Method and apparatus for determining fidelity of single quantum gate

Abstract

The present disclosure relates to the technical field of quantum information, and particularly relates to the technical fields of quantum computing, performance testing, etc. Provided are a method and apparatus for determining the fidelity of a single quantum gate. The method for determining the fidelity of a single quantum gate comprises: on the basis of a preset signal-to-noise ratio, generating a noise-containing microwave signal corresponding to a target single quantum gate; generating an initial state of a quantum bit, and determining an ideal final state corresponding to the initial state; on the basis of the noise-containing microwave signal, determining a noise-containing final state corresponding to the initial state; on the basis of the ideal final state and the noise-containing final state, determining a quantum state fidelity; and on the basis of the quantum state fidelity, determining the fidelity of the target single quantum gate.

Description

Methods and apparatus for determining the fidelity of a single quantum gate Technical Field

[0001] This disclosure relates to the field of quantum information technology, specifically to the fields of quantum computing and performance testing, and particularly to a method and apparatus for determining the fidelity of a single quantum gate. Background Technology

[0002] A quantum gate is the fundamental operational unit in quantum computing, used to operate on quantum bits (qubits or qbits). The number of qubits as input and output are the same. A qubit is a unit of quantum information. A quantum gate can operate on one, two, or more qubits, while a single quantum gate operates on a single qubit.

[0003] In the field of computer science, fidelity often refers to the integrity of data and the correctness of calculations. Higher fidelity means greater reliability and computing power of the computing device. Simply put, quantum gate fidelity refers to the accuracy of a quantum computer performing basic operations.

[0004] Determining the fidelity of quantum gates is a problem that needs to be solved. Summary of the Invention

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

[0006] According to one aspect of this 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 this disclosure, an apparatus for determining the fidelity of a single quantum gate is provided, comprising: a first generation module for generating a noisy microwave signal corresponding to a target single quantum gate based on a preset signal-to-noise ratio; a first determination module for generating an initial state of a quantum bit and determining an ideal final state corresponding to the initial state; a second determination module for determining a noisy final state corresponding to the initial state based on the noisy microwave signal; a third determination module for determining the quantum state fidelity based on the ideal final state and the noisy final state; and a fourth determination module for determining the fidelity of the target single quantum gate based on the quantum state fidelity.

[0008] According to another aspect of this disclosure, an electronic device is provided, comprising: at least one processor; and a memory communicatively connected to said at least one processor; wherein the memory stores instructions executable by said at least one processor, said instructions being executed by said at least one processor to enable said at least one processor to perform the method as described in any of the foregoing aspects.

[0009] According to another aspect of this disclosure, a non-transitory computer-readable storage medium is provided storing computer instructions, wherein the computer instructions are configured to cause the computer to perform the method according to any of the preceding aspects.

[0010] According to another aspect of this disclosure, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the method according to any of the preceding aspects.

[0011] This disclosure enables accurate and efficient determination of single-quantum gate fidelity.

[0012] It should be understood that the description in this section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0013] The accompanying drawings are provided to better understand this solution and do not constitute a limitation of this disclosure. Wherein:

[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 the first curve and the 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 is a schematic diagram of an electronic device used to implement the method for determining the fidelity of a single quantum gate according to embodiments of the present disclosure. Detailed Implementation

[0020] The exemplary embodiments of this disclosure are described below with reference to the accompanying drawings, including various details of the embodiments to aid understanding, and should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this disclosure. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

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

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

[0023] 102. Generate the initial state of the qubit and determine the ideal final state corresponding to the initial state.

[0024] 103. Based on the noisy microwave signal, determine the noisy final state corresponding to the initial state.

[0025] 104. Based on the ideal final state and the noisy final state, determine the quantum state fidelity.

[0026] 105. Based on the quantum state fidelity, determine the fidelity of the target single quantum gate.

[0027] The target quantum gate is the quantum gate to be tested, which means that 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. Single quantum gate operations of a superconducting quantum bit can be realized through a capacitively coupled microwave drive line.

