Method and device for determining the fidelity of a single quantum gate

Abstract

The present disclosure provides a method and device for determining the fidelity of a single quantum gate, which relates to the field of quantum information technology, specifically to the technical fields of quantum computing, performance detection, etc. The method for determining the fidelity of a single quantum gate includes: generating a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio; generating an initial state of a quantum bit, and determining an ideal final state corresponding to the initial state; determining a noisy final state corresponding to the initial state based on the noisy microwave signal; determining a quantum state fidelity based on the ideal final state and the noisy final state; and determining the fidelity of the target single quantum gate based on the quantum state fidelity.

Description

Technical Field

[0001] The present disclosure relates to the field of quantum information technology, specifically to the technical fields of quantum computing, performance detection, etc., and in particular to a method and device for determining the fidelity of a single quantum gate. Background Art

[0002] A quantum gate is a basic computing unit in quantum computing. It is used to operate on quantum bits (qubit or qbit for short). The number of quantum bits in its input and output is the same. A quantum bit is a unit of quantum information. A quantum gate can operate on one, two or more quantum bits. A single quantum gate operates on one quantum bit.

[0003] In the field of computational science, fidelity often refers to the integrity of data and the correctness of calculations. The higher the fidelity, the greater the reliability and computing power of the computing equipment. Simply put, quantum gate fidelity refers to the accuracy of quantum computers when performing basic operations.

[0004] How to determine the fidelity of quantum gates is a problem that needs to be solved. Summary of the invention

[0005] The present disclosure provides a method, apparatus, device and medium for determining the fidelity of a single quantum gate.

[0006] According to one aspect of the present disclosure, a method for determining the fidelity of a single quantum gate is provided, comprising: generating a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio; generating an initial state of a quantum bit, and determining an ideal final state corresponding to the initial state; determining a noisy final state corresponding to the initial state based on the noisy microwave signal; determining a quantum state fidelity based on the ideal final state and the noisy final state; and determining the fidelity of the target single quantum gate based on the quantum state fidelity.

[0007] According to another aspect of the present disclosure, a device for determining the fidelity of a single quantum gate is provided, comprising: a first generating module, for generating a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio; a first determining module, for generating an initial state of a quantum bit, and determining an ideal final state corresponding to the initial state; a second determining module, for determining the noisy final state corresponding to the initial state based on the noisy microwave signal; a third determining module, for determining the quantum state fidelity based on the ideal final state and the noisy final state; and a fourth determining module, for determining the fidelity of the target single quantum gate based on the quantum state fidelity.

[0008] According to another aspect of the present disclosure, an electronic device is provided, comprising: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor so that the at least one processor can execute any method as described in any of the above aspects.

[0009] According to another aspect of the present disclosure, a non-transitory computer-readable storage medium storing computer instructions is provided, wherein the computer instructions are used to enable the computer to execute any one of the methods according to any one of the above aspects.

[0010] According to another aspect of the present disclosure, a computer program product is provided, including a computer program, wherein when the computer program is executed by a processor, the computer program implements any one of the methods described in any one of the above aspects.

[0011] The present disclosure can accurately and efficiently determine the fidelity of a single quantum gate.

[0012] It should be understood that the content described in this section is not intended to identify the key or important features of the embodiments of the present disclosure, nor is it intended to limit the scope of the present disclosure. Other features of the present disclosure will become easily understood through the following description. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] The accompanying drawings are used to better understand the present solution and do not constitute a limitation of the present disclosure.

[0014] Figure 1 is a schematic diagram according to a first embodiment of the present disclosure;

[0015] Figure 2 is a schematic diagram of microwave drive and quantum bit coupling according to an embodiment of the present disclosure;

[0016] Figure 3 is a schematic diagram according to a second embodiment of the present disclosure;

[0017] Figure 4 is a schematic diagram of a first curve and a second curve provided according to an embodiment of the present disclosure;

[0018] Figure 5 is a schematic diagram according to a third embodiment of the present disclosure;

[0019] Figure 6 Schematic diagram of an electronic device used to implement the method for determining the fidelity of a single quantum gate according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0020] The following is a description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, including various details of the embodiments of the present disclosure to facilitate understanding, which should be considered as merely exemplary. Therefore, it should be recognized by those of ordinary skill in the art that various changes and modifications may be made to the embodiments described herein without departing from the scope and spirit of the present disclosure. Similarly, for the sake of clarity and conciseness, descriptions of well-known functions and structures are omitted in the following description.

[0021] Figure 1 is a schematic diagram according to the first embodiment of the present disclosure. This embodiment provides a method for determining the fidelity of a single quantum gate, such as Figure 1 As shown, the method includes:

[0022] 101. Based on a preset signal-to-noise ratio, a noisy microwave signal corresponding to a target single quantum gate is generated.

[0023] 102. Generate an initial state of the quantum bit, and determine an ideal final state corresponding to the initial state.

[0024] 103. Determine a noisy final state corresponding to the initial state based on the noisy microwave signal.

[0025] 104. Determine quantum state fidelity based on the ideal final state and the noisy final state.

[0026] 105. Determine the fidelity of the target single quantum gate based on the quantum state fidelity.

