CN115994582B - Quantum measurement device performance comparison method and device, electronic device and medium - Google Patents
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Abstract
The present disclosure provides a performance comparison method, apparatus, electronic device, computer readable storage medium and computer program product for quantum measurement device, and relates to the field of computers, in particular to the technical field of quantum computers. The implementation scheme is as follows: determining a first quantum measurement device and a second quantum measurement device to be compared; the following operations were repeated K times: randomly sampling n single-quantum bit unitary matrixes in a single-quantum bit unitary matrix set; the following operations are repeated N shots times for each of the plurality of combinations of the first ground state and the second ground state: respectively applying n unitary matrices to each bit of the first ground state and the second ground state in the same sequence to respectively measure the applied first ground state and second ground state; for each combination, determining a first probability and a second probability of occurrence of a preset measurement result; and determining measurement fidelity of POVM elements corresponding to the first quantum measurement device and the second quantum measurement device and a preset measurement result based on the first probability and the second probability.
Description
Technical Field
The present disclosure relates to the field of computers, and more particularly to the field of quantum computer technology, and in particular to a method, an apparatus, an electronic device, a computer readable storage medium, and a computer program product for comparing performance of a quantum measurement device.
Background
Quantum computer technology has evolved rapidly in recent years, but noise problems in foreseeable future quantum computers are difficult to avoid: the heat dissipation in the qubit or random fluctuation generated in the underlying quantum physical process can cause the state of the qubit to be overturned or randomized, and the deviation of the calculation result read by the measuring device can cause the calculation process to fail.
Quantum measurement (Quantum Measurement) is one of the most important devices in quantum technology, and is a core resource and an essential component of quantum computing and quantum information processing. It is therefore also important to characterize the performance of quantum measurement devices. Typically, we measure the performance of a measurement device by calculating the Fidelity (Fidelity) between the measurement device and the ideal measurement. However, with the scale of quantum computers, the analog cost of "ideal measurement" increases exponentially, resulting in fidelity estimation becoming very difficult. It becomes necessary to directly compare the performance of two quantum measurement devices.
Disclosure of Invention
The present disclosure provides a quantum measurement device performance comparison method, apparatus, electronic device, computer readable storage medium, and computer program product.
According to an aspect of the present disclosure, there is provided a quantum measurement device performance comparison method, including: determining a first quantum measurement device and a second quantum measurement device to be compared, wherein the quantum bit numbers of the first quantum measurement device and the second quantum measurement device are n, and n is a positive integer; the following operations are repeated a total of K times, where K is a positive integer: randomly sampling n single-quantum bit unitary matrixes in a single-quantum bit unitary matrix set; for each of the plurality of combinations of the first ground state and the second ground state, the following operations are repeated a total of N shots times, where N shots is a positive integer: respectively acting the n single-quantum bit unitary matrices on each bit of the first base state and each bit of the second base state according to the same sequence to respectively measure the first base state and the second base state after the action through the first quantum measuring device and the second quantum measuring device so as to obtain a measurement result, wherein the first base state is a quantum state prepared on a quantum system corresponding to the first quantum measuring device, and the second base state is a quantum state prepared on a quantum system corresponding to the second quantum measuring device; for each combination, determining a first probability of occurrence of a preset measurement result when the first quantum measurement device measures and a second probability of occurrence of the preset measurement result when the second quantum measurement device measures based on the corresponding N shots times of measurement results; and determining measurement fidelity of POVM elements corresponding to the preset measurement results of the first quantum measurement device and the second quantum measurement device based on the first probability and the second probability corresponding to the K times of operation.
According to another aspect of the present disclosure, there is provided a quantum measurement device performance comparing apparatus, comprising: a first determination unit configured to determine a first quantum measurement device and a second quantum measurement device to be compared, wherein the number of qubits of the first quantum measurement device and the second quantum measurement device are both n, n being a positive integer; an operation unit configured to repeat the following operations a total of K times, where K is a positive integer: randomly sampling n single-quantum bit unitary matrixes in a single-quantum bit unitary matrix set; for each of the plurality of combinations of the first ground state and the second ground state, the following operations are repeated a total of N shots times, where N shots is a positive integer: respectively acting the n single-quantum bit unitary matrices on each bit of the first base state and each bit of the second base state according to the same sequence to respectively measure the first base state and the second base state after the action through the first quantum measuring device and the second quantum measuring device so as to obtain a measurement result, wherein the first base state is a quantum state prepared on a quantum system corresponding to the first quantum measuring device, and the second base state is a quantum state prepared on a quantum system corresponding to the second quantum measuring device; for each combination, determining a first probability of occurrence of a preset measurement result when the first quantum measurement device measures and a second probability of occurrence of the preset measurement result when the second quantum measurement device measures based on the corresponding N shots times of measurement results; and the second determining unit is configured to determine measurement fidelity of POVM elements corresponding to the preset measurement result of the first quantum measurement device and the second quantum measurement device based on the first probability and the second probability corresponding to K times of operations.