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

[0030] As shown in Figure 2, a microwave signal is used as the driving signal. This microwave signal is typically a pulse signal, referred to as a microwave pulse signal. When the frequency of the microwave pulse signal is the same as the frequency of the qubit, the quantum state will rotate around an axis in the XY plane of the Bloch sphere. The angle between this rotation axis and the X-axis is determined by the phase of the microwave pulse signal; this phenomenon is also called Rabi oscillation. After rotating the quantum state into the XY plane using a resonant microwave pulse signal, turning off the microwave pulse signal and changing the frequency of the qubit allows the quantum state to rotate along the Z-axis. Therefore, arbitrary single-quantum gate operations can be achieved by controlling the microwave signal.

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

[0032] Noise exists in actual single-quantum operations, therefore a noisy microwave signal is used.

[0033] Noisy microwave signals are microwave signals that contain noise. For example, a noisy microwave signal is obtained by superimposing a noise signal on an ideal microwave signal (without noise).

[0034] An ideal final state refers to the final state obtained from an initial state under an ideal evolutionary environment (free of noise).

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

[0036] The initial state can be one or more, usually multiple, and can be represented 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, we obtain M ideal final states and M noisy final states.

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

[0039] After obtaining the fidelity of M quantum states, the minimum value can be obtained among these 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 a single quantum gate, microwave signals can be used to drive the 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 can be generated based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the qubit, 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 time;

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

[0045] The generation of the noisy microwave signal based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the qubit, and a preset normalized signal includes:

[0046] The maximum amplitude is determined based on the rotation polar angle, the electrical parameters, the operating time, and the normalized signal;

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

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

[0049] A first signal is generated based on the maximum amplitude, the normalized signal, the included angle, and the orthogonal noise signal.

[0050] A second signal is generated based on the maximum amplitude, the normalized signal, the included angle, and the in-phase noise signal.

[0051] Based on the first signal and the second signal, determine the amplitude signal;

[0052] Based on the first signal and the second signal, determine the phase signal;

[0053] The frequency of the quantum bit is used as the frequency of the microwave signal.

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

[0055] The formula is expressed as follows:

[0056] A common single-qubit quantum gate operation can be described as rotating a single-qubit quantum state on a Bloch sphere by a polar angle along a rotation axis on the equatorial plane (XY plane). Therefore, the angle between the rotation axis and the X-axis can be used as the reference angle. A single quantum gate is represented by a rotation polar angle θ.

[0057] The ideal microwave signal V required to realize this single quantum gate d (t) is represented as:

[0058] Where t is time; s(t) is the normalized signal, set as a symmetrical Gaussian or cosine waveform with a peak value of 1; ω d It is the microwave signal frequency, and its value is set to be the same as the quantum bit frequency ω. q same; It is the initial phase of the microwave signal, set as the angle between the rotation axis of the quantum state on the Bloch sphere and the X-axis.

[0059] V0 is the maximum amplitude of the microwave signal, determined by the rotation polar angle θ of the quantum state and the electrical parameters such as capacitance and inductance of the quantum bit, and is expressed as:

[0060] in, To reduce Planck's constant; C d C is the coupling capacitance between the quantum bit and the XY driving line. Σ L is the total capacitance to ground of a quantum bit. J Let T be the total inductance of the qubit, and T be the operation time of the single quantum gate, i.e., the total duration of the microwave signal.

[0061] Since signal transmission in a practical system can be considered a narrowband process, we assume here that the noise is in the form of narrowband normally distributed random noise n(t), expressed as: n(t) = n c (t)cos(ω d t)-n s (t)sin(ω d t)

[0062] Where, n c (t),n s (t) represents the in-phase component and the quadrature component, respectively.

[0063] The actual microwave signal after adding noise (noisy microwave signal) V' d (t) can be represented as:

[0064] Where V(t) is the amplitude function of the noisy microwave signal. It is the phase function of the noisy microwave signal; the calculation formula is:

[0065] in,

[0066] Considering that the average power of normally distributed random noise is equal to its variance σ 2 Therefore, the signal-to-noise ratio (SNR) of a noisy microwave signal is expressed as:

[0067] Based on the above principles, noisy microwave signals are generated in the following manner:

[0068] Obtain 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 θ, operation time T;

[0069] Obtain the parameters of the qubit, including: electrical parameters, such as the capacitance and inductance parameters involved in formula (2); and the qubit frequency ω. q;

[0070] Obtain the preset signal-to-noise ratio (SNR);

[0071] The parameters of the target single quantum gate, the parameters of the qubit, and the SNR mentioned above are known values.