[0027] Among them, the target quantum gate is the quantum gate to be tested, that is, the fidelity of the target single quantum gate needs to be obtained in the end.

[0028] A quantum bit in a superconducting environment is called a superconducting quantum bit. The single quantum gate operation of a superconducting quantum bit can be achieved through a capacitively coupled microwave drive line.

[0029] Figure 2 It is a schematic diagram of microwave drive and quantum bit coupling provided according to an embodiment of the present disclosure.

[0030] like Figure 2 As shown, a microwave signal is used as a driving signal. The microwave signal is usually a pulse signal, which can be called a microwave pulse signal. When the frequency of the microwave pulse signal is the same as the frequency of the quantum bit, the quantum state will rotate around a certain axis in the XY plane of the Bloch sphere. The angle between the rotation axis and the X axis is determined by the phase of the microwave pulse signal. This phenomenon is also called Rabi oscillation. After the quantum state is rotated to the XY plane by the resonant microwave pulse signal, the rotation of the quantum state along the Z axis can be achieved by turning off the microwave pulse signal and changing the frequency of the quantum bit. Therefore, any single quantum gate operation can be achieved by controlling the microwave signal.

[0031] Since there is a coupling relationship between the control of microwave signals and the single quantum gate operation, microwave signals can be used to simulate the single quantum gate operation, and then the fidelity of the single quantum gate can be obtained based on the relevant parameters of the microwave signal control process.

[0032] There is noise in actual single quantum operation, so the microwave signal uses a noisy microwave signal.

[0033] A noisy microwave signal refers to a microwave signal containing noise. For example, a noisy microwave signal is obtained by superimposing a noise signal on an ideal microwave signal (without noise).

[0034] The ideal final state refers to the final state obtained from the initial state under an ideal evolutionary environment (without noise).

[0035] The noisy final state refers to the final state obtained from the initial state under a noisy evolution environment.

[0036] Initial state, the number is one or more, usually multiple, which can be expressed as M, where M is a positive integer.

[0037] Each initial state corresponds to an ideal final state and a noisy final state. Thus, for M initial states, M ideal final states and M noisy final states are obtained.

[0038] Quantum state fidelity is used to characterize the correctness of quantum states. It is calculated using corresponding ideal final states and noisy final states. For example, if there are M ideal final states and M noisy final states, then M quantum state fidelity can be obtained.

[0039] After obtaining the fidelities of M quantum states, the minimum value can be obtained among the M quantum state fidelities, and then the fidelity of the target single quantum gate can be obtained based on the minimum value.

[0040] In this embodiment, since the control of microwave signals can realize the operation of single quantum gates, microwave signals can be used to drive quantum bits to obtain the noisy final state corresponding to the initial state, the quantum state fidelity is determined based on the ideal final state and the noisy final state, and the single quantum gate fidelity is obtained based on the quantum state fidelity, thereby accurately and efficiently obtaining the single quantum gate fidelity.

[0041] For noisy microwave signals:

[0042] The noisy microwave signal may be generated based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the quantum bit, and a preset normalized signal.

[0043] Specifically, the parameters of the target single quantum gate include: the angle between the rotation axis and the X-axis in the XY plane of the Bloch sphere, the rotation polar angle, and the operation duration;

[0044] The parameters of the quantum bit include: electrical parameters and quantum bit frequency;

[0045] The generating the noisy microwave signal based on the signal-to-noise ratio, the parameter of the target single quantum gate, the parameter of the quantum bit and the preset normalized signal comprises:

[0046] Determining a maximum amplitude based on the rotation polar angle, the electrical parameter, the operation duration, and the normalized signal;

[0047] Based on the signal-to-noise ratio, determining a target variance of the noise signal;

[0048] Generate an in-phase noise signal and an orthogonal noise signal that conform to a normal distribution and have the target variance;

[0049] Generate a first signal based on the maximum amplitude, the normalized signal, the angle, and the orthogonal noise signal;

[0050] Generate a second signal based on the maximum amplitude, the normalized signal, the angle, and the in-phase noise signal;

[0051] determining an amplitude signal based on the first signal and the second signal;

[0052] determining a phase signal based on the first signal and the second signal;

[0053] Using the quantum bit frequency as the microwave signal frequency;

[0054] The noisy microwave signal is generated based on the amplitude signal, the phase signal and the microwave signal frequency.

[0055] The formula is as follows:

[0056] The operation of a common single quantum gate can be described as rotating a single-bit quantum state on the Bloch sphere along a rotation axis on the equatorial plane (XY plane) by a polar angle, so the angle between the rotation axis and the X-axis can be expressed as and the rotation angle to represent a single quantum gate.

[0057] The ideal microwave signal required to realize this single quantum gate It is expressed as:

[0058] (1)

[0059] in, For time; It is a normalized signal, set to a symmetrical Gaussian waveform or cosine waveform with a peak value of 1; is the microwave signal frequency, set to the same value as the qubit frequency same; is the initial phase of the microwave signal, which is set to the angle between the rotation axis of the quantum state on the Bloch sphere and the X-axis.