According to another aspect of the present disclosure, there is provided an electronic device including: at least one processor; and a memory communicatively coupled to the at least one processor; the memory stores instructions executable by the at least one processor to enable the at least one processor to perform the methods described in the present disclosure.
According to another aspect of the present disclosure, there is provided a non-transitory computer-readable storage medium storing computer instructions for causing a computer to perform the method described in the present disclosure.
According to another aspect of the present disclosure, there is provided a computer program product comprising a computer program which, when executed by a processor, implements the method described in the present disclosure.
According to one or more embodiments of the present disclosure, by inputting ground states at different quantum measurement devices and making random unitary matrix evolution, measurement fidelity between different measurement devices can be efficiently estimated from the measurement results through a data post-processing process after obtaining the measurement results, with high scalability.
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.
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The accompanying drawings illustrate exemplary embodiments and, together with the description, serve to explain exemplary implementations of the embodiments. The illustrated embodiments are for exemplary purposes only and do not limit the scope of the claims. Throughout the drawings, identical reference numerals designate similar, but not necessarily identical, elements.
FIG. 1 illustrates a schematic diagram of an exemplary system in which various methods described herein may be implemented, in accordance with an embodiment of the present disclosure;
FIG. 2 illustrates a flow chart of a quantum measurement device performance comparison method according to an embodiment of the present disclosure;
FIG. 3 illustrates a block diagram of a quantum measurement device performance comparison apparatus according to an embodiment of the present disclosure; and
Fig. 4 illustrates a block diagram of an exemplary electronic device that can be 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 of the present disclosure. Also, descriptions of well-known functions and constructions are omitted in the following description for clarity and conciseness.
In the present disclosure, the use of the terms "first," "second," and the like to describe various elements is not intended to limit the positional relationship, timing relationship, or importance relationship of the elements, unless otherwise indicated, and such terms are merely used to distinguish one element from another. In some examples, a first element and a second element may refer to the same instance of the element, and in some cases, they may also refer to different instances based on the description of the context.
The terminology used in the description of the various illustrated examples in this disclosure is for the purpose of describing particular examples only and is not intended to be limiting. Unless the context clearly indicates otherwise, the elements may be one or more if the number of the elements is not specifically limited. Furthermore, the term "and/or" as used in this disclosure encompasses any and all possible combinations of the listed items.
Embodiments of the present disclosure will be described in detail below with reference to the accompanying drawings.
To date, various types of computers in use are based on classical physics as the theoretical basis for information processing, known as traditional or classical computers. Classical information systems store data or programs using binary data bits that are physically easiest to implement, each binary data bit being represented by a 0 or a1, called a bit or a bit, as the smallest unit of information. Classical computers themselves have the inevitable weakness: first, the most basic limitation of energy consumption in the calculation process. The minimum energy required by the logic element or the memory cell should be more than several times of kT to avoid malfunction under thermal expansion; secondly, information entropy and heating energy consumption; thirdly, when the wiring density of the computer chip is large, the uncertainty of momentum is large when the uncertainty of the electronic position is small according to the uncertainty relation of the Hessenberg. Electrons are no longer bound and there is a quantum interference effect that can even destroy the performance of the chip.
Quantum computers (QWs) are a class of physical devices that perform high-speed mathematical and logical operations, store and process quantum information, following quantum mechanical properties, laws. When a device processes and calculates quantum information and a quantum algorithm is operated, the device is a quantum computer. Quantum computers follow unique quantum dynamics (particularly quantum interferometry) to achieve a new model of information processing. For parallel processing of computational problems, quantum computers have an absolute advantage in speed over classical computers. The transformation implemented by the quantum computer on each superposition component is equivalent to a classical computation, all of which are completed simultaneously and are superimposed according to a certain probability amplitude to give the output result of the quantum computer, and the computation is called quantum parallel computation. Quantum parallel processing greatly improves the efficiency of quantum computers so that they can perform tasks that classical computers cannot do, such as factorization of a large natural number. Quantum coherence is essentially exploited in all quantum ultrafast algorithms. Therefore, quantum parallel computation with quantum state instead of classical state can reach incomparable operation speed and information processing function of classical computer, and save a large amount of operation resources.