[0072] Then, a noisy microwave signal is generated based on the above parameters:

[0073] Using formula (2), the maximum amplitude V0 is determined based on the rotation polar angle, the electrical parameters, the operation time, and the normalized signal;

[0074] Using formula (8), the target variance σ of the noise signal is determined based on the signal-to-noise ratio, the maximum amplitude, the operation time, and the normalized signal. 2 ;

[0075] After obtaining the target variance, an orthogonal noise signal n with the target variance and conforming to a normal distribution is generated. s (t) and in-phase noise signal n c (t);

[0076] Using formula (6), a first signal a(t) is generated based on the maximum amplitude, the normalized signal, the included angle, and the orthogonal noise signal;

[0077] Using formula (7), a second signal b(t) is generated based on the maximum amplitude, the normalized signal, the included angle, and the in-phase noise signal;

[0078] Using formula (4), the amplitude signal V(t) is determined based on the first signal and the second signal;

[0079] Using formula (5), the phase signal is determined based on the first signal and the second signal.

[0080] The frequency ω of the quantum bit q As the microwave signal frequency ω d ;

[0081] Using formula (3), the noisy microwave signal V' is generated based on the amplitude signal, the phase signal, and the microwave signal frequency. d (t).

[0082] This generates a noisy microwave signal.

[0083] In addition, the various related signals mentioned above are usually discretized signals, which can be discretized using a preset number of time points.

[0084] Assuming the preset number of time points is N, then the following time point sequence can be obtained: t0, t1, t2, ..., t N The time interval between two adjacent time points is T / N; T is the operation time of the target single quantum gate.

[0085] After discretizing the signal using the above multiple time points, the resulting signal can be called a sequence, which can be obtained as orthogonal noise signal sequence, in-phase noise signal sequence, amplitude signal sequence, phase signal sequence, noisy microwave signal sequence, etc.

[0086] Regarding the initial state:

[0087] Random sampling can be performed within a preset angle range to obtain at least one set of first angles and second angles; based on the at least one set of first angles and second angles, at least one initial state can be generated.

[0088] Assuming the initial number of states is M, α and β are the first and second angles respectively, and the preset angle range is [0, 2π], then:

[0089] In the Bloch sphere, α is the angle between the initial state and the Z-axis, and β is the angle between the projection of the initial state onto the XY plane and the X-axis. The values ​​of α and β range from [0, 2π]. Randomly sampling α and β within the range of [0, 2π] yields M different initial states.

[0090] In this way, M initial states were obtained.

[0091] For the ideal final state:

[0092] The ideal evolution matrix can be determined 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.

[0093] The initial state |ψ0> of a qubit can be represented as a column vector as follows:

[0094] According to parameters And θ, the ideal single-qubit gate can be represented by the following ideal evolution matrix:

[0095] Therefore, the ideal final state is:

[0096] Each initial state is multiplied by the ideal evolution matrix shown in formula (10) to obtain each ideal final state. In the case of M initial states, M ideal final states are obtained.

[0097] For noisy final states:

[0098] 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.

[0099] 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 qubit, 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.

[0100] Expressed as a formula:

[0101] in,

[0102] δt=T / N (13)

[0103] in, It is the noisy evolution matrix at time point t;

[0104] T is the operation time of the target single quantum gate; N is the number of time points;

[0105] δt is the time interval;

[0106] V(t) is the amplitude signal of the noisy microwave signal;

[0107] C d C Σ ,L J , These are the electrical parameters of a quantum bit;

[0108] δθ(t) is the interval polar angle signal.

[0109] In this way, the noisy evolution matrix at each time point can be obtained.

[0110] Then, the pre-evolution quantum state at the current time point is multiplied by the noisy evolution matrix at the current time point to obtain the post-evolution quantum state at the current time point, which is used 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 plurality of time points, and the pre-evolution quantum state of the first time point is the initial state;

[0111] Repeat the above process until the evolved quantum state of the last time point among the multiple time points is obtained, which is taken as the noisy final state.

