CN115564051A - Method and device for acquiring eigen state of system to be tested based on quantum gate - Google Patents
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Abstract
The embodiment of the invention provides a method and a device for acquiring an eigen state of a system to be tested based on a quantum gate, wherein the method comprises the following steps: preparing a first quantum state; sampling to obtain a first evolution time, a second evolution time and a third evolution time based on preset probability distribution; determining a Hamiltonian corresponding to a system to be tested; determining first, second and third hamiltonian evolution operations according to the hamiltonian and the first, second and third evolution times; measuring a first expected value of a first operation combination applied to the first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to system observation measurement and a second Hamiltonian evolution operation; measuring a second expectation value of a third Hamiltonian evolution operation applied to the first quantum state to obtain a second measurement result, wherein the first, second and third Hamiltonian evolution operations are respectively composed of a plurality of quantum gates; and combining the first measurement result and the second measurement result to obtain the observed quantity of the system to be measured.
Description
Technical Field
The invention relates to the field of quantum computation, in particular to a method and a device for acquiring an eigen state of a system to be measured based on a quantum gate.
Background
Efficient preparation of eigenstates of quantum systems, and estimation of the properties of eigenstates of systems are fundamental problems that have long existed in quantum computing, and have been widely used in a very large number of technical fields. For example, in differential equations in the physical and chemical fields, continuous or discrete dynamic systems, principal component analysis in image processing; in the preparation and synthesis of chemical molecules and materials, synthesis of molecules; in the establishment of a series of functional materials, such as superconducting materials, nano materials, ferroelectric materials, magnetic materials, topological materials, metals, organic matters, semiconductors, semimetals, thermoelectric materials, polymers, catalysts and the like, and chemical reaction products for predicting the properties of materials. In these predictions, it is important to obtain information on the excited state (non-ground state) of the material.
In the prior art, eigen state | u of the system is obtained i >And obtaining information about its eigenstates, typically consumes a significant amount of time and space computational resources, e.g., with time and space complexity that exponentially escalates with the scale of the problem. Specifically, a scheme for acquiring system eigen-state information using diagonalized matrices, which requires O (D) 3 ) Time complexity of (2) and O (D) 2 ) Spatial complexity, where D is the size of the phase space of the system, for quantum systems D grows exponentially with the number of qubits. Another solution may trade off space resource savings by sacrificing some of the time complexity, but it can only be a partial improvement based on the complexity of this polynomial, but it cannot gain the eigenstates of a real physical system (system size usually grows exponentially with the number of particles or physical degrees of freedom) or some property of the eigenstates of the system, such as the response function of the physical material (resistance, photoconductivity, magnetic susceptibility, etc.). There are also some solutions to estimate the eigenstates of the system by a series of controlled quantum gates, which require long quantum wire depths and use a large number of qubits.
Therefore, a new scheme for obtaining the eigenstate of the system under test is needed.
Disclosure of Invention
The embodiment of the invention provides a method and a device for acquiring an eigen state of a system to be tested based on a quantum gate. By using the method, the quantum evolution circuit and the post-processing formed by the quantum gate can be utilized to efficiently acquire the observable information of the system and equivalently acquire the eigen-state information of the system.
In order to solve the above technical problems, the present invention provides a method for obtaining an eigen state of a system to be measured based on a quantum gate, the method comprising:
preparing a first quantum state;
sampling to obtain a first evolution time, a second evolution time and a third evolution time based on preset probability distribution;
determining a Hamiltonian corresponding to a system to be tested; determining a first Hamiltonian evolution operation according to the Hamiltonian and the first evolution time, and determining a second Hamiltonian evolution operation according to the Hamiltonian and the second evolution time; measuring a first expected value of a first operation combination applied to a first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to an observed quantity of the system to be measured and a second Hamiltonian evolution operation; the first Hamiltonian evolution operation and the second Hamiltonian evolution operation are respectively composed of a plurality of quantum gates;
determining a third Hamiltonian evolution operation according to the Hamiltonian and the third evolution time; measuring a second expected value of a third Hamiltonian evolution operation applied to the first quantum state to obtain a second measurement result, wherein the third Hamiltonian evolution operation is composed of a plurality of quantum gates;
and combining the first measurement result and the second measurement result to obtain the observed quantity of the system to be measured.