With the rapid development of quantum computer technology, quantum computers are increasingly used because of their powerful computing power and faster operating speeds. For example, chemical simulation refers to a process of mapping the hamiltonian of a real chemical system to a physically operable hamiltonian, and then modulating parameters and evolution time to find an eigenstate that can reflect the real chemical system. When an N-electron chemical system is simulated on a classical computer, the solution of a 2 N -dimensional Schrodinger equation is involved, and the calculated amount increases exponentially with the increase of the electron number of the system. Classical computers therefore have very limited utility in chemical simulation problems. To break this bottleneck, one must rely on the powerful computational power of quantum computers. The quantum eigensolver algorithm (Variational Quantum Eigensolver, VQE) is a high-efficiency quantum algorithm for performing chemical simulation on quantum hardware, is one of the most promising applications of quantum computers recently, and opens up a number of new chemical research fields. However, the current-stage quantum computer measurement noise rate significantly limits the VQE capability, so the quantum measurement noise problem must be addressed first.
One core computational process of the quantum eigensolver algorithm VQE is to estimate the expectation value Tr O ρ, where ρ is the quantum state of n qubits (n-qubit quantum state) generated by the quantum computer, and n qubit observables O are the hamiltonian to physically operable hamiltonian of the real chemical system. The above process is the most general form of quantum computing to extract classical information, and is the core step of reading classical information from quantum information. In general, it can be assumed that O is a diagonal matrix under a calculation basis, and thus the expected value Tr [ oρ ] can be calculated theoretically by the formula (1):
Where O (i) represents the ith row and column element of O (assuming that the matrix element index starts numbering from 0). The above-described quantum computing process may be as shown in fig. 1, in which a process of generating an n-qubit quantum state ρ by a quantum computer 101 and measuring the quantum state ρ via a measuring device 102 to obtain a computation result is performed M times, the number of times M i of outputting the result i is counted, ρ (i) ≡m i/M is estimated, and Tr [ O ρ ] may be estimated by a classical computer 103. The measurement device 102 is formed by concatenating n (positive integer) single-qubit measurement devices 1021 to realize measurement of the n-qubit quantum state ρ to obtain a measurement result. The law of large numbers ensures that the estimation process described above is correct when M is sufficiently large.
However, due to the presence of quantum measurement noise (noise in the measurement device 102 in fig. 1), the number of times M i of statistical output result i is inaccurate, and the actual estimated values M i/M and ρ (i) deviate, resulting in errors in Tr [ O ρ ] calculated using the above formula.
From the above examples, quantum measurement devices are one of the most important devices in quantum technology, and are core resources and basic components of quantum computing and quantum information processing. It is therefore also important to characterize the performance of quantum measurement devices. In general, the performance of a measurement device can be measured by calculating the Fidelity (Fidelity) between the measurement device and the "ideal measurement". However, with the scale of quantum computers, the analog cost of "ideal measurement" increases exponentially, resulting in fidelity estimation becoming very difficult. Therefore, it becomes necessary to directly compare the performance of the two measuring devices.
It is assumed that there are two measuring devices a and B, which both claim to achieve the ideal measurement P. The gap between measuring devices a and B and ideal measurement P can be generally determined, respectively, to infer the relative performance of measuring devices a and B. However, this is indirect, and it is likely that the gap between measuring devices a and B and the ideal measurement P is the same, but in practice measuring devices a and B are far from each other.
In general, the task of "estimating fidelity among multiple quantum measurement devices" can be achieved by two technical means: quantum measurement device chromatography (Quantum Detector Tomography) and quantum measurement device calibration (Quantum Detector Calibration).
The quantum measurement device chromatography method prepares different input states and uses different measurement bases to construct a measurement operator E x from the statistical data. The measurement operators obtained by the measurement chromatography technique can completely characterize the measurement equipment, thereby accurately calculating the fidelity. In the quantum measurement equipment chromatography technology, although the quantum noise can be completely characterized by the chromatography technology, the quantum state and the measurement base need to be stretched into the whole quantum space, so that the chromatography cost is very high, and the required resource is O (4 n), so that the method is not expandable.