[0112] Specifically, at the first time point t1, the noisy evolution matrix at the first time point is used. Multiplying with the initial state |ψ0> yields the evolved quantum state |ψ1> of t1, which is then used as the pre-evolutionary quantum state of t2. The noisy evolution matrix from the second time point is then employed. With |ψ 1> Multiplying these values ​​yields the evolved quantum state |ψ2> at time point t2, and so on, until the evolved quantum state |ψ2> at the last time point is obtained. N >, which is the noisy final state corresponding to the initial state.

[0113] Each initial state undergoes the above-described noisy evolution process to obtain a noisy final state. In the case of M initial states, M noisy final states are obtained.

[0114] Regarding quantum state fidelity:

[0115] Based on the ideal final state, determine the ideal density matrix;

[0116] Based on the noisy final state, determine the noisy density matrix;

[0117] The quantum state fidelity is determined based on the ideal density matrix and the noisy density matrix.

[0118] Specifically, the relationship between the density matrix and the quantum state is: ρ=|ψ><ψ| (14)

[0119] Where |ψ> is a quantum state and is a column vector; <ψ| is the conjugate transpose of |ψ> and is a row vector; ρ is the density matrix and is a 2*2 matrix.

[0120] Thus, 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). Based on these two density matrices, the quantum state fidelity is calculated using the following formula:

[0121] Where F is the quantum state fidelity; σ is the ideal density matrix; σ N It is a noisy density matrix.

[0122] For each initial state, based on the ideal final state and the noisy final state corresponding to that initial state, the quantum state fidelity corresponding to that initial state can be obtained. In the case of M initial states, M quantum state fidelities can be obtained.

[0123] Therefore, the minimum quantum state fidelity can be used as the fidelity of the target single quantum gate.

[0124] 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 among the at least two quantum state fidelities is used as the fidelity of the target single quantum gate.

[0125] In this way, the fidelity of the target quantum gate is obtained.

[0126] Figure 3 is a schematic diagram according to a second embodiment of the present disclosure. This embodiment provides a method for determining the fidelity of a single quantum gate, as shown in Figure 3. The method includes:

[0127] 301. Based on the preset signal-to-noise ratio, generate the noisy microwave signal corresponding to the target single quantum gate.

[0128] 302. Generate the initial state of the qubit and determine the ideal final state corresponding to the initial state.

[0129] 303. Based on the noisy microwave signal, determine the noisy final state corresponding to the initial state.

[0130] 304. Based on the ideal final state and the noisy final state, determine the quantum state fidelity.

[0131] 305. Based on the quantum state fidelity, determine the fidelity of the target single quantum gate.

[0132] 306. Obtain multiple fidelities of the target single quantum gate.

[0133] Specifically, the process is repeated 301-305 times to obtain multiple fidelities of the target single quantum gate. "Multiple times" is denoted by L, where L is an integer greater than or equal to 2.

[0134] 307. Based on the multiple fidelities, determine the fidelity mean and fidelity variance.

[0135] By executing the procedure L times, L fidelity values ​​can be obtained. The mean of these L fidelity values ​​is calculated, and then the variance is obtained using the variance calculation formula.

[0136] 308. Based on the mean fidelity and the signal-to-noise ratio, generate a first curve, which is used to characterize the correspondence between the signal-to-noise ratio and the mean fidelity.

[0137] 309. Based on the fidelity variance and the signal-to-noise ratio, generate a second curve, which is used to characterize the correspondence between the signal-to-noise ratio and the fidelity variance.

[0138] 310. Display the first curve and the second curve.

[0139] For each signal-to-noise ratio (SNR), the mean fidelity and variance corresponding to that SNR are obtained using parameters 301-307. By changing the SNR, the first and second curves described above are generated based on multiple SNRs.

[0140] Figure 4 is a schematic diagram of the first curve and the second curve provided according to an embodiment of the present disclosure. The first curve represents the correspondence between the signal-to-noise ratio (SNR) and the mean fidelity of the target quantum gate, while the second curve represents the correspondence between the SNR and the variance of the fidelity of the target quantum gate. This allows for the selection of a suitable SNR based on the performance requirements of a single quantum gate.