Preferably, the system to be tested comprises any one of a molecular system, a superconducting material system, a metal crystal quantum system and a nano material subsystem; the observed quantity comprises one or more of resistance, photoconductivity, magnetic susceptibility, absorption spectrum.
Preferably, preparing the first quantum state comprises:
the first quantum state is prepared based on any one of state preparation operation and a variational quantum intrinsic solver.
Preferably, applying the first desired value of the first combination of operations for the first quantum state may be expressed as:
wherein N is a first desired value, ψ 0 Is a first quantum state, U 1 、U 2 Respectively a first hamiltonian evolution operation and a second hamiltonian evolution operation,
for conjugate transpose, O is the hermitian corresponding to the observed quantity.
Preferably, the second desired value for applying the third unitary operation to the first quantum state can be expressed as:
P＝<ψ 0 |U 3 |ψ 0 >
wherein P is a second desired value, ψ 0 Is a first quantum state, U 3 Is the third unitary operation.
Preferably, the first hamiltonian evolution operation includes a plurality of quantum gates, determined by:
dividing the first evolution time into a plurality of time segments in sequence;
and decomposing the first Hamiltonian evolution operation into a plurality of evolution sub-operations respectively corresponding to the time periods, wherein the evolution sub-operations comprise a Pauli revolving door and a Pauli door.
Preferably, the rotation angle and the door category of the pauli rotary door are respectively obtained by random sampling.
Preferably, the measuring applies a first desired value of a first combination of operations for a first quantum state, comprising:
and respectively measuring the real part and the imaginary part of the first expected value by a Harder code test method.
In a second aspect, an apparatus for obtaining eigenstates of a system under test based on a quantum gate is provided, the apparatus comprising:
an initial state preparation unit configured to prepare a first quantum state;
the evolution time sampling unit is configured to sample to obtain a first evolution time, a second evolution time and a third evolution time based on preset probability distribution;
the first measurement unit is configured to determine a Hamiltonian corresponding to a system to be measured; determining a first Hamiltonian evolution operation according to the Hamiltonian and the first evolution time, and determining a second Hamiltonian evolution operation according to the Hamiltonian and the second evolution time; measuring a first expected value of a first operation combination applied to a first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to an observed quantity of the system to be measured and a second Hamiltonian evolution operation; the first Hamiltonian evolution operation and the second Hamiltonian evolution operation are respectively composed of a plurality of quantum gates;
a second measurement unit configured to determine a third hamiltonian evolution operation according to the hamiltonian and a third evolution time; measuring a second expected value of a third Hamiltonian evolution operation applied to the first quantum state to obtain a second measurement result, wherein the third Hamiltonian evolution operation is composed of a plurality of quantum gates;
and the observed quantity determining unit is configured to combine the first measurement result and the second measurement result to obtain the observed quantity of the system to be measured.
In a third aspect, there is provided a quantum computer comprising one or more quantum wires configured to implement the method of the first aspect.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a method for obtaining an eigen state of a system under test based on a quantum gate according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of different quantum state preparation methods provided by embodiments of the present invention;
FIG. 3 is a schematic diagram of a measurement circuit according to an embodiment of the present invention;
fig. 4 is a structural diagram of an apparatus for obtaining an eigen state of a system under test based on a quantum gate according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As mentioned above, the existing solution for obtaining the eigenstates of the quantum system has the drawback of consuming a large amount of computational resources, both time and space, or the drawback of requiring a long depth of quantum wires and using an excessive number of qubits, by estimating the eigenstates of the system through controlled quantum gates. In order to more clearly express the advantages of the scheme for acquiring the eigenstate of the system under test through the sub-gate provided by the embodiment of the specification. The following provides a further summary of the prior art schemes for obtaining the eigenstates of the system and the disadvantages thereof.
