Method and device for obtaining two-qubit logic gate unitary operator and quantum computer

Abstract

The application provides a two-qubit logic gate unitary operator acquisition method, device and quantum computer. The unitary operator acquisition method comprises the following steps: acquiring a first equivalent frequency of a first qubit, a second equivalent frequency of a second qubit and an equivalent coupling strength of the first qubit and the second qubit; acquiring the unitary operator based on the acquired first equivalent frequency, second equivalent frequency and equivalent coupling strength; acquiring a theoretical probability of the first qubit and the second qubit being in an excited state after performing a two-qubit logic gate based on the acquired unitary operator; and judging whether the unitary operator is accurate based on the acquired theoretical probability, and acquiring the unitary operator if the unitary operator is accurate. The unitary operator acquired by the technical scheme of the application can be used to determine the working point of an adjustable coupler in a two-qubit logic gate execution process.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of quantum computing, and particularly relates to a method and device for obtaining a two-qubit logical gate unitary operator and a quantum computer. BACKGROUND

[0002] A quantum computer is a physical device that performs high-speed mathematical and logical operations, stores and processes quantum information in accordance with the laws of quantum mechanics. A quantum logic gate is a basic unit for completing quantum computing. During the execution of the entire quantum circuit, different quantum logic gates need to be executed at different times and need to meet different working conditions, especially the frequency of the qubits.

[0003] One of the execution conditions of a two-qubit logic gate is that the frequency of the adjustable coupler should work at a proper position. In order to determine the optimal working point of the adjustable coupler, the relationship between the probability of the two qubits being in an excited state after the execution of the two-qubit logic gate and the frequency value of the adjustable coupler needs to be obtained. The probability of the two qubits being in an excited state after the execution of the two-qubit logic gate is defined as the fidelity of the two-qubit logic gate, and the fidelity of the two-qubit logic gate is also related to the frequency value of one of the qubits. In order to obtain the corresponding relationship between the fidelity and the two frequency values, the frequency of the other qubit can be fixed, the frequency value of one of the qubits and the frequency value of the adjustable coupler can be changed, the two-qubit logic gate can be repeatedly executed, and the corresponding fidelity can be obtained. The corresponding relationship is obtained through a limited number of experiments.

[0004] Reference Figure 1 , Figure 1 The corresponding relationship between the fidelity of the two-qubit logic gate and the frequency value of the adjustable coupler and the frequency value of one of the qubits is shown in the graph, Figure 1 In the graph, the horizontal coordinate is the frequency value of one of the qubits, and the vertical coordinate is the frequency value of the adjustable coupler. The points on the curve in the graph indicate that when the frequency value of one of the qubits is the horizontal coordinate and the frequency value of the adjustable coupler is the vertical coordinate of the current point, the fidelity of the two-qubit logic gate can be maximized.

[0005] However, the corresponding relationship between the fidelity of the two-qubit logic gate and the frequency values of the adjustable coupler and one of the qubits obtained by the above method needs to be repeatedly executed multiple times, which is too cumbersome.

[0006] Therefore, it is necessary to propose a method for obtaining a two-qubit logic gate unitary operator to solve the problems in the prior art.

[0007] It should be noted that the information disclosed in the background section of the present application is only intended to deepen the understanding of the general background of the present application, and should not be regarded as acknowledging or implying in any form that the information constitutes prior art known to those skilled in the art. SUMMARY

[0008] The purpose of the present application is to provide a two-qubit logic gate unitary operator acquisition method and device and quantum computer, which is used to solve the problem of determining the optimal working point of the adjustable coupler in the prior art, which requires repeated experiments to obtain the corresponding relationship between the probability of the two qubits in the excited state and the frequency value of the adjustable coupler and the frequency value of one of the qubits.

[0009] To achieve the above-mentioned purpose, in a first aspect, the present application provides a two-qubit logic gate unitary operator acquisition method, comprising:

[0010] acquiring a first equivalent frequency of a first qubit, a second equivalent frequency of a second qubit, and an equivalent coupling strength of the first qubit and the second qubit;

[0011] acquiring the unitary operator based on the acquired first equivalent frequency, second equivalent frequency, and equivalent coupling strength;

[0012] acquiring the theoretical probability of the first qubit and the second qubit being in the excited state after performing a two-qubit logic gate based on the acquired unitary operator;

[0013] judging whether the unitary operator is accurate based on the acquired theoretical probability, and if so, acquiring the unitary operator.