[0141] In this embodiment, generating a noisy microwave signal based on narrowband noise signal is more consistent with the actual state of a superconducting quantum computer system and better reflects the influence of manipulation signals on the quantum chip, thereby improving the accuracy of fidelity calculation. Generating a noisy microwave signal based on signal-to-noise ratio allows noise signals under different signal-to-noise ratios to be superimposed on an ideal microwave signal. This enables simulation analysis of quantum state fidelity and gate fidelity, obtaining gate fidelity indices under different signal-to-noise ratios. By generating a first curve and a second curve, the signal-to-noise ratio of the microwave signal used as the driving source can be determined under the actual required gate fidelity index, and then a suitable microwave signal can be used for driving.

[0142] Figure 5 is a schematic diagram according to 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 generation module 501, a first determination module 502, a second determination module 503, a third determination module 504, and a fourth determination module 505.

[0143] The first generation module 501 is used to generate a noisy microwave signal corresponding to the target single quantum gate based on a preset signal-to-noise ratio; the first determination module 502 is used to generate the initial state of the quantum bit and determine the ideal final state corresponding to the initial state; the second determination module 503 is used to determine the noisy final state corresponding to the initial state based on the noisy microwave signal; the third determination module 504 is used to determine the quantum state fidelity based on the ideal final state and the noisy final state; the fourth determination module 505 is used to determine the fidelity of the target single quantum gate based on the quantum state fidelity.

[0144] In some embodiments, the first generation module is further configured 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 qubit, and a preset normalized signal.

[0145] 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 qubit include: electrical parameters and qubit frequency; the first generation module is further configured 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 in-phase noise signal and quadrature 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 quadrature noise signal; generate a second signal based on the maximum amplitude, the normalized signal, the angle, and the in-phase noise signal; determine the amplitude signal based on the first signal and the second signal; determine the phase signal based on the first signal and the second signal; use the qubit 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.

[0146] In some embodiments, the first determining module is further configured to: randomly sample within a preset angle range to obtain at least one set of first angles and second angles; and generate at least one initial state based on the at least one set of first angles and second angles.

[0147] In some embodiments, the first determining module is further configured to: determine an ideal evolution matrix based on the parameters of the target single quantum gate; and multiply the initial state with the ideal evolution matrix to obtain the ideal final state.

[0148] In some embodiments, the second determining module is further configured 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 of the multiple time points; and determine the noisy final state based on the noisy evolution matrix of each time point and the initial state.

[0149] In some embodiments, the second determining module is further configured 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; and 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.

[0150] In some embodiments, the second determining module is further configured to: multiply the pre-evolution quantum state at the current time point with 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 plurality of time points, and the pre-evolution quantum state at the first time point is the initial state; repeat the above process until the post-evolution quantum state at the last time point among the plurality of time points is obtained, which is used as the noisy final state.

[0151] In some embodiments, the third determining module is further configured 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 quantum state fidelity based on the ideal density matrix and the noisy density matrix.

[0152] In some embodiments, the fourth determining module is further configured 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 among the at least two quantum state fidelities as the fidelity of the target single quantum gate.

[0153] 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 executes the method multiple times to obtain multiple fidelities of the target single quantum gate; the fifth determination module determines the fidelity mean and fidelity variance based on the multiple fidelities; the second generation module generates a first curve based on the fidelity mean and the signal-to-noise ratio (SNR), the first curve representing the correspondence between the SNR and the fidelity mean; the third generation module generates a second curve based on the fidelity variance and the SNR, the second curve representing the correspondence between the SNR and the fidelity variance; and the display module displays the first curve and the second curve.

[0154] It is understood that the same or similar content in different embodiments of this disclosure can be referred to each other.

[0155] It is understood that the terms "first" and "second" in the embodiments of this disclosure are only used for distinction and do not indicate the degree of importance or the order of events.

[0156] It is understandable that, unless otherwise specified, the order of steps in the process indicates that the temporal relationship between these steps is not limited.