The existing technical scheme mainly comprises a variational quantum eigen solver and a derivation scheme thereof, and a quantum phase estimation (quantum phase estimation) scheme.
The approximate process of the variational quantum intrinsic solver is as follows: preparing a quantum state in a parameterized quantum circuit; measuring the average value of the Hamiltonian of the subsystem to be measured in a parameterized quantum state; optimizing parameters by using a classical computer; repeating the measurement and optimization processes to minimize the energy average value, namely optimizing to a final result, wherein the corresponding quantum state is the ground state prepared in production; performing quantum measurements on the ground state to obtain an average of observables on the ground state<u i |O|u i >Where O represents observability. For example in the special case when O = H,<u i |O|u i >gives the intrinsic energy E of the system i . However, the variational quantum intrinsic solver and its derivative scheme have the following problemsTitle: first, the variational quantum eigensolver algorithm and its derivatives are usually focused on the optimization of parameters using classical computers and the quantum gate form of quantum wires. Therefore, the quantum entanglement characteristics that can be actually expressed are limited due to the limitations of the existing quantum chip resources. For more complex and deeply entangled systems, the precision and resources of the prior art are limited, which cannot be solved by the technical method of the prior structure. Secondly, classical calculation assistance is needed for optimizing parameters of the variational quantum eigen solver. For a real problem, the variational quantum intrinsic solver cannot guarantee that a real ground state can be obtained. In particular, the complexity of the process of classical optimization can likewise be increased in exponential order. Third, the variational quantum intrinsic solver generally focuses on solving the ground state of the system, which is extremely difficult to solve for any excited state, and the preparation of the excited state is particularly important for solving many practical problems.
The quantum phase estimation scheme can estimate the eigen state of the system through a series of controlled quantum gates. However, it has the following problems: first, it is difficult to operate on existing or near-term quantum devices because of the long line depth required and the large number of qubits required. Furthermore, it is generally very resistant to noise and therefore needs to rely on fault tolerant quantum computing. Second, the number of qubits depends on the precision
E is the precision of the target. However, it requires a controlled multi-bit coherent operation Ctrl-U, wherein the operation is a coherent operation. Therefore, in actual production, a greater number of single and double bit gates are required to achieve this operation. Thirdly, the coherence time is long. Since the depth of the line is proportional to pi/. Epsilon, for applications with higher accuracy requirements, such as chemical molecules (. Epsilon. = 10) -3 ) The line depth is very long.
To solve the above technical problems. The embodiment of the specification provides a scheme for acquiring an eigen state of a system to be tested based on a quantum gate. The core idea is that Hamilton evolution U = exp iHt is obtained through sampling, a projection operator which cannot be directly realized on a quantum computer is realized, and evolution time t is obtained through probability sampling. Then, hamiltonian evolution is achieved using quantum wires composed of quantum gates. Further, the observables of the system are obtained by measurements on the manipulated quantum system and post-processing of the measurements.
The method has the following advantages: on the first hand, because the conventional unitary evolution operation based on the piecewise evolution (rooter method) brings an evolution error, the conventional unitary evolution operation cannot achieve the technical effect of high-precision evolution of the scheme. And no additional auxiliary qubits need to be introduced in the evolution. Existing quantum signal processing schemes and the like also fail to achieve this technical effect because they introduce more complex operations. Compared with the scheme based on the Hamiltonian evolution of quantum simulation, the scheme only needs a single-bit quantum gate and a double-bit quantum gate, and does not need an analog quantum device for realizing the Hamiltonian evolution. Moreover, the method can be applied to more general fault-tolerant quantum computers (non-fault-tolerant quantum computers) and noise-containing quantum computers (or NISQ devices). In a third aspect, the method can be conveniently expanded to process a more general problem Hamiltonian H, and is not limited to quantum analog evolution U = expiHt, namely, the target problem is more flexibly coded and the problem which can be processed is more extensive.