The quantum measurement device calibration technology constructs a calibration matrix A through the calibration data generated by running a calibration circuit, wherein the matrix characterizes classical noise information of the noisy measurement device, and the average value of diagonal lines characterizes fidelity between actual measurement and ideal measurement. Among quantum measurement device calibration techniques, the calibration techniques, although requiring relatively low computational resources, can only characterize classical noise. Classical noise reflects only a partial source of measuring device noise, such as statistical errors, which can be statistically sustained during subsequent data processing. However, if the quantum noise of the measuring device is significant, the main source of noise is quantum noise.
Thus, embodiments according to the present disclosure provide a quantum measurement device performance comparison method. Fig. 2 shows a flow chart of a quantum measurement device performance comparison method according to an embodiment of the present disclosure, as shown in fig. 2, method 200 includes: determining a first quantum measurement device and a second quantum measurement device to be compared, wherein the number of qubits of the first quantum measurement device and the second quantum measurement device are both n, n being a positive integer (step 210); the following operations are repeated a total of K times, where K is a positive integer (step 220): randomly sampling n single-qubit unitary matrices in a single-qubit unitary matrix set (step 2201); for each of the plurality of combinations of the first ground state and the second ground state, the following operations are repeated a total of N shots times, where N shots is a positive integer (step 2202): respectively acting the n single-quantum bit unitary matrices on each bit of the first base state and each bit of the second base state according to the same sequence to respectively measure the first base state and the second base state after the action through the first quantum measuring device and the second quantum measuring device so as to obtain a measurement result, wherein the first base state is a quantum state prepared on a quantum system corresponding to the first quantum measuring device, and the second base state is a quantum state prepared on a quantum system corresponding to the second quantum measuring device; for each combination, determining a first probability of occurrence of a preset measurement result when measured by the first quantum measurement device and a second probability of occurrence of the preset measurement result when measured by the second quantum measurement device based on the corresponding N shots measurement results (step 2203); and determining measurement fidelity of POVM elements corresponding to the preset measurement results of the first quantum measurement device and the second quantum measurement device based on the first probability and the second probability corresponding to the K times of operation (step 230).
In the embodiment according to the disclosure, by inputting the ground states at different quantum measurement devices and making random unitary matrix evolution, measurement fidelity among different measurement devices can be efficiently estimated from the measurement results through a data post-processing process after the measurement results are obtained, and the method has high scalability.
According to some embodiments, determining measurement fidelity of POVM elements of the first and second quantum measurement devices corresponding to the preset measurement result comprises: and determining measurement fidelity of POVM elements corresponding to the preset measurement results of the first quantum measurement device and the second quantum measurement device based on the product of the first probability and the second probability corresponding to each combination of the multiple combinations and the similarity of character strings corresponding to the first ground state and the second ground state in the corresponding combination.
In an embodiment according to the present disclosure, a POVM-membered fidelity formula corresponding to the measurement result m of two quantum measurement devices may be defined first as follows:
Wherein E {1,m} and E {2,m} represent POVM elements corresponding to the measurement result m, 1 and 2 in the subscripts represent systems 1 and 2 corresponding to the two quantum measurement devices, and the fidelity may be used to characterize the distance between the respective measurement operators of the two quantum measurement devices.
Specifically, tr [ E {1,m} E{2,m} ] can be determined according to the following formula:
Wherein,
Wherein,Representing unitary matrices of single qubitsActing on a first ground state prepared on the system 1Then, the probability of the occurrence of a measurement result m is preset after N shots times of measurement are executed; Representing unitary matrices of single qubits Acting on the second ground state prepared on system 2Then, the probability of the occurrence of a measurement result m is preset after N shots times of measurement are executed; d [ x, y ] represents the similarity of the character strings x and y corresponding to the prepared ground state.
According to some embodiments, the combination of the first ground state and the second ground state is 4 n. I.e. the exhaustive first ground stateSecond ground stateThe operations of acting the same unitary matrix N shots times and measuring to obtain measurement results are repeated for each combination of the first ground state and the second ground state (4 n). Thus, the similarity between the two quantum measurement devices is evaluated more comprehensively.