[0060] is the maximum amplitude of the microwave signal, which is determined by the rotation angle of the quantum state The electrical parameters such as capacitance and inductance of the quantum bit are determined and expressed as:

[0061] (2)

[0062] in, , is the reduced Planck constant; is the coupling capacitance between the qubit and the XY driving line, is the total capacitance of the qubit to ground, is the total inductance of the qubit, is the operation duration of the single quantum gate, that is, the total duration of the microwave signal.

[0063] Since the transmission of signals in actual systems can be regarded as a narrowband process, it is assumed here that the noise is in the form of narrowband normally distributed random noise. , expressed as:

[0064]

[0065] in, are the in-phase component and the quadrature component respectively.

[0066] The actual microwave signal after superimposing noise (noisy microwave signal) It can be expressed as:

[0067] (3)

[0068] in, is the amplitude function of the noisy microwave signal, is the phase function of the noisy microwave signal; the calculation formula is:

[0069] (4)

[0070] (5)

[0071] in, (6)

[0072] (7)

[0073] Considering that the average power of normally distributed random noise is equal to its variance , so the signal-to-noise ratio (SNR) of the noisy microwave signal is expressed as:

[0074] (8)

[0075] According to the above principle, the noisy microwave signal is generated in the following way:

[0076] Get the parameters of the target single quantum gate, including: the angle between the rotation axis and the X-axis in the XY plane of the Bloch sphere , Rotation polar angle , Operation time ;

[0077] Obtain the parameters of the quantum bit, including: electrical parameters, such as the capacitance and inductance parameters involved in formula (2); quantum bit frequency ;

[0078] Get the preset signal-to-noise ratio SNR;

[0079] The parameters of the target single quantum gate, the parameters of the quantum bit and the SNR mentioned above are known values.

[0080] Afterwards, a noisy microwave signal is generated based on the above parameters:

[0081] Formula (2) is used to determine the maximum amplitude based on the rotation polar angle, the electrical parameter, the operation time and the normalized signal. ;

[0082] Formula (8) is used to determine the target variance of the noise signal based on the signal-to-noise ratio, the maximum amplitude, the operation duration and the normalized signal. ;

[0083] After obtaining the target variance, an orthogonal noise signal with the target variance and a normal distribution is generated. and the in-phase noise signal ;

[0084] Formula (6) is used to generate a first signal based on the maximum amplitude, the normalized signal, the angle and the orthogonal noise signal. ;

[0085] Formula (7) is used to generate a second signal based on the maximum amplitude, the normalized signal, the angle and the in-phase noise signal. ;

[0086] Formula (4) is used to determine the amplitude signal based on the first signal and the second signal. ;

[0087] Formula (5) is used to determine the phase signal based on the first signal and the second signal.

[0088] The qubit frequency As microwave signal frequency ;

[0089] Formula (3) is used to generate the noisy microwave signal based on the amplitude signal, the phase signal and the microwave signal frequency. .

[0090] In this way, a noisy microwave signal is generated.

[0091] In addition, the various related signals mentioned above are usually discretized signals, which can be discretized using a preset number of time points.

[0092] Assuming that the number of preset time points is N, the following time point sequence can be obtained: ; The time interval between two adjacent time points is T / N; T is the operation duration of the target single quantum gate.

[0093] After the signal is discretized using the above-mentioned multiple time points, the obtained signal can be called a sequence, that is, an orthogonal noise signal sequence, an in-phase noise signal sequence, an amplitude signal sequence, a phase signal sequence, a noisy microwave signal sequence, etc. can be obtained.

[0094] For the initial state:

[0095] Random sampling can be performed within a preset angle range to obtain at least one group of first angles and second angles; and at least one initial state can be generated based on the at least one group of first angles and second angles.

[0096] Assume that the number of initial states is M, are the first angle and the second angle respectively, and the preset angle range is ,So:

[0097] In the Bloch sphere, is the angle between the initial state and the Z axis, is the angle between the projection of the initial state on the XY plane and the X axis, and The value range is .exist within the range of and Random sampling is performed to obtain M different initial states.

[0098] In this way, M initial states are obtained.

[0099] For the ideal final state:

[0100] An ideal evolution matrix may be determined based on the parameters of the target single quantum gate; and the initial state is multiplied by the ideal evolution matrix to obtain the ideal final state.

[0101] Among them, the initial state of the quantum bit It can be represented as the following column vector:

[0102] (9)

[0103] According to the parameters and , the ideal single-qubit gate can be represented as the following ideal evolution matrix:

[0104] (10)

[0105] Then: The ideal final state is: .

[0106] Each initial state is multiplied by the ideal evolution matrix shown in formula (10) to obtain each ideal final state. When there are M initial states, M ideal final states are obtained.

[0107] For the noisy final state:

[0108] The time interval between two adjacent time points can be determined based on the number of time points and the operation duration; the noisy evolution matrix of each time point among the multiple time points can be determined; and the noisy final state can be determined based on the noisy evolution matrix of each time point and the initial state.

[0109] Furthermore, regarding the noisy evolution matrix: based on the number of time points and the operation duration, the time interval between two adjacent time points is determined; based on the electrical parameters of the quantum bit, the amplitude signal of the noisy microwave signal and the time interval, the interval polar angle signal is determined; based on the interval polar angle signal and the phase signal of the noisy microwave signal, the noisy evolution matrix of each time point is determined.