Fig. 1 is a flowchart of a method for obtaining an eigen state of a system under test based on a quantum gate according to an embodiment of the present invention. As shown in fig. 1, the method comprises at least the following steps:
and step 15, combining the first measurement result and the second measurement result to obtain the observed quantity of the system to be measured.
First, in step 11, a first quantum state is prepared.
In different embodiments, the system under test may characterize quantum systems of different specific problems. In one embodiment, the system under test includes any one of a molecular system, a superconducting material system, a metal crystal system, and a nanomaterial system.
In different embodiments, the first quantum state may be prepared in different specific ways, which are not limited in this specification. For example, in one embodiment, the first quantum state | ψ can be prepared based on any of a state preparation operation, a variational quantum eigensolver 0 >. For example, in one embodiment, the first quantum state may be prepared on an initial state, which may be, for example, a simple direct product state, such as a chemical problem, which may be obtained using a mean field scheme, also known as the Hartree-Fock method. In various embodiments, the initial state may be any experimentally realizable state, such as a microduct state
Fig. 2 is a schematic diagram of different preparation methods of quantum states according to an embodiment of the present invention. As shown in FIG. 2, in one example, an initial direct product state may be applied
The allowed operation on an analog quantum device results in the preparation of the initial state. In one example, a state obtained by the variation optimization can be used as an initial state by using a variation quantum intrinsic solver. In one example, the initial state method can be prepared using a unitary operation, as shown in fig. 2 (a 1). In one example, the initial state can also be prepared using Hermite's procedure, as shown in FIG. 2 (a 2). In other examples, a multiple-body perturbation approach for chemical problems, a unitary coupled cluster approach, and the like may also be used.
Then, in step 12, based on the preset probability distribution, a first evolution time, a second evolution time and a third evolution time are obtained by sampling.
In different embodiments, the first evolution time, the second evolution time and the third evolution time may be obtained in different specific manners based on different probability distributions. In one embodiment, the evolution time t = y τ may be obtained, where y may be sampled from the probability distribution p (y), τ being a preset parameter. In a specific example, the probability distribution may be specific to
In one embodiment, multiple sampling may be performed according to the probability distribution to obtain the first evolution time t m ＝y m τ, second evolution time t n ＝y n τ, third evolution time t k ＝y k And tau, m, n and k are sampling identifiers.
In one embodiment, this operation may be implemented by a classical computational unit. In various embodiments, this operation may also be implemented by analog quantum devices, such as ion traps, semiconductor chips, silicon-based quantum devices, quantum dots, superconducting chips (superconducting quantum wires, superconducting cavities, josephson junctions), optical lattices, reed-burgh atoms, optical waveguides, etc.
Next, in step 13, determining a Hamiltonian corresponding to the system to be tested; determining a first Hamiltonian evolution operation according to the Hamiltonian and the first evolution time, and determining a second Hamiltonian evolution operation according to the Hamiltonian and the second evolution time; measuring a first expected value of a first operation combination applied to a first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to an observed quantity of the system to be measured and a second Hamiltonian evolution operation; the first and second hamiltonian evolution operations are each comprised of a plurality of quantum gates.
In this step, a first hamiltonian evolution operation and a second hamiltonian evolution operation, which may be respectively expressed as hamiltonian evolution times, and a hamiltonian H corresponding to the system to be tested, which are obtained in step 12, may be respectively determined
It should be noted that the first and second hamiltonian evolution operations are not implemented by analog quantum devices, but are respectively composed of a plurality of quantum gates (note that, unlike analog quantum devices that can independently simulate the hamiltonian evolution, individual quantum gates themselves, such as a pauli gate, a controlled not gate, etc., cannot independently simulate the hamiltonian evolution).