It will be appreciated that the number of components,AndOnly the 2 in Tr [ E {1,m} E{2,m} ] is changed to 1 and the 1 is changed to 2 respectively.
According to some embodiments, the similarity of the character strings corresponding to the first ground state and the second ground state is determined based on a hamming distance. That is to say,Representing the hamming distance between the strings x and y.
According to some embodiments, the preset measurements include 2 n measurements, and the method further includes: and determining the similarity between the first quantum measurement device and the second quantum measurement device based on the measurement fidelity corresponding to the 2 n measurement results. That is, further, measurement fidelity between two measurement devices can be characterized using the following formula:
According to some embodiments, the single-bit quantum gates in the set of single-bit quantum gates satisfy unitary-design properties.
In one embodiment according to the present disclosure, first, two quantum measurement devices E 1 and E 2 and their corresponding systems are determined to be a 1 and a 2, respectively, where the number of qubits for systems a 1 and a 2 are both N A. The iteration number K can be preset by an experimenter according to the precision requirement. The measurement times N shots corresponding to each input ground state combination can be preset by an experimenter according to the precision requirement. Then, the following operations are performed:
the first step: the iteration parameter k=0 is initialized.
And a second step of: updating the iteration parameter k=k+1, and performing the following judgment:
if K is greater than or equal to K, jumping to a fifth step (the verification process is finished and all detection states pass the test);
if K < K, a third step is performed (preparing a new probe state, continuing to test the unknown measuring device).
And a third step of: randomly and independently sampling N A single-qubit unitary matrices from unitary-design setWhere the superscript k indicates that it is currently the kth round and the subscript i indicates that the matrix is to be applied to the ith qubit.
Fourth step: preparation of the first ground state on systems A1 and A2, respectivelyAnd a second ground stateFor each ground state combination ρ x = |x > < x| and ρ y = |y > < y| (4 n total), the following is done:
For each ground state combination Will beActing on the ground state combination, whereinTarget measurements E1 and E2 are performed on the two platforms, respectively. The above procedure N shots was repeated.
Recording the number of times that the measurement results of the systems A1 and A2 are m respectivelyAndAnd after the completion, jumping to the second step.
Fifth step: and the data acquisition process is completed, and a data post-processing link is entered. First, the probability of occurrence of the measurement result m after each N shots operations is calculated based on the acquired data:
where j=1, 2, corresponding to systems a 1 and a 2.
Sixth step: utilization dataEstimating the degree of overlap between measurement operators by the following formula
Wherein,Representation ofIs used, that is,
WhileRepresenting the hamming distance between the strings x, y.
It should be noted that the number of the components,AndOnly respectively let the formulaI=j=1 and i=j=2.
Seventh step: based on the estimated Tr [ E {1,m} E{2,m} ],The measurement fidelity of POVM elements corresponding to measurement result m can be determined using the following formula:
and, measurement fidelity between the two quantum measurement devices E 1 and E 2:
Further, methods according to embodiments of the present disclosure are applicable to calculating fidelity between any quantum measurement devices. As described above, data has been collected for calculating measurement fidelity between the two quantum measurement devices E 1 and E 2. If a new measuring device E 3 exists now and it is desired to calculate the fidelity of the two measuring devices E 1 and E 3, or E 2 and E 3, the data previously acquired on E 1 and E 2 can be multiplexed, and only the second, third and fourth data acquisition processes described above need to be performed on E 3, and then the data post-processing process is completed according to the subsequent steps. The fidelity between the measuring equipment and any measuring equipment can be calculated only by collecting data once by each measuring equipment, so that the similarity and the measuring capability between the equipment are measured, the difference of the measuring equipment in time and space is shielded, and the measuring equipment has excellent expandability.
According to the scheme of the embodiment of the disclosure, the fidelity of the quantum measurement devices can be estimated efficiently, the similarity degree and the measurement capability of the quantum measurement devices can be measured, and the computing capability of the medium-scale quantum device can be improved.