[0014] Preferably, the acquiring the unitary operator based on the acquired first equivalent frequency, second equivalent frequency, and equivalent coupling strength comprises:

[0015] acquiring a matrix form Hamiltonian based on the first equivalent frequency, second equivalent frequency, and equivalent coupling strength;

[0016] acquiring the unitary operator based on the matrix form Hamiltonian.

[0017] Preferably, the acquiring a matrix form Hamiltonian based on the first equivalent frequency, second equivalent frequency, and equivalent coupling strength comprises:

[0018] According to the formula:

[0019]

[0020] acquiring a matrix form Hamiltonian;

[0021] Where ω1 is the first equivalent frequency, ω2 is the second equivalent frequency, and g 12 For the equivalent coupling strength, a1 and a2 are the anharmonicity of the first qubit and the second qubit, respectively.

[0022] Preferably, obtaining the unitary operator based on the Hamiltonian in matrix form includes:

[0023] According to the formula:

[0024]

[0025] Obtain the unitary operator;

[0026] Where U is the unitary operator, The Hamiltonian in matrix form is... Let t be Planck's constant, t be time, and i be the imaginary unit.

[0027] Preferably, the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate based on the acquired unitary operator includes:

[0028] Based on the formula:

[0029] P = U|11>

[0030] Obtain the probability amplitude matrix; where P is the probability amplitude matrix;

[0031] The theoretical probability is obtained based on the probability amplitude matrix.

[0032] Preferably, determining whether the unitary operator is accurate based on the acquired theoretical probability includes:

[0033] Execute a two-qubit logic gate to obtain the actual probability that the first and second qubits are in an excited state after executing the two-qubit logic gate;

[0034] Compare whether the difference between the actual probability and the theoretical probability does not exceed a set threshold. If it does not exceed the threshold, then the unitary operator is accurate.

[0035] Preferably, the set threshold is 5%.

[0036] Secondly, this application provides a readable storage medium having a computer program stored thereon, which, when executed, can implement the method for obtaining the unitary operator as described in any of the claims of the first aspect of this application.

[0037] Thirdly, this application provides a device for acquiring a two-qubit logic gate unitary operator, comprising:

[0038] The parameter acquisition module is configured to acquire the first equivalent frequency of the first qubit, the second equivalent frequency of the second qubit, and the equivalent coupling strength between the first qubit and the second qubit.

[0039] The unitary operator acquisition module is configured to acquire the unitary operator based on the acquired first equivalent frequency, second equivalent frequency, and equivalent coupling strength;

[0040] The theoretical probability acquisition module is configured to acquire the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate based on the acquired unitary operator.

[0041] The judgment module is configured to determine whether the unitary operator is accurate based on the acquired theoretical probability; if so, the unitary operator is acquired.

[0042] Fourthly, this application provides a quantum computer, including the device for acquiring the unitary operator provided in the third aspect of this application.

[0043] Compared with the prior art, the technical solution of the present invention has the following beneficial effects:

[0044] The present invention provides a method for obtaining the unitary operator of a two-qubit logic gate. The method comprises the following steps: First, obtaining the first equivalent frequency of the first qubit, the second equivalent frequency of the second qubit, and the equivalent coupling strength between the first and second qubits; second, obtaining the unitary operator based on the obtained first equivalent frequency, second equivalent frequency, and equivalent coupling strength; third, obtaining the theoretical probability that the first and second qubits are in an excited state after executing the two-qubit logic gate based on the obtained unitary operator; fourth, determining whether the unitary operator is accurate based on the obtained theoretical probability, and if so, obtaining the unitary operator. This technical solution, by obtaining the unitary operator, thereby obtaining the theoretical probability of the excited state, and by determining whether the theoretical probability is accurate, obtains an accurate unitary operator. The obtained unitary operator can determine the optimal operating point of an tunable coupler based on the frequency value of one of the qubits, and can also be extended to the selection of the operating point of tunable couplers for other two-qubit logic gates on quantum chips. Attached Figure Description

[0045] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0046] Figure 1This is a graph showing the correspondence between the fidelity of a two-qubit logic gate, the frequency value of the tunable coupler, and the frequency value of one of the qubits.