In one embodiment, applying a first desired value of a first combination of operations for a first quantum state may be expressed as:
wherein N is a first desired value, # 0 Is in a first quantum state, U 1 、U 2 Respectively a first hamiltonian evolution operation and a second hamiltonian evolution operation,
for conjugate transposition, O is the Hermite calculation corresponding to observed quantityAnd (4) sign.
In various embodiments, the plurality of quantum gates that make up the first hamiltonian evolution operation may be determined in various specific ways. In one embodiment, the plurality of quantum gates comprised by the first hamiltonian evolution operation may be determined by: dividing the first evolution time into a plurality of time periods in sequence; and decomposing the first Hamiltonian evolution operation into a plurality of evolution sub-operations respectively corresponding to the time periods, wherein the evolution sub-operations comprise a Pauli revolving door and a Pauli door. In another embodiment, the rotation angle and the gate class of the pauli rotary gate may be obtained by random sampling, respectively. For example, the error compensation operation may be derived based on compensating for an algorithmic error of the hamiltonian evolution operation. And according to the operation form and the probability distribution of the error compensation operation, randomly sampling to obtain the rotation angle and the door type.
In this step, measurement can be made
Wherein O denotes Hermite operation. U shape 1 、U 2 Respectively, the first hamiltonian evolution operation and the second hamiltonian evolution operation, and may be denoted as
Wherein, t m ＝y m τ，t n ＝y n τ. y is sampled in step 12 from the probability distribution p (y) (in step 12). In particular, quantum circuit implementation that can be constructed with quantum gates
The measurement of (2). In different embodiments, the measurements may be performed in different specific ways. In one embodiment, the real and imaginary parts of the first desired value may be measured separately by a hadamard test. In a specific embodiment, for example, a pair of quantum wires as shown in fig. 3 (a), (b) may be utilized
The real part and the imaginary part of the first desired value are measured, respectively, to obtain the real part and the imaginary part of the first desired value. Here due to U 1 ，U 2 Are Hamiltonian evolution operations, which are collectively denoted by U below for simplicity of description. The quantum wires that make up U can be determined by the following process: first, the evolution time of U is segmented. And according to a plurality of time ends obtained after segmentation, converting U = e iHt Is divided into a plurality of evolution sub-operations respectively corresponding to a plurality of time periods, and the evolution sub-operations can be expressed as
Further, the original Hamiltonian evolution operation may be represented as
As shown in FIG. 3 (c). Secondly, realize U r . In one example, U r This can be achieved by the circuitry shown in fig. 3 (d). I.e. each U r Realized through pauli revolving door and pauli door. Wherein the Paglian door can be expressed as
It consists of only one layer of single-bit gate (P) 1 、P 2 、...P n ) The structure of the utility model is that the material,
indicating a direct product. In one embodiment, the Paglian gate P can be obtained by classical computer sampling. Where the pauli rotary gate is in the form of exp iV θ, V being the set category of pauli gates. In one embodiment, the angle θ of the pauli rotary gate and the classification of the pauli gate V may be sampled by classical computer post-processing. The pauli revolving gate can be realized by disassembling into a basic CNOT gate (a controlled NOT-gate, a 2-qubit control gate) and a single-bit pauli gate. It should be noted that U is r The determination may be random, and the specific determination manner may be different in different specific embodiments, which is not limited in this specification. For example, in one specific example, only one sample may be used for each time segment r, resulting inTo a U r Of (i.e. a
) U is implemented. In another example, the sampling may be repeated several times to obtain several groups U r To implement U.
At step 14, determining a third hamiltonian evolution operation according to the hamiltonian and the third evolution time; and measuring a second expected value of applying a third Hamiltonian evolution operation to the first quantum state to obtain a second measurement result, wherein the third Hamiltonian evolution operation is composed of a plurality of quantum gates.