[0157] The collection, storage, use, processing, transmission, provision, and disclosure of user personal information involved in the technical solution disclosed herein comply with the provisions of relevant laws and regulations and do not violate public order and good morals.

[0158] According to embodiments of this disclosure, this disclosure also provides an electronic device, a readable storage medium, and a computer program product.

[0159] Figure 6 illustrates a schematic block diagram of an example electronic device 600 that can be used to implement embodiments of the present disclosure. 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 may also represent various forms of mobile devices, such as personal digital assistants, cellular phones, smartphones, wearable devices, and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the present disclosure described and / or claimed herein.

[0160] As shown in Figure 6, the electronic device 600 includes a computing unit 601, which can perform various appropriate actions and processes based on 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. The RAM 603 can also store various programs and data required for the operation of the electronic device 600. The computing unit 601, ROM 602, and RAM 603 are interconnected via a bus 604. An input / output (I / O) interface 605 is also connected to the bus 604.

[0161] Multiple components in electronic device 600 are connected to I / O interface 605, including: input unit 606, such as keyboard, mouse, etc.; output unit 607, such as various types of displays, speakers, etc.; storage unit 608, such as disk, optical disk, etc.; and communication unit 609, such as network card, modem, wireless transceiver, etc. Communication unit 609 allows electronic device 600 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0162] The computing unit 601 can be a variety of general-purpose and / or special-purpose 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 special-purpose artificial intelligence (AI) computing chips, various computing units running machine learning model algorithms, a digital signal processor (DSP), and any suitable processor, controller, microcontroller, etc. The computing unit 601 performs the various methods and processes described above, such as the method for determining single-quantum gate fidelity. For example, in some embodiments, the method for determining single-quantum gate fidelity may be implemented as a computer software program tangibly contained in a machine-readable medium, such as 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 ROM 602 and / or communication unit 609. When the computer program is loaded into RAM 603 and executed by the computing unit 601, one or more steps of the method for determining single-quantum gate fidelity described above may be performed. Alternatively, in other embodiments, computing unit 601 may be configured by any other suitable means (e.g., by means of firmware) to perform a method for determining single quantum gate fidelity.

[0163] Various embodiments 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-a-chip (SoCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0164] Program code used to implement the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, special-purpose computer, or other programmable data processing apparatus, such that when executed by the processor or controller, the program code causes the functions / operations specified in the flowcharts and / or block diagrams to be implemented. The program code may be executed entirely on a machine, partially on a machine, partially on a machine and partially on a remote machine as a standalone software package, or entirely on a remote machine or server. In the context of this 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, apparatus, or device. 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, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination of the foregoing. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination of the foregoing.

[0165] To provide interaction with a user, the systems and techniques described herein can be implemented on a computer having: a display device for displaying information to the user (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor); and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the computer. Other types of devices can also be used to provide interaction with the user; for example, 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 sound input, voice input, or tactile input).

[0166] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as a data server), or computing systems that include middleware components (e.g., an application server), or computing systems that include frontend components (e.g., a user computer with a graphical user interface or web browser through which a user can interact with embodiments of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., a communication network). Examples of communication networks include local area networks (LANs), wide area networks (WANs), and the Internet.

[0167] Computer systems can include clients and servers. Clients and servers are generally geographically separated and typically interact via communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. A server can be a cloud server, also known as a cloud computing server or cloud host, a hosting product within the cloud computing service system that addresses the management difficulties and weak business scalability inherent in traditional physical hosts and VPS (Virtual Private Server) services. Servers can also be servers for distributed systems or servers integrated with blockchain technology.

[0168] 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 described in this disclosure can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution disclosed in this disclosure can be achieved, and this is not limited herein.

[0169] The specific embodiments described above do not constitute a limitation on the scope of protection of this disclosure. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for determining single quantum gate fidelity, the method comprising: determining a plurality of quantum gate fidelities; and determining a single quantum gate fidelity from the plurality of quantum gate fidelities. include: Based on the preset signal-to-noise ratio, generate the noisy microwave signal corresponding to the target single quantum gate; Generate the initial state of the qubit and determine the ideal final state corresponding to the initial state; Based on the noisy microwave signal, determine the noisy final state corresponding to the initial state; Based on the ideal final state and the noisy final state, the quantum state fidelity is determined; Based on the quantum state fidelity, the fidelity of the target single quantum gate is determined.