[0047] Figure 2 This is a flowchart illustrating the method for obtaining a two-qubit logic gate unitary operator provided in an embodiment of the present invention;

[0048] Figure 3 This is a schematic diagram of the structure of the device for acquiring a unitary operator of a two-qubit logic gate provided in an embodiment of the present invention. Detailed Implementation

[0049] The specific embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. The advantages and features of the present invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0050] In the description of this invention, it should be understood that the terms "center", "upper", "lower", "left", "right", etc., indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on this invention.

[0051] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0052] As described in the background section, in order to obtain the optimal operating point of the tunable coupler by executing a two-qubit logic gate, it is necessary to obtain the correspondence between the probability of the two qubits being in an excited state and the frequency of the tunable coupler after the two qubits execute the two-qubit logic gate. In order to obtain this correspondence, it is necessary to repeat the experiment, which is cumbersome, and the obtained correspondence cannot be generalized to other two-qubit logic gates on the quantum chip.

[0053] This invention provides a method for obtaining a unitary operator of a two-qubit logic gate, see reference. Figure 2 , Figure 2 This is a flowchart illustrating the method for obtaining a two-qubit logic gate unitary operator according to an embodiment of the present invention. Figure 2 As can be seen from this, the acquisition method includes:

[0054] Step S1: Obtain the first equivalent frequency of the first qubit, the second equivalent frequency of the second qubit, and the equivalent coupling strength between the first qubit and the second qubit;

[0055] Step S2: Obtain the unitary operator based on the obtained first equivalent frequency, second equivalent frequency, and equivalent coupling strength;

[0056] Step S3: Based on the acquired unitary operator, obtain the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate;

[0057] Step S4: Based on the obtained theoretical probability, determine whether the unitary operator is accurate. If so, obtain the unitary operator.

[0058] In this embodiment, both the first qubit and the second qubit are disposed on a quantum chip. The first qubit and the second qubit are directly coupled through a capacitor. At the same time, the first qubit and the second qubit are also indirectly coupled through an adjustable coupler. The equivalent coupling strength between the first qubit and the second qubit depends on the strength of the direct coupling and the indirect coupling. If the indirect coupling has the opposite effect to the direct coupling, then the equivalent coupling strength between the first qubit and the second qubit is 0.

[0059] The quantum chip may also contain other qubits. All qubits are coupled to a first control signal transmission line (XY line) and a second control signal transmission line (Z line). The first control signal transmission line provides a first control signal, including a qubit modulation signal, which controls the change in the quantum state of the qubit. The second control signal transmission line provides a second control signal, including a DC bias signal and a fast modulation signal (AC). Both the DC bias signal and the fast modulation signal can modulate the frequency of the target qubit. Each qubit is also coupled to a resonant cavity. The resonant frequency of the resonant cavity shifts according to the quantum state of the qubit. By applying a readout signal to the resonant cavity, a readout feedback signal transmitted or reflected from the readout cavity can be obtained. The quantum state of the qubit can then be obtained by analyzing the readout feedback signal.

[0060] The frequencies of the first and second qubits are controlled not only by the second control signal but also by crosstalk from the tunable coupler and other qubits. The first equivalent frequency is the actual frequency of the first qubit under the influence of crosstalk from the tunable coupler and other qubits. Similarly, the second equivalent frequency is the actual frequency of the second qubit under the influence of crosstalk from the tunable coupler and other qubits. The equivalent coupling strength is the actual coupling strength between the first and second qubits.

[0061] In this embodiment of the invention, the unitary operator is used to describe the evolution and transformation of quantum states. Obtaining the unitary operator allows for the acquisition of the theoretical state of the two qubits after the execution of the two-qubit logic gate. By verifying the reliability of the unitary operator, if it is reliable, the first and second equivalent frequencies required for the execution of the two-qubit logic gate can be obtained, thereby enabling the acquisition of the optimal operating point of the tunable coupler during the execution of the two-qubit logic gate. If the unitary operator is unreliable, the first and second equivalent frequencies, as well as the equivalent coupling strength, need to be retested and obtained, and the scheme of this application needs to be repeated until a reliable unitary operator is obtained.

[0062] Specifically, obtaining the unitary operator based on the acquired first equivalent frequency, second equivalent frequency, and equivalent coupling strength includes:

[0063] Based on the first equivalent frequency, the second equivalent frequency, and the equivalent coupling strength, a Hamiltonian in matrix form is obtained.