[0110] The formula is:

[0111] (11)

[0112] in, ; (12)

[0113] (13)

[0114] in, is the noisy evolution matrix at time point t;

[0115] T is the operation duration of the target single quantum gate; N is the number of time points;

[0116] is the time interval;

[0117] is the amplitude signal of the noisy microwave signal;

[0118] is the electrical parameter of the quantum bit;

[0119] is the interval polar angle signal.

[0120] In this way, the noisy evolution matrix at each time point can be obtained.

[0121] Afterwards, the quantum state before evolution at the current time point is multiplied by the noisy evolution matrix at the current time point to obtain the quantum state after evolution at the current time point, and the quantum state before evolution at the next time point is used as the quantum state before evolution at the next time point; the initial value of the current time point is the first time point among the multiple time points, and the quantum state before evolution at the first time point is the initial state;

[0122] The above process is repeated until the evolved quantum state at the last time point among the multiple time points is obtained as the noisy final state.

[0123] Specifically, at the first time point t1, the noisy evolution matrix at the first time point is used With initial state Multiply them to get the evolved quantum state of t1 , and as the quantum state before evolution at t2, and then use the noisy evolution matrix at the second time point and Multiply them to get the evolved quantum state of t2 , and so on, we get the quantum state after evolution at the last time point , as the noisy final state corresponding to the initial state.

[0124] Each initial state is subjected to the above-mentioned noisy evolution process to obtain each noisy final state. When there are M initial states, M noisy final states are obtained.

[0125] Regarding quantum state fidelity:

[0126] Based on the ideal final state, determining an ideal density matrix;

[0127] Based on the noisy final state, determining a noisy density matrix;

[0128] The quantum state fidelity is determined based on the ideal density matrix and the noisy density matrix.

[0129] Specifically, the relationship between the density matrix and the quantum state is:

[0130] (14)

[0131] in, is a quantum state, which is a column vector; for The conjugate transpose of is a row vector; It is a density matrix, which is a 2*2 matrix.

[0132] In this way, for each ideal final state, the corresponding ideal density matrix is ​​obtained using formula (14), and for each noisy final state, the corresponding noisy density matrix is ​​obtained using formula (14). The quantum state fidelity is calculated based on these two density matrices. The calculation formula is:

[0133] (15)

[0134] in, is the quantum state fidelity; is the ideal density matrix; is the noisy density matrix.

[0135] In this way, corresponding to each initial state, based on the ideal final state and the noisy final state corresponding to the initial state, the quantum state fidelity corresponding to the initial state can be obtained. When there are M initial states, M quantum state fidelities can be obtained.

[0136] The smallest quantum state fidelity can then be used as the fidelity of the target single quantum gate.

[0137] That is, if the quantum state fidelity is one, the quantum state fidelity is used as the fidelity of the target single quantum gate; or, if the quantum state fidelity is at least two, the minimum value of the at least two quantum state fidelity is used as the fidelity of the target single quantum gate.

[0138] In this way, the fidelity of the target quantum gate is obtained.

[0139] Figure 3 is a schematic diagram according to the second embodiment of the present disclosure. This embodiment provides a method for determining the fidelity of a single quantum gate, such as Figure 3 As shown, the method includes:

[0140] 301. Based on a preset signal-to-noise ratio, generate a noisy microwave signal corresponding to a target single quantum gate.

[0141] 302. Generate an initial state of the quantum bit, and determine an ideal final state corresponding to the initial state.

[0142] 303. Determine a noisy final state corresponding to the initial state based on the noisy microwave signal.

[0143] 304. Determine quantum state fidelity based on the ideal final state and the noisy final state.

[0144] 305. Determine the fidelity of the target single quantum gate based on the quantum state fidelity.

[0145] 306. Obtain multiple fidelities of the target single quantum gate.

[0146] Specifically, steps 301 to 305 are repeatedly performed multiple times to obtain multiple fidelities of the target single quantum gate.

[0147] Multiple times is represented by L times, where L is an integer greater than or equal to 2.

[0148] 307. Based on the multiple fidelities, determine a fidelity mean and a fidelity variance.

[0149] Among them, L fidelities can be obtained by executing L times, and the mean of these L fidelities is calculated to obtain the fidelity mean, and then the variance calculation formula is used to obtain the fidelity variance.

[0150] 308. Generate a first curve based on the fidelity mean value and the signal-to-noise ratio, where the first curve is used to represent a corresponding relationship between the signal-to-noise ratio and the fidelity mean value.

[0151] 309. Generate a second curve based on the fidelity variance and the signal-to-noise ratio, where the second curve is used to represent a corresponding relationship between the signal-to-noise ratio and the fidelity variance.

[0152] 310. Display the first curve and the second curve.

[0153] For each signal-to-noise ratio, the fidelity mean and fidelity variance corresponding to the signal-to-noise ratio are obtained through 301 to 307. By changing the signal-to-noise ratio, the first curve and the second curve are generated based on multiple signal-to-noise ratios.