In one embodiment, applying the second expected value of the third hamiltonian evolution operation for the first quantum state may be expressed as:
P k ＝<ψ 0 |U 3 |ψ 0 >
wherein P is a second desired value, ψ 0 Is in a first quantum state, U 3 Is the third hamiltonian evolution operation.
t k ＝y k τ. Where τ is a predetermined parameter, t k Is the third evolution time.
In different embodiments, the second desired value may be measured in different specific ways. The measurement is similar to the measurement of the first expected value in step 13 (for example, in the quantum wire diagram shown in fig. 2, the corresponding operation of the first expected value is changed to the corresponding operation of the first expected value, for example, U is changed 1 And O is an identity operation, that is, the latter two operations are not performed, so that the detailed content of the real part and the virtual step of the second desired value are measured in the same manner, for example, by using a hadamard test method) refer to the description of step 13, which is not described herein.
It should be noted that step 13 and step 14 are not limited to be performed sequentially. In one embodiment, steps 13 and 14 may be performed in parallel. In another embodiment, steps 13 and 14 may be performed in any order.
Thereafter, in step 15, the observed quantity of the system under test is obtained by combining the first measurement result and the second measurement result.
In different embodiments, the observed quantity may be determined in different specific ways. In one embodiment, step 13 and step 14 may be executed multiple times (e.g., M times) according to the execution result of step 12, for example, to obtain multiple different times
And P k ＝<ψ 0 |U 3 |ψ 0 >In one embodiment, the multiple steps 13 and 14 can be performed in parallel by multiple quantum wires, without the results interfering with each other. Then, according to the measurement results, an estimation value observable on the eigen state is obtained through classical calculation post-processing, and then the eigen state information of the system is equivalently obtained.
In different embodiments, the observations may be different specific observations. For example, in one embodiment, the observed quantity may include one or more of electrical resistance, photoconductivity, magnetic susceptibility, absorption energy spectrum.
According to an embodiment of another aspect, an apparatus for obtaining eigenstates of a system under test based on a quantum gate is provided. Fig. 4 is a structural diagram of an apparatus for obtaining an eigen state of a system under test based on a quantum gate according to an embodiment of the present invention, as shown in fig. 4, the apparatus 400 includes:
an initial state preparation unit 41 configured to prepare a first quantum state;
an evolution time sampling unit 42 configured to sample a first evolution time, a second evolution time and a third evolution time based on a preset probability distribution;
a first measurement unit 43 configured to determine a hamiltonian corresponding to the system under test; determining a first Hamiltonian evolution operation according to the Hamiltonian and the first evolution time, and determining a second Hamiltonian evolution operation according to the Hamiltonian and the second evolution time; measuring a first expected value of a first operation combination applied to a first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to an observed quantity of the system to be measured and a second Hamiltonian evolution operation; the first Hamiltonian evolution operation and the second Hamiltonian evolution operation are respectively composed of a plurality of quantum gates;
a second measurement unit 44 configured to determine a third hamiltonian evolution operation based on the hamiltonian and the third evolution time; measuring a second expectation value of a third Hamiltonian evolution operation applied to the first quantum state to obtain a second measurement result, wherein the third Hamiltonian evolution operation is composed of a plurality of quantum gates;
and an observed quantity determining unit 45 configured to obtain the observed quantity of the system under test by combining the first measurement result and the second measurement result.
According to an embodiment of yet another aspect, there is also provided a computer readable medium comprising a computer program stored thereon, which computer when executed performs the method described above.
According to an embodiment of yet another aspect, there is also provided a quantum computer comprising one or more quantum wires configured to implement the method described above.