2. The method of claim 1, wherein, The generation of the noisy microwave signal corresponding to the target single quantum gate based on the preset signal-to-noise ratio includes: The noisy microwave signal is generated based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the qubit, and the preset normalized signal.

3. The method according to claim 2, characterized in that, 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 generation of the noisy microwave signal based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the qubit, and a preset normalized signal includes: The maximum amplitude is determined based on the rotation polar angle, the electrical parameters, the operating time, and the normalized signal; Based on the signal-to-noise ratio, the maximum amplitude, the operation time, and the normalized signal, the target variance of the noise signal is determined. Generate in-phase noise signals and quadrature noise signals that conform to a normal distribution and have the target variance; A first signal is generated based on the maximum amplitude, the normalized signal, the included angle, and the orthogonal noise signal. A second signal is generated based on the maximum amplitude, the normalized signal, the included angle, and the in-phase noise signal. Based on the first signal and the second signal, determine the amplitude signal; Based on the first signal and the second signal, determine the phase signal; The frequency of the quantum bit is used as the frequency of the microwave signal. The noisy microwave signal is generated based on the amplitude signal, the phase signal, and the microwave signal frequency.

4. The method of claim 1, wherein, The initial state for generating the qubit includes: Randomly sample within a preset angle range to obtain at least one set of first and second angles; At least one initial state is generated based on the at least one set of first and second angles.

5. The method of claim 1, wherein, Determining the ideal final state corresponding to the initial state includes: Based on the parameters of the target single quantum gate, determine the ideal evolution matrix; The initial state is multiplied by the ideal evolution matrix to obtain the ideal final state.

6. The method of claim 1, wherein, Determining the noisy final state corresponding to the initial state based on the noisy microwave signal includes: Multiple time points are determined based on the preset number of time points and the operation duration of the target single quantum gate; Determine the noisy evolution matrix for each of the plurality of time points; Based on the noisy evolution matrix at each time point and the initial state, the noisy final state is determined.

7. The method of claim 6, wherein, Determining the noisy evolution matrix for each of the plurality of time points includes: 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 at each time point is determined.

8. The method of claim 6, wherein, The determination of the noisy final state based on the noisy evolution matrix at each time point and the initial state includes: The pre-evolution quantum state at the current time point is multiplied by the noisy evolution matrix at the current time point to obtain the post-evolution quantum state at the current time point, which is then used 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 plurality of time points, and the pre-evolution quantum state of the first time point is the initial state; Repeat the above process until the evolved quantum state of the last time point among the multiple time points is obtained, which is taken as the noisy final state.

9. The method of claim 1, wherein, Determining the quantum state fidelity based on the ideal final state and the noisy final state includes: Based on the ideal final state, determine the ideal density matrix; Based on the noisy final state, determine the noisy density matrix; The quantum state fidelity is determined based on the ideal density matrix and the noisy density matrix.

10. The method of claim 1, wherein, Determining the fidelity of the target single quantum gate based on the quantum state fidelity includes: If the quantum state fidelity is one, then 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 among the at least two quantum state fidelities shall be taken as the fidelity of the target single quantum gate.

11. The method of claim 1, wherein, Also includes: The method is executed multiple times to obtain multiple fidelities of the target single quantum gate; Based on the multiple fidelities, determine the fidelity mean and fidelity variance; Based on the mean fidelity and the signal-to-noise ratio, a first curve is generated, which is used to characterize the correspondence between the signal-to-noise ratio and the mean fidelity. Based on the fidelity variance and the signal-to-noise ratio, a second curve is generated, which is used to characterize the correspondence between the signal-to-noise ratio and the fidelity variance. Display the first curve and the second curve.