[0064] The unitary operator is obtained based on the Hamiltonian in matrix form.

[0065] First, obtain the Hamiltonian in matrix form, and then obtain the unitary operator based on the Hamiltonian in matrix form.

[0066] Specifically, obtaining a matrix-form Hamiltonian based on the first equivalent frequency, the second equivalent frequency, and the equivalent coupling strength includes:

[0067] According to the formula:

[0068]

[0069] Obtain the Hamiltonian in matrix form;

[0070] Where ω1 is the first equivalent frequency, ω2 is the second equivalent frequency, and g 12 For the equivalent coupling strength, a1 and a2 are the anharmonicity of the first qubit and the second qubit, respectively.

[0071] The Hamiltonian in matrix form can be obtained using the above formula, and can then be used to obtain unitary operators.

[0072] Specifically, obtaining the unitary operator based on the Hamiltonian in matrix form includes:

[0073] According to the formula:

[0074]

[0075] Obtain the unitary operator;

[0076] Where U is the unitary operator, The Hamiltonian in matrix form is... Let t be Planck's constant and t be time.

[0077] In this embodiment, a unitary operator is obtained through a formula. The unitary operator includes a time parameter, which is the duration of the pulse during the execution of a two-qubit logic gate. This time parameter can accurately describe the evolution of two qubits when executing a two-qubit logic gate, and can then be used to obtain the quantum state that two qubits should theoretically be in after executing a two-qubit logic gate.

[0078] Specifically, the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate based on the acquired unitary operator includes:

[0079] Based on the formula:

[0080] P = U|11>

[0081] Obtain the probability amplitude matrix; where P is the probability amplitude matrix;

[0082] The theoretical probability is obtained based on the probability amplitude matrix.

[0083] In this embodiment, the probability amplitude matrix takes the following form:

[0084]

[0085] Where i is the imaginary unit.

[0086] The theoretical probability is obtained based on the probability magnitude matrix:

[0087] P 11 =[d·t 4 ·(ω1+ω2) 4 +a·i·t 3 ·(ω1+ω2) 3 -0.5·t 2·(ω1+ω2) 2 -i·t·(ω1+ω2)+1] 2 .

[0088] In this embodiment, by using the obtained unitary operator to multiply the quantum state of the two qubits when executing the two-qubit logic gate, the quantum state that the two qubits should be in after executing the two-qubit logic gate can be accurately obtained.

[0089] Specifically, determining whether the unitary operator is accurate based on the obtained theoretical probability includes:

[0090] Execute a two-qubit logic gate to obtain the actual probability that the first and second qubits are in an excited state after executing the two-qubit logic gate;

[0091] Compare whether the difference between the actual probability and the theoretical probability does not exceed a set threshold. If it does not exceed the threshold, then the unitary operator is accurate.

[0092] In this embodiment, by comparing the actual probability with the obtained theoretical probability, it can be determined whether the obtained unitary operator can accurately describe the evolution of the quantum state. The accuracy of the unitary operator is limited by setting a threshold. The closer the actual probability is to the theoretical probability, the more accurate the obtained unitary operator is.

[0093] Specifically, this includes setting the threshold to 5%.

[0094] In this embodiment, the set threshold is set to 5%. In other embodiments, the set threshold may be limited to other values, and no specific restrictions are made here.

[0095] Based on the same inventive concept, this application also provides a readable storage medium storing a computer program thereon, which, when executed, can implement the method for obtaining the unitary operator provided in the embodiments of the present invention.

[0096] Based on the same inventive concept, this application also provides a device for acquiring a two-qubit logic gate unitary operator, see reference. Figure 3 , Figure 3 This is a schematic diagram of a device for obtaining a unitary operator of a two-qubit logic gate according to an embodiment of the present invention. The device for obtaining the unitary operator includes:

[0097] The parameter acquisition module is configured to acquire the first equivalent frequency of the first qubit, the second equivalent frequency of the second qubit, and the equivalent coupling strength between the first qubit and the second qubit.

[0098] The unitary operator acquisition module is configured to acquire the unitary operator based on the acquired first equivalent frequency, second equivalent frequency, and equivalent coupling strength;

[0099] The theoretical probability acquisition module is configured to acquire the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate based on the acquired unitary operator.