[0154] Figure 4 is a schematic diagram of a first curve and a second curve provided according to an embodiment of the present disclosure. The first curve represents the corresponding relationship between the signal-to-noise ratio and the mean fidelity of the target quantum gate, and the second curve represents the corresponding relationship between the signal-to-noise ratio and the fidelity variance of the target quantum gate, so that a suitable signal-to-noise ratio can be selected according to the performance requirements of a single quantum gate.

[0155] In the disclosed embodiments, generating a noisy microwave signal based on a narrowband noise signal is more in line with the actual conditions of a superconducting quantum computer system and can better reflect the influence of a manipulation signal on a quantum chip, thereby improving the accuracy of fidelity calculations; generating a noisy microwave signal based on a signal-to-noise ratio can superimpose noise signals under different signal-to-noise ratios on an ideal microwave signal, thereby simulating and analyzing the quantum state fidelity and gate fidelity to obtain gate fidelity indicators under different signal-to-noise ratios; by generating a first curve and a second curve, the signal-to-noise ratio of a microwave signal as a driving source can be determined under the actually required gate fidelity indicator, and then a suitable microwave signal can be used for driving.

[0156] Figure 5 1 is a schematic diagram of a third embodiment of the present disclosure, which provides a device for determining the fidelity of a single quantum gate. The device 500 includes: a first generating module 501, a first determining module 502, a second determining module 503, a third determining module 504 and a fourth determining module 505.

[0157] The first generating module 501 is used to generate a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio; the first determining module 502 is used to generate an initial state of a quantum bit and determine an ideal final state corresponding to the initial state; the second determining module 503 is used to determine a noisy final state corresponding to the initial state based on the noisy microwave signal; the third determining module 504 is used to determine a quantum state fidelity based on the ideal final state and the noisy final state; and the fourth determining module 505 is used to determine the fidelity of the target single quantum gate based on the quantum state fidelity.

[0158] In some embodiments, the first generating module is further used to generate the noisy microwave signal based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the quantum bit and a preset normalized signal.

[0159] In some embodiments, the parameters of the target single quantum gate include: the angle between the rotation axis and the X-axis in the XY plane of the Bloch sphere, the rotation polar angle, and the operation time; the parameters of the quantum bit include: electrical parameters and quantum bit frequency; the first generation module is further used to: determine the maximum amplitude based on the rotation polar angle, the electrical parameters, the operation time and the normalized signal; determine the target variance of the noise signal based on the signal-to-noise ratio, the maximum amplitude, the operation time and the normalized signal; generate an in-phase noise signal and an orthogonal noise signal that conform to the normal distribution and have the target variance; generate a first signal based on the maximum amplitude, the normalized signal, the angle and the orthogonal noise signal; generate a second signal based on the maximum amplitude, the normalized signal, the angle and the in-phase noise signal; determine an amplitude signal based on the first signal and the second signal; determine a phase signal based on the first signal and the second signal; use the quantum bit frequency as the microwave signal frequency; and generate the noisy microwave signal based on the amplitude signal, the phase signal and the microwave signal frequency.

[0160] In some embodiments, the first determination module is further used to: randomly sample within a preset angle range to obtain at least one group of first angles and second angles; and generate at least one initial state based on the at least one group of first angles and second angles.

[0161] In some embodiments, the first determination module is further used to: determine an ideal evolution matrix based on the parameters of the target single quantum gate; and multiply the initial state by the ideal evolution matrix to obtain the ideal final state.

[0162] In some embodiments, the second determination module is further used to: determine multiple time points based on a preset number of time points and the operation duration of the target single quantum gate; determine the noisy evolution matrix of each time point among the multiple time points; and determine the noisy final state based on the noisy evolution matrix of each time point and the initial state.

[0163] In some embodiments, the second determination module is further used to: determine the time interval between two adjacent time points based on the number of time points and the operation duration; determine the interval polar angle signal based on the electrical parameters of the quantum bit, the amplitude signal of the noisy microwave signal and the time interval; determine the noisy evolution matrix of each time point based on the interval polar angle signal and the phase signal of the noisy microwave signal.

[0164] In some embodiments, the second determination module is further used to: multiply the pre-evolution quantum state at the current time point by the noisy evolution matrix at the current time point to obtain the post-evolution quantum state at the current time point, and use it as the pre-evolution quantum state at the next time point; the initial value of the current time point is the first time point among the multiple time points, and the pre-evolution quantum state of the first time point is the initial state; repeat the above process until the post-evolution quantum state of the last time point among the multiple time points is obtained as the noisy final state.

[0165] In some embodiments, the third determination module is further used to: determine an ideal density matrix based on the ideal final state; determine a noisy density matrix based on the noisy final state; and determine the fidelity of the quantum state based on the ideal density matrix and the noisy density matrix.

[0166] In some embodiments, the fourth determination module is further used to: if the quantum state fidelity is one, use the quantum state fidelity as the fidelity of the target single quantum gate; or, if the quantum state fidelity is at least two, use the minimum value of the at least two quantum state fidelity as the fidelity of the target single quantum gate.