The foregoing description has been directed to specific embodiments of this disclosure. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims can be performed in a different order than in the embodiments and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
Those of skill would further appreciate that the various illustrative components and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied in hardware, a software module executed by a processor, or a combination of the two. A software module may reside in Random Access Memory (RAM), memory, read Only Memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A method for obtaining eigenstates of a system to be tested based on a quantum gate comprises the following steps:
preparing a first quantum state;
sampling to obtain a first evolution time, a second evolution time and a third evolution time based on preset probability distribution;
determining a Hamiltonian corresponding to a system to be tested; determining a first Hamiltonian evolution operation according to the Hamiltonian and the first evolution time, and determining a second Hamiltonian evolution operation according to the Hamiltonian and the second evolution time; measuring a first expected value of a first operation combination applied to a first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to an observed quantity of the system to be measured and a second Hamiltonian evolution operation; the first Hamiltonian evolution operation and the second Hamiltonian evolution operation are respectively composed of a plurality of quantum gates;
determining a third Hamiltonian evolution operation according to the Hamiltonian and the third evolution time; measuring a second expectation value of a third Hamiltonian evolution operation applied to the first quantum state to obtain a second measurement result, wherein the third Hamiltonian evolution operation is composed of a plurality of quantum gates;
and combining the first measurement result and the second measurement result to obtain the observed quantity of the system to be measured.
2. The method of claim 1, wherein the system under test comprises any one of a molecular system, a superconducting material system, a metal crystal quantum system, and a nano material quantum system; the observed quantity comprises one or more of resistance, photoconductivity, magnetic susceptibility, absorption spectrum.
3. The method of claim 1, wherein preparing the first quantum state comprises:
and preparing the first quantum state based on any one of state preparation operation and a variational quantum intrinsic solver.
4. The method of claim 1, wherein applying the first desired value of the first combination of operations for the first quantum state is expressed as:
wherein N is a first desired value, ψ 0 Is in a first quantum state, U 1 、U 2 Respectively a first hamiltonian evolution operation and a second hamiltonian evolution operation,
for conjugate transpose, O is the hermitian corresponding to the observed quantity.
5. The method of claim 1, wherein applying the second expected value of the third hamiltonian evolution operation for the first quantum state may be expressed as:
P＝<ψ 0 |U 3 |ψ 0 >
wherein P is a second desired value, ψ 0 Is in a first quantum state, U 3 Is the third hamiltonian evolution operation.
6. The method of claim 1 wherein the first hamiltonian evolution operation includes a plurality of quantum gates determined by:
dividing the first evolution time into a plurality of time segments in sequence;
and decomposing the first Hamiltonian evolution operation into a plurality of evolution sub-operations respectively corresponding to the time periods, wherein the evolution sub-operations are composed of a Pagli revolving door and a Pagli door.
7. The method of claim 6, wherein the angle of rotation and the gate class of the Pally revolving gate are obtained by random sampling, respectively.
8. The method of claim 1, wherein said measuring applies a first desired value of a first operational combination for a first quantum state comprises:
and respectively measuring the real part and the imaginary part of the first expected value by a Harder code test method.
9. An apparatus for obtaining eigenstates of a system under test based on a quantum simulator, the apparatus comprising:
an initial state preparation unit configured to prepare a first quantum state;
the evolution time sampling unit is configured to sample to obtain a first evolution time, a second evolution time and a third evolution time based on preset probability distribution;
the first measurement unit is configured to determine a Hamiltonian corresponding to a system to be measured; determining a first Hamiltonian evolution operation according to the Hamiltonian and the first evolution time, and determining a second Hamiltonian evolution operation according to the Hamiltonian and the second evolution time; measuring a first expected value of a first operation combination applied to a first quantum state to obtain a first measurement result, wherein the first operation combination comprises a conjugate operation of a first Hamiltonian evolution operation, a Hermite operation corresponding to an observed quantity of the system to be measured and a second Hamiltonian evolution operation; the first Hamiltonian evolution operation and the second Hamiltonian evolution operation are respectively composed of a plurality of quantum gates;
a second measurement unit configured to determine a third hamiltonian evolution operation according to the hamiltonian and a third evolution time; measuring a second expected value of a third Hamiltonian evolution operation applied to the first quantum state to obtain a second measurement result, wherein the third Hamiltonian evolution operation is composed of a plurality of quantum gates;
and the observed quantity determining unit is configured to combine the first measurement result and the second measurement result to obtain the observed quantity of the system to be measured.