12. An apparatus for determining single quantum gate fidelity, comprising: include: The first generation module is used to generate a noisy microwave signal corresponding to the target single quantum gate based on a preset signal-to-noise ratio. The first determining module is used to generate the initial state of the qubit and determine the ideal final state corresponding to the initial state; The second determining module is used to determine the noisy final state corresponding to the initial state based on the noisy microwave signal; The third determining module is used to determine the quantum state fidelity based on the ideal final state and the noisy final state; The fourth determining module is used to determine the fidelity of the target single quantum gate based on the quantum state fidelity.

13. The apparatus of claim 12, wherein, The first generation module is further used for: The noisy microwave signal is generated based on the signal-to-noise ratio, the parameters of the target single quantum gate, the parameters of the qubit, and the preset normalized signal.

14. The apparatus according to claim 13, characterized in that, 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 for: The maximum amplitude is determined based on the rotation polar angle, the electrical parameters, the operating time, and the normalized signal; Based on the signal-to-noise ratio, the maximum amplitude, the operation time, and the normalized signal, the target variance of the noise signal is determined. Generate in-phase noise signals and quadrature noise signals that conform to a normal distribution and have the target variance; A first signal is generated based on the maximum amplitude, the normalized signal, the included angle, and the orthogonal noise signal. A second signal is generated based on the maximum amplitude, the normalized signal, the included angle, and the in-phase noise signal. Based on the first signal and the second signal, determine the amplitude signal; Based on the first signal and the second signal, determine the phase signal; The frequency of the quantum bit is used as the frequency of the microwave signal. The noisy microwave signal is generated based on the amplitude signal, the phase signal, and the microwave signal frequency.

15. The apparatus of claim 12, wherein, The first determining module is further configured to: Randomly sample within a preset angle range to obtain at least one set of first and second angles; At least one initial state is generated based on the at least one set of first and second angles.

16. The apparatus of claim 12, wherein, The first determining module is further configured to: Based on the parameters of the target single quantum gate, determine the ideal evolution matrix; The initial state is multiplied by the ideal evolution matrix to obtain the ideal final state.

17. The apparatus of claim 12, wherein, The second determining module is further used for: Multiple time points are determined based on the preset number of time points and the operation duration of the target single quantum gate; Determine the noisy evolution matrix for each of the plurality of time points; Based on the noisy evolution matrix at each time point and the initial state, the noisy final state is determined.

18. The apparatus of claim 17, wherein, The second determining module is further used for: 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 at each time point is determined.

19. The apparatus of claim 17, wherein, The second determining module is further used for: The pre-evolution quantum state at the current time point is multiplied by the noisy evolution matrix at the current time point to obtain the post-evolution quantum state at the current time point, which is then used 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 plurality of time points, and the pre-evolution quantum state of the first time point is the initial state; Repeat the above process until the evolved quantum state of the last time point among the multiple time points is obtained, which is taken as the noisy final state.

20. The apparatus of claim 12, wherein, The third determining module is further used for: Based on the ideal final state, determine the ideal density matrix; Based on the noisy final state, determine the noisy density matrix; The quantum state fidelity is determined based on the ideal density matrix and the noisy density matrix.

21. The apparatus of claim 12, wherein, The fourth determining module is further used for: If the quantum state fidelity is one, then 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 among the at least two quantum state fidelities shall be taken as the fidelity of the target single quantum gate.

22. The apparatus of claim 12, further comprising: An acquisition module is used to execute the method multiple times to obtain multiple fidelities of the target single quantum gate; The fifth determining module is used to determine the mean and variance of the fidelity based on the multiple fidelities. The second generation module is used to generate a first curve based on the mean fidelity and the signal-to-noise ratio, wherein the first curve is used to characterize the correspondence between the signal-to-noise ratio and the mean fidelity. The third generation module is used to generate a second curve based on the fidelity variance and the signal-to-noise ratio, the second curve being used to characterize the correspondence between the signal-to-noise ratio and the fidelity variance; The display module is used to display the first curve and the second curve.

23. 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 to enable the at least one processor to perform the method of any one of claims 1-11.

24. A non-transitory computer readable storage medium having stored thereon computer instructions, wherein, The computer instructions are used to cause the computer to perform the method according to any one of claims 1-11.

25. A computer program product comprising a computer program that, when executed by a processor, implements the method according to any one of claims 1-11.

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