[0167] In some embodiments, the method further includes: an acquisition module, a fifth determination module, a second generation module, a third generation module, and a display module. The acquisition module is used to execute the method multiple times to obtain multiple fidelities of the target single quantum gate; the fifth determination module is used to determine the fidelity mean and the fidelity variance based on the multiple fidelities; the second generation module is used to generate a first curve based on the fidelity mean and the signal-to-noise ratio, and the first curve is used to characterize the corresponding relationship between the signal-to-noise ratio and the fidelity mean; the third generation module is used to generate a second curve based on the fidelity variance and the signal-to-noise ratio, and the second curve is used to characterize the corresponding relationship between the signal-to-noise ratio and the fidelity variance; the display module is used to display the first curve and the second curve.

[0168] It can be understood that in the embodiments of the present disclosure, the same or similar contents in different embodiments can be referenced to each other.

[0169] It can be understood that the “first”, “second”, etc. in the embodiments of the present disclosure are only used for distinction and do not indicate the degree of importance, time sequence, etc.

[0170] It is understandable that, unless otherwise specified, the sequence of steps in the process indicates that the timing relationship between these steps is not limited.

[0171] In the technical solution of the present disclosure, the collection, storage, use, processing, transmission, provision and disclosure of user personal information involved are in compliance with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0172] According to an embodiment of the present disclosure, the present disclosure also provides an electronic device, a readable storage medium and a computer program product.

[0173] Figure 6 A schematic block diagram of an example electronic device 600 that can be used to implement an embodiment of the present disclosure is shown. The electronic device 600 is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smart phones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely examples and are not intended to limit the implementation of the present disclosure described and / or required herein.

[0174] like Figure 6 As shown, the electronic device 600 includes a computing unit 601, which can perform various appropriate actions and processes according to a computer program stored in a read-only memory (ROM) 602 or a computer program loaded from a storage unit 608 into a random access memory (RAM) 603. In the RAM 603, various programs and data required for the operation of the electronic device 600 can also be stored. The computing unit 601, the ROM 602, and the RAM 603 are connected to each other via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0175] Multiple components in the electronic device 600 are connected to the I / O interface 605, including: an input unit 606, such as a keyboard, a mouse, etc.; an output unit 607, such as various types of displays, speakers, etc.; a storage unit 608, such as a disk, an optical disk, etc.; and a communication unit 609, such as a network card, a modem, a wireless communication transceiver, etc. The communication unit 609 allows the electronic device 600 to exchange information / data with other devices through a computer network such as the Internet and / or various telecommunication networks.

[0176] The computing unit 601 may be a variety of general and / or special processing components with processing and computing capabilities. Some examples of the computing unit 601 include, but are not limited to, a central processing unit (CPU), a graphics processing unit (GPU), various dedicated artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, digital signal processors (DSPs), and any appropriate processors, controllers, microcontrollers, etc. The computing unit 601 performs the various methods and processes described above, such as a method for determining the fidelity of a single quantum gate. For example, in some embodiments, the method for determining the fidelity of a single quantum gate may be implemented as a computer software program, which is tangibly included in a machine-readable medium, such as a storage unit 608. In some embodiments, part or all of the computer program may be loaded and / or installed on the electronic device 600 via the ROM 602 and / or the communication unit 609. When the computer program is loaded into the RAM 603 and executed by the computing unit 601, one or more steps of the method for determining the fidelity of a single quantum gate described above may be performed. Alternatively, in other embodiments, the computing unit 601 may be configured to execute the method for determining the fidelity of a single quantum gate in any other appropriate manner (for example, by means of firmware).

[0177] Various implementations of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field programmable gate arrays (FPGAs), application specific integrated circuits (ASICs), application specific standard products (ASSPs), systems on chips (SOCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various implementations can include: being implemented in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which can be a special purpose or general purpose programmable processor that can receive data and instructions from a storage system, at least one input device, and at least one output device, and transmit data and instructions to the storage system, the at least one input device, and the at least one output device.

[0178] The program code for implementing the method of the present disclosure may be written in any combination of one or more programming languages. These program codes may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program code, when executed by the processor or controller, enables the functions / operations specified in the flow chart and / or block diagram to be implemented. The program code may be executed entirely on the machine, partially on the machine, partially on the machine and partially on a remote machine as a stand-alone software package, or entirely on a remote machine or server.

[0179] In the context of the present disclosure, a machine-readable medium may be a tangible medium that may contain or store a program for use by or in conjunction with an instruction execution system, device, or equipment. A machine-readable medium may be a machine-readable signal medium or a machine-readable storage medium. A machine-readable medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, device, or device, or any suitable combination of the foregoing. A more specific example of a machine-readable storage medium may include an electrical connection based on one or more lines, a portable computer disk, 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 disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.

[0180] To provide interaction with a user, the systems and techniques described herein 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 the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user can provide input to the computer. Other types of devices can also be used to provide interaction with the user; for example, the feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including acoustic input, voice input, or tactile input).

[0181] The systems and techniques described herein may be implemented in a computing system that includes back-end components (e.g., as a data server), or a computing system that includes middleware components (e.g., an application server), or a computing system that includes front-end components (e.g., a user computer with a graphical user interface or a web browser through which a user can interact with implementations of the systems and techniques described herein), or a computing system that includes any combination of such back-end components, middleware components, or front-end components. The components of the system may be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: a local area network (LAN), a wide area network (WAN), and the Internet.