There is also provided, in accordance with an embodiment of the present disclosure, as shown in fig. 3, a quantum measurement device performance comparing apparatus 300, including: a first determining unit 310 configured to determine a first quantum measurement device and a second quantum measurement device to be compared, wherein the number of qubits of the first quantum measurement device and the second quantum measurement device are both n, n being a positive integer; an operation unit 320 configured to repeat the following operations a total of K times, where K is a positive integer: randomly sampling n single-quantum bit unitary matrixes in a single-quantum bit unitary matrix set; for each of the plurality of combinations of the first ground state and the second ground state, the following operations are repeated a total of N shots times, where N shots is a positive integer: respectively acting the n single-quantum bit unitary matrices on each bit of the first base state and each bit of the second base state according to the same sequence to respectively measure the first base state and the second base state after the action through the first quantum measuring device and the second quantum measuring device so as to obtain a measurement result, wherein the first base state is a quantum state prepared on a quantum system corresponding to the first quantum measuring device, and the second base state is a quantum state prepared on a quantum system corresponding to the second quantum measuring device; for each combination, determining a first probability of occurrence of a preset measurement result when the first quantum measurement device measures and a second probability of occurrence of the preset measurement result when the second quantum measurement device measures based on the corresponding N shots times of measurement results; and a second determining unit 330 configured to determine measurement fidelity of POVM elements corresponding to the preset measurement result of the first quantum measurement device and the second quantum measurement device based on the first probability and the second probability corresponding to K operations.
Here, the operations of the above units 310 to 330 of the quantum measurement device performance comparing apparatus 300 are similar to the operations of the steps 210 to 230 described above, respectively, and are not repeated here.
According to embodiments of the present disclosure, there is also provided an electronic device, a readable storage medium and a computer program product.
Referring to fig. 4, a block diagram of an electronic device 400 that may be a server or a client of the present disclosure, which is an example of a hardware device that may be applied to aspects of the present disclosure, will now be described. Electronic devices are intended to represent various forms of digital electronic computer devices, such as laptops, desktops, workstations, personal digital assistants, servers, blade servers, mainframes, and other suitable 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 electronic device 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 the RAM 403, various programs and data required for the operation of the electronic 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 electronic device 400 are connected to I/O interface 405, including: an input unit 406, an output unit 407, a storage unit 408, and a communication unit 409. The input unit 406 may be any type of device capable of inputting information to the electronic device 400, the input unit 406 may receive input numeric or character information and generate key signal inputs related to user settings and/or function control of the electronic device, and may include, but is not limited to, a mouse, a keyboard, a touch screen, a trackpad, a trackball, a joystick, a microphone, and/or a remote control. The output unit 407 may be any type of device capable of presenting information and may include, but is not limited to, a display, speakers, video/audio output terminals, vibrators, and/or printers. Storage unit 408 may include, but is not limited to, magnetic disks, optical disks. The communication unit 409 allows the electronic device 400 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunications networks, and may include, but is not limited to, modems, network cards, infrared communication devices, wireless communication transceivers and/or chipsets, such as bluetooth (TM) devices, 802.11 devices, wiFi devices, wiMax devices, cellular communication devices, and/or the like.
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 method 200. For example, in some embodiments, the method 200 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 electronic device 400 via the ROM 402 and/or the communication unit 409. One or more of the steps of the method 200 described above may be performed when a computer program is loaded into RAM 403 and executed by computing unit 401. Alternatively, in other embodiments, the computing unit 401 may be configured to perform the method 200 by any other suitable means (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), complex 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), the internet, and blockchain networks.
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.
Although embodiments or examples of the present disclosure have been described with reference to the accompanying drawings, it is to be understood that the foregoing methods, systems, and apparatus are merely exemplary embodiments or examples, and that the scope of the present invention is not limited by these embodiments or examples but only by the claims following the grant and their equivalents. Various elements of the embodiments or examples may be omitted or replaced with equivalent elements thereof. Furthermore, the steps may be performed in a different order than described in the present disclosure. Further, various elements of the embodiments or examples may be combined in various ways. It is important that as technology evolves, many of the elements described herein may be replaced by equivalent elements that appear after the disclosure.
