wherein the third element comprises the element corresponding to the second label and an element positioned before the element corresponding to the second label;
Outputting a first target norm of the first schmitt vector if the first variable is less than the second label;
wherein the first target norm is s i * (K-N) +P, N being the second label, P being the first sum, s i And the second element corresponding to the first index i in the target vector.
33. The apparatus of claim 31, wherein the obtaining unit is specifically configured to:
determining W second labels of elements corresponding to the W first labels in the first Schmitt vector based on W first labels of the W second elements in the target vector and the repetition times of the second elements in the target vector;
performing dichotomy search on the first variable, and outputting a first target norm of the first Schmitt vector when the first variable is located in a target interval;
wherein the target interval is two adjacent second labels corresponding to the binary values in the binary search in the W second labelsThe interval determined by the number, the first target norm is s c+1 *(K-N c )+P c C is the scoring value, s c+1 N being the second element corresponding to the first index c+1 in the target vector c A second index, P, corresponding to the element corresponding to the first index c in the first Schmitt vector c And a second summation of a fourth element in the first schmitt vector, wherein the fourth element comprises an element corresponding to the first mark c and an element before the element corresponding to the first mark c.
34. The apparatus of claim 30, wherein the fourth determining unit is specifically configured to:
under the condition that a first objective gradient function value is greater than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle lower boundary of the objective value range, and obtaining the value of the optimal conversion rate, wherein the first objective gradient function value is the value of the gradient function when the value of the first variable is the middle lower boundary of the objective value range;
under the condition that a second objective gradient function value is smaller than or equal to zero, determining that the value of a first variable of the optimization function under the minimum optimization function value is the middle upper boundary of the objective value range to obtain the value of the optimal conversion rate, wherein the second objective gradient function value is the value d of the first variable n -1 a value of a gradient function, d being a quantum system dimension of the input state information, n being a copy number of the input state information;
under the condition that the first target gradient function value is smaller than zero and the second target gradient function value is larger than zero, performing dichotomy search based on the lower bound of the target value range and a first target value, and under the condition that the upper bound of the dichotomy search interval is smaller than or equal to a second target value, determining that the value of a first variable of the optimization function under the minimum optimization function value is the upper bound of the dichotomy search interval, and obtaining the value of the optimal conversion rate, wherein the first target value is d n -1, the second target value is the lower bound of the dichotomy search interval plus 1;
in the dichotomy search, when the third objective gradient function value is greater than or equal to zero, the upper bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and when the third objective gradient function value is less than zero, the lower bound of the dichotomy search interval is adjusted to be a dichotomy value in the dichotomy search, and the third objective gradient function value is a value of the gradient function when the value of the first variable is the dichotomy value in the dichotomy search.
35. The apparatus of claim 19, wherein the conversion error is measured based on a trace norm of a schmitt vector of quantum states in the quantum entanglement purification scene.
36. The apparatus of claim 35, wherein the conversion error is represented as:
wherein T (|beta)>→|λ>) For the conversion error, |λ>Is the maximum entangled state, |beta>For input state information in quantum entanglement purification scene, p λ Schmitt vector p, which is the maximum entangled state β The method comprises the steps that a Schmitt vector r of input state information in a quantum entanglement purification scene is a Schmitt vector r of output state information in the quantum entanglement purification scene, prob (d) represents a set of probability distribution vectors with all dimensions d, and d is a quantum system dimension of the input state information.
37. An electronic device, comprising:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein,
the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the method of any one of claims 1-18.
38. A non-transitory computer readable storage medium storing computer instructions for causing the computer to perform the method of any one of claims 1-18.
39. A computer program product comprising a computer program which, when executed by a processor, implements the method according to any of claims 1-18.
CN202311196888.6A 2023-09-15 2023-09-15 Quantum entanglement resource scheduling method and device and electronic equipment Pending CN117236450A (en)

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