10. A quantum computer comprising one or more quantum wires configured to implement the method of any of claims 1-8.
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Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110224763A (en) * | 2019-06-28 | 2019-09-10 | 中南大学 | Novel quantum state transfer method based on Hamilton study |
| CN111464154A (en) * | 2019-01-22 | 2020-07-28 | 华为技术有限公司 | Control pulse calculation method and device |
| CN111599414A (en) * | 2020-03-25 | 2020-08-28 | 清华大学 | Quantum computer-based full-quantum molecular simulation method |
| CN112313677A (en) * | 2018-01-31 | 2021-02-02 | 谷歌有限责任公司 | Universal control for realizing quantum gate |
| CN112534448A (en) * | 2018-07-23 | 2021-03-19 | Q-Ctrl股份有限公司 | Multi-qubit control |
| CN112561068A (en) * | 2020-12-10 | 2021-03-26 | 北京百度网讯科技有限公司 | Simulation method, computing device, classical device, storage device and product |
| US20210174236A1 (en) * | 2018-08-07 | 2021-06-10 | Google Llc | Variational quantum state preparation |
| CN113408733A (en) * | 2021-06-29 | 2021-09-17 | 腾讯科技（深圳）有限公司 | Method, device and equipment for acquiring ground state of quantum system and storage medium |
| CN114580647A (en) * | 2022-02-24 | 2022-06-03 | 北京百度网讯科技有限公司 | Simulation method, computing device, apparatus and storage medium of quantum system |
| CN114861928A (en) * | 2022-06-07 | 2022-08-05 | 北京大学 | Quantum measurement method and device and computing equipment |
| CN114897174A (en) * | 2022-05-19 | 2022-08-12 | 北京大学 | Hybrid calculation method and device based on tensor network and quantum line |
| CN114936646A (en) * | 2022-06-09 | 2022-08-23 | 清华大学 | Quantized data processing method and device |
-
2022
- 2022-09-26 CN CN202211182617.0A patent/CN115564051B/en active Active
Patent Citations (12)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112313677A (en) * | 2018-01-31 | 2021-02-02 | 谷歌有限责任公司 | Universal control for realizing quantum gate |
| CN112534448A (en) * | 2018-07-23 | 2021-03-19 | Q-Ctrl股份有限公司 | Multi-qubit control |
| US20210174236A1 (en) * | 2018-08-07 | 2021-06-10 | Google Llc | Variational quantum state preparation |
| CN111464154A (en) * | 2019-01-22 | 2020-07-28 | 华为技术有限公司 | Control pulse calculation method and device |
| CN110224763A (en) * | 2019-06-28 | 2019-09-10 | 中南大学 | Novel quantum state transfer method based on Hamilton study |
| CN111599414A (en) * | 2020-03-25 | 2020-08-28 | 清华大学 | Quantum computer-based full-quantum molecular simulation method |
| CN112561068A (en) * | 2020-12-10 | 2021-03-26 | 北京百度网讯科技有限公司 | Simulation method, computing device, classical device, storage device and product |
| CN113408733A (en) * | 2021-06-29 | 2021-09-17 | 腾讯科技（深圳）有限公司 | Method, device and equipment for acquiring ground state of quantum system and storage medium |
| CN114580647A (en) * | 2022-02-24 | 2022-06-03 | 北京百度网讯科技有限公司 | Simulation method, computing device, apparatus and storage medium of quantum system |
| CN114897174A (en) * | 2022-05-19 | 2022-08-12 | 北京大学 | Hybrid calculation method and device based on tensor network and quantum line |
| CN114861928A (en) * | 2022-06-07 | 2022-08-05 | 北京大学 | Quantum measurement method and device and computing equipment |
| CN114936646A (en) * | 2022-06-09 | 2022-08-23 | 清华大学 | Quantized data processing method and device |
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