Claims (13)
1. A quantum measurement device performance comparison method, comprising:
Determining a first quantum measurement device and a second quantum measurement device to be compared, wherein the number of qubits of the first quantum measurement device and the second quantum measurement device are both ,Is a positive integer;
repeating the following operations Secondary, whereinIs a positive integer:
random sampling in single-qubit unitary matrix set A single qubit unitary matrix;
for each of the plurality of combinations of the first ground state and the second ground state, the following operations are repeated Secondary, whereinIs a positive integer:
The said The single-quantum bit unitary matrix acts on each bit of the first ground state and each bit of the second ground state respectively according to the same sequence so as to measure the first ground state and the second ground state after the action through the first quantum measuring equipment and the second quantum measuring equipment respectively, so as to obtain a measurement result, wherein the first ground state is a quantum state prepared on a quantum system corresponding to the first quantum measuring equipment, and the second ground state is a quantum state prepared on a quantum system corresponding to the second quantum measuring equipment;
For each of the combinations, based on the corresponding Determining a first probability of occurrence of a preset measurement result when the first quantum measurement device measures and a second probability of occurrence of the preset measurement result when the second quantum measurement device measures;
Based on Determining measurement fidelity of POVM elements of the first quantum measurement device and the second quantum measurement device corresponding to the preset measurement result according to the first probability and the second probability corresponding to secondary operation, wherein the preset measurement result comprisesA plurality of measurement results;
Based on And determining the similarity between the first quantum measurement device and the second quantum measurement device according to the measurement fidelity corresponding to the measurement results.
2. The method of claim 1, wherein determining measurement fidelity of POVM elements of the first and second quantum measurement devices corresponding to the preset measurement result comprises: and determining measurement fidelity of POVM elements corresponding to the preset measurement results of the first quantum measurement device and the second quantum measurement device based on the product of the first probability and the second probability corresponding to each combination of the multiple combinations and the similarity of character strings corresponding to the first ground state and the second ground state in the corresponding combination.
3. The method of claim 1, wherein the combination of the first ground state and the second ground state isAnd each.
4. The method of claim 2, wherein the similarity of the character strings corresponding to the first ground state and the second ground state is determined based on a hamming distance.
5. The method of claim 1, wherein a single-qubit unitary matrix in the set of single-qubit unitary matrices satisfies unitary-design properties.
6. A quantum measurement device performance comparison apparatus, comprising:
a first determination unit configured to determine a first quantum measurement device and a second quantum measurement device to be compared, wherein the number of qubits of the first quantum measurement device and the second quantum measurement device are both ,Is a positive integer;
an operation unit configured to repeat the following operations Secondary, whereinIs a positive integer:
random sampling in single-qubit unitary matrix set A single qubit unitary matrix;
for each of the plurality of combinations of the first ground state and the second ground state, the following operations are repeated Secondary, whereinIs a positive integer:
The said The single-quantum bit unitary matrix acts on each bit of the first ground state and each bit of the second ground state respectively according to the same sequence so as to measure the first ground state and the second ground state after the action through the first quantum measuring equipment and the second quantum measuring equipment respectively, so as to obtain a measurement result, wherein the first ground state is a quantum state prepared on a quantum system corresponding to the first quantum measuring equipment, and the second ground state is a quantum state prepared on a quantum system corresponding to the second quantum measuring equipment;
For each of the combinations, based on the corresponding Determining a first probability of occurrence of a preset measurement result when the first quantum measurement device measures and a second probability of occurrence of the preset measurement result when the second quantum measurement device measures;
A second determination unit configured to be based on Determining measurement fidelity of POVM elements of the first quantum measurement device and the second quantum measurement device corresponding to the preset measurement result according to the first probability and the second probability corresponding to secondary operation, wherein the preset measurement result comprisesA plurality of measurement results;
A third determination unit configured to be based on And determining the similarity between the first quantum measurement device and the second quantum measurement device according to the measurement fidelity corresponding to the measurement results.
7. The apparatus of claim 6, wherein the second determining unit comprises: a determination subunit configured to: and determining measurement fidelity of POVM elements corresponding to the preset measurement results of the first quantum measurement device and the second quantum measurement device based on the product of the first probability and the second probability corresponding to each combination of the multiple combinations and the similarity of character strings corresponding to the first ground state and the second ground state in the corresponding combination.
8. The apparatus of claim 6, wherein the combination of the first ground state and the second ground state isAnd each.
9. The apparatus of claim 7, wherein the similarity of the character strings corresponding to the first ground state and the second ground state is determined based on a hamming distance.
10. The apparatus of claim 6, wherein a single-qubit unitary matrix in the set of single-qubit unitary matrices satisfies unitary-design properties.
11. An electronic device, comprising:
At least one processor; and
A memory communicatively coupled to the at least one processor; wherein the method comprises the steps of
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 1-5.
12. A non-transitory computer readable storage medium storing computer instructions for causing the computer to perform the method of any one of claims 1-5.
13. A computer program product comprising a computer program, wherein the computer program, when executed by a processor, implements the method of any of claims 1-5.
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