[0182] A computer system may include a client and a server. The client and the server are generally remote from each other and usually interact through a communication network. The relationship between the client and the server is generated by computer programs running on the corresponding computers and having a client-server relationship with each other. The server may be a cloud server, also known as a cloud computing server or cloud host, which is a host product in the cloud computing service system to solve the defects of difficult management and weak business scalability in traditional physical hosts and VPS services ("Virtual Private Server", or "VPS" for short). The server may also be a server of a distributed system, or a server combined with a blockchain.

[0183] It should be understood that the various forms of processes shown above can be used to reorder, add or cancel steps. For example, the steps recorded in this disclosure can be executed in parallel, sequentially or in different orders, as long as the desired results of the technical solutions disclosed in this disclosure can be achieved, and this document does not limit this.

[0184] The above specific implementations do not constitute a limitation on the protection scope of the present disclosure. It should be understood by those skilled in the art that various modifications, combinations, sub-combinations and substitutions can be made according to design requirements and other factors. Any modification, equivalent substitution and improvement made within the spirit and principle of the present disclosure shall be included in the protection scope of the present disclosure.

Claims

1. A method for determining the fidelity of a single quantum gate, characterized in that: include: Based on a preset signal-to-noise ratio, a noisy microwave signal corresponding to a target single quantum gate is generated; Generate an initial state of a quantum bit and determine an ideal final state corresponding to the initial state; Based on the noisy microwave signal, determining a noisy final state corresponding to the initial state; Determining quantum state fidelity based on the ideal final state and the noisy final state; Determining the fidelity of the target single quantum gate based on the quantum state fidelity; The parameters of the target single quantum gate include: the angle between the rotation axis and the X-axis in the XY plane of the Bloch sphere, the rotation polar angle, and the operation duration; The parameters of the quantum bit include: electrical parameters and quantum bit frequency; The step of generating a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio includes: Determining a maximum amplitude based on the rotation polar angle, the electrical parameter, the operation duration, and a preset normalized signal; Determining a target variance of a noise signal based on the signal-to-noise ratio, the maximum amplitude, the operation duration, and the normalized signal; Generate an in-phase noise signal and an orthogonal noise signal that conform to a normal distribution and have the target variance; Generate a first signal based on the maximum amplitude, the normalized signal, the angle, and the orthogonal noise signal; Generate a second signal based on the maximum amplitude, the normalized signal, the angle, and the in-phase noise signal; determining an amplitude signal based on the first signal and the second signal; determining a phase signal based on the first signal and the second signal; Using the quantum bit frequency as the microwave signal frequency; The noisy microwave signal is generated based on the amplitude signal, the phase signal and the microwave signal frequency.

2. The method according to claim 1, characterized in that The generating the initial state of the quantum bit comprises: Random sampling within a preset angle range to obtain at least one set of first angle and second angle; At least one initial state is generated based on the at least one set of first angles and second angles.

3. The method according to claim 1, characterized in that The determining of the ideal final state corresponding to the initial state comprises: Determining an ideal evolution matrix based on the parameters of the target single quantum gate; The initial state is multiplied by the ideal evolution matrix to obtain the ideal final state.

4. The method according to claim 1, characterized in that: The determining, based on the noisy microwave signal, a noisy final state corresponding to the initial state comprises: Determining multiple time points based on a preset number of time points and an operation duration of the target single quantum gate; Determining a noisy evolution matrix for each of the multiple time points; The noisy final state is determined based on the noisy evolution matrix at each time point and the initial state.

5. The method according to claim 4, characterized in that The determining of the noisy evolution matrix of each time point among the multiple time points includes: Determine the time interval between two adjacent time points based on the number of time points and the operation duration; Determining an interval polar angle signal based on the electrical parameters of the quantum bit, the amplitude signal of the noisy microwave signal and the time interval; Based on the interval polar angle signal and the phase signal of the noisy microwave signal, the noisy evolution matrix at each time point is determined.

6. The method according to claim 4, characterized in that The determining the noisy final state based on the noisy evolution matrix at each time point and the initial state includes: Multiplying the quantum state before evolution at the current time point by the noisy evolution matrix at the current time point to obtain the quantum state after evolution at the current time point, and using it as the quantum state before evolution at the next time point; the initial value of the current time point is the first time point among the multiple time points, and the quantum state before evolution at the first time point is the initial state; The above process is repeated until the evolved quantum state at the last time point among the multiple time points is obtained as the noisy final state.

7. The method according to claim 1, characterized in that The step of determining the quantum state fidelity based on the ideal final state and the noisy final state comprises: Based on the ideal final state, determining an ideal density matrix; Based on the noisy final state, determining a noisy density matrix; The quantum state fidelity is determined based on the ideal density matrix and the noisy density matrix.

8. The method according to claim 1, characterized in that Determining the fidelity of the target single quantum gate based on the quantum state fidelity includes: If the quantum state fidelity is one, the quantum state fidelity is used as the fidelity of the target single quantum gate; or, If the number of the quantum state fidelities is at least two, the minimum value of the at least two quantum state fidelities is used as the fidelity of the target single quantum gate.