[0100] The judgment module is configured to determine whether the unitary operator is accurate based on the acquired theoretical probability; if so, the unitary operator is acquired.

[0101] Based on the same inventive concept, embodiments of the present invention also provide a quantum computer, including the device for acquiring the two-qubit logic gate unitary operator provided in the embodiments of the present invention.

[0102] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," or "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0103] The above description is merely a description of preferred embodiments of the present invention and is not intended to limit the scope of the present invention in any way. Any changes or modifications made by those skilled in the art based on the above disclosure shall fall within the protection scope of the claims.

Claims

1. A method for obtaining a unitary operator of a two-qubit logic gate, characterized in that, include: Obtain the first equivalent frequency of the first qubit, the second equivalent frequency of the second qubit, and the equivalent coupling strength between the first qubit and the second qubit; wherein, the first equivalent frequency is the actual frequency value of the first qubit under the influence of crosstalk from the tunable coupler and other qubits, the second equivalent frequency is the actual frequency value of the second qubit under the influence of crosstalk from the tunable coupler and other qubits, and the equivalent coupling strength is the actual coupling strength between the first qubit and the second qubit; Based on the first equivalent frequency, the second equivalent frequency, and the equivalent coupling strength, a Hamiltonian in matrix form is obtained. According to the formula: Obtain the unitary operator; in, For the unitary operator, The Hamiltonian in matrix form is... It is Planck's constant. For time, i is the imaginary unit; Based on the acquired unitary operator, the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate is obtained; Based on the obtained theoretical probability, determine whether the unitary operator is accurate; if so, obtain the unitary operator.

2. The method for obtaining the unitary operator as described in claim 1, characterized in that, The step of obtaining a matrix-form Hamiltonian based on the first equivalent frequency, the second equivalent frequency, and the equivalent coupling strength includes: According to the formula: Obtain the Hamiltonian in matrix form; in, The first equivalent frequency, The second equivalent frequency, For equivalent coupling strength, , These are the anharmonicity of the first qubit and the anharmonicity of the second qubit, respectively.

3. The method for obtaining the unitary operator as described in claim 1, characterized in that, The theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate based on the acquired unitary operator includes: Based on the formula: Obtain the probability amplitude matrix; where P is the probability amplitude matrix; The theoretical probability is obtained based on the probability amplitude matrix.

4. The method for obtaining the unitary operator as described in claim 1, characterized in that, The determination of whether the unitary operator is accurate based on the obtained theoretical probability includes: Execute a two-qubit logic gate to obtain the actual probability that the first and second qubits are in an excited state after executing the two-qubit logic gate; Compare whether the difference between the actual probability and the theoretical probability does not exceed a set threshold. If it does not exceed the threshold, then the unitary operator is accurate.

5. The method for obtaining the unitary operator as described in claim 4, characterized in that, The set threshold is 5%.

6. A readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed, it can implement the method for obtaining the unitary operator as described in any one of claims 1 to 5.

7. A device for acquiring a two-qubit logic gate unitary operator, characterized in that, include: The parameter acquisition module is configured to acquire the first equivalent frequency of the first qubit, the second equivalent frequency of the second qubit, and the equivalent coupling strength between the first qubit and the second qubit; wherein, the first equivalent frequency is the actual frequency value of the first qubit under the influence of crosstalk from the tunable coupler and other qubits, the second equivalent frequency is the actual frequency value of the second qubit under the influence of crosstalk from the tunable coupler and other qubits, and the equivalent coupling strength is the actual coupling strength between the first qubit and the second qubit; The unitary operator acquisition module is configured to acquire a matrix-form Hamiltonian based on the first equivalent frequency, the second equivalent frequency, and the equivalent coupling strength, and according to the formula: Obtain the unitary operator; in, For the unitary operator, The Hamiltonian in matrix form is... It is Planck's constant. For time, i is the imaginary unit; The theoretical probability acquisition module is configured to acquire the theoretical probability that the first and second qubits are in an excited state after executing a two-qubit logic gate based on the acquired unitary operator. The judgment module is configured to determine whether the unitary operator is accurate based on the acquired theoretical probability; if so, the unitary operator is acquired.

8. A quantum computer, characterized in that, The device includes the acquisition device for a two-qubit logic gate unitary operator as described in claim 7.

Images