9. The method according to claim 1, characterized in that: Also includes: Executing the method multiple times to obtain multiple fidelities of the target single quantum gate; Based on the plurality of fidelities, determining a fidelity mean and a fidelity variance; Based on the fidelity mean value and the signal-to-noise ratio, generating a first curve, wherein the first curve is used to represent a corresponding relationship between the signal-to-noise ratio and the fidelity mean value; Based on the fidelity variance and the signal-to-noise ratio, generating a second curve, wherein the second curve is used to characterize a corresponding relationship between the signal-to-noise ratio and the fidelity variance; The first curve and the second curve are displayed.

10. A device for determining the fidelity of a single quantum gate, characterized in that: include: A first generating module is used to generate a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio; A first determination module, used to generate an initial state of a quantum bit and determine an ideal final state corresponding to the initial state; A second determination module, configured to determine a noisy final state corresponding to the initial state based on the noisy microwave signal; A third determination module, configured to determine the quantum state fidelity based on the ideal final state and the noisy final state; A fourth determination module, configured to determine the fidelity of the target single quantum gate based on the quantum state fidelity; The parameters of the target single quantum gate include: the angle between the rotation axis and the X-axis in the XY plane of the Bloch sphere, the rotation polar angle, and the operation duration; The parameters of the quantum bit include: electrical parameters and quantum bit frequency; The first generating module is further used for: Determining a maximum amplitude based on the rotation polar angle, the electrical parameter, the operation duration, and a preset normalized signal; Determining a target variance of a noise signal based on the signal-to-noise ratio, the maximum amplitude, the operation duration, and the normalized signal; Generate an in-phase noise signal and an orthogonal noise signal that conform to a normal distribution and have the target variance; Generate a first signal based on the maximum amplitude, the normalized signal, the angle, and the orthogonal noise signal; Generate a second signal based on the maximum amplitude, the normalized signal, the angle, and the in-phase noise signal; determining an amplitude signal based on the first signal and the second signal; determining a phase signal based on the first signal and the second signal; Using the quantum bit frequency as the microwave signal frequency; The noisy microwave signal is generated based on the amplitude signal, the phase signal and the microwave signal frequency.

11. The device according to claim 10, characterized in that The first determining module is further configured to: Random sampling within a preset angle range to obtain at least one set of first angle and second angle; At least one initial state is generated based on the at least one set of first angles and second angles.

12. The device according to claim 10, characterized in that The first determining module is further configured to: Determining an ideal evolution matrix based on the parameters of the target single quantum gate; The initial state is multiplied by the ideal evolution matrix to obtain the ideal final state.

13. The device according to claim 10, characterized in that The second determining module is further used for: Determining multiple time points based on a preset number of time points and an operation duration of the target single quantum gate; Determining a noisy evolution matrix for each of the multiple time points; The noisy final state is determined based on the noisy evolution matrix at each time point and the initial state.

14. The device according to claim 13, characterized in that The second determining module is further used for: Determine the time interval between two adjacent time points based on the number of time points and the operation duration; Determining an interval polar angle signal based on the electrical parameters of the quantum bit, the amplitude signal of the noisy microwave signal and the time interval; Based on the interval polar angle signal and the phase signal of the noisy microwave signal, the noisy evolution matrix at each time point is determined.

15. The device according to claim 13, characterized in that The second determining module is further used for: Multiplying the quantum state before evolution at the current time point by the noisy evolution matrix at the current time point to obtain the quantum state after evolution at the current time point, and using it as the quantum state before evolution at the next time point; the initial value of the current time point is the first time point among the multiple time points, and the quantum state before evolution at the first time point is the initial state; The above process is repeated until the evolved quantum state at the last time point among the multiple time points is obtained as the noisy final state.

16. The device according to claim 10, characterized in that The third determination module is further used for: Based on the ideal final state, determining an ideal density matrix; Based on the noisy final state, determining a noisy density matrix; The quantum state fidelity is determined based on the ideal density matrix and the noisy density matrix.

17. The device according to claim 10, characterized in that The fourth determination module is further configured to: If the quantum state fidelity is one, the quantum state fidelity is used as the fidelity of the target single quantum gate; or, If the number of the quantum state fidelities is at least two, the minimum value of the at least two quantum state fidelities is used as the fidelity of the target single quantum gate.

18. The apparatus according to claim 10, further comprising: An acquisition module, configured to execute the method according to any one of claims 1 to 9 multiple times to obtain multiple fidelities of the target single quantum gate; A fifth determination module, configured to determine a fidelity mean and a fidelity variance based on the plurality of fidelities; A second generating module, configured to generate a first curve based on the fidelity mean value and the signal-to-noise ratio, wherein the first curve is used to represent a corresponding relationship between the signal-to-noise ratio and the fidelity mean value; A third generating module, configured to generate a second curve based on the fidelity variance and the signal-to-noise ratio, wherein the second curve is used to characterize a corresponding relationship between the signal-to-noise ratio and the fidelity variance; A display module is used to display the first curve and the second curve.

19. An electronic device comprising: at least one processor; as well as a memory communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the method according to any one of claims 1 to 9.

20. A non-transitory computer-readable storage medium storing computer instructions, wherein: The computer instructions are used to cause the computer to execute the method according to any one of claims 1-9.

21. A computer program product comprising a computer program, which, when executed by a processor, implements the method according to any one of claims 1 to 9.

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