Method for realizing quantum gate based on physical model containing sub-coupler

Abstract

The invention discloses a method for realizing a quantum gate based on a physical model containing a quantum coupler, and the method comprises the steps: exerting a transverse field on a quantum bit, and exerting a longitudinal field on the quantum coupler at the same time, thereby increasing the adjustable degree of freedom of Hamiltonian, and achieving the quantum gate. A way for realizing quantum gate or quantum unitary operation in the field of superconducting quantum calculation is expanded, a feasible scheme is provided for large-scale quantum calculation, the use freedom degree of Hamiltonian is increased, the quantum unitary operation which cannot be directly realized by a previous scheme can be realized by matching with a numerical method, the quantum gate realization time is shorter than that of a traditional scheme, and the quantum gate realization efficiency is improved. A 250ns CNOT gate can be realized under the condition of 4Mhz coupling of a longitudinal field, and errors caused by a de-coherence mechanism are reduced.

Description

Technical Field

[0001] The present invention belongs to the field of superconducting quantum computing, and in particular relates to a method for realizing a quantum gate based on a physical model containing a quantum coupler. Background Art

[0002] Currently in the field of superconducting quantum computing, existing solutions all rely on applying only a transverse field or only a longitudinal field to realize a quantum gate, or applying both the longitudinal and transverse fields successively to realize a quantum gate. These solutions do not fully utilize the adjustable degrees of freedom of superconducting quantum bits, resulting in poor scalability and a long time to realize quantum gate operations. Summary of the Invention

[0003] The object of the present invention is to provide a method for realizing a quantum gate based on a physical model containing a quantum coupler, so as to solve the above-mentioned problem.

[0004] To achieve the above objectives, the present invention provides the following technical solution: a method for realizing a quantum gate based on a physical model containing a quantum coupler, comprising at least two quantum bits and a quantum coupler, and the specific steps are as follows:

[0005] S1. The quantum coupler placed between the two qubits has a direct coupling with one of the qubits g. 1C , there is a direct coupling g with another qubit 2C , the Hamiltonian of two qubits and a quantum coupler is written as:

[0006]

[0007] in and are the Pauli operators of qubit 1 and qubit 2 and the quantum coupler, and is the first quantum bit's raise and lower operator, and is the raise and lower operator for the second qubit, and is the raising and lowering operator of the quantum coupler, ω1, ω2 and ω c is the eigenfrequency of the two qubits and the quantum coupler, J(Φ) is the effective coupling between the two qubits;

[0008] S2, at the same time, apply transverse field microwave Ω1(t)cos(ω d1 t), applying transverse field microwave Ω2(t)cos(ω d2 t) and applying a longitudinal field drive Φ(t)=Θ+δcos(ω Φt), after applying two beams of transverse field microwave driving and one beam of longitudinal field microwave driving, the Hamiltonian can be written as

[0009]

[0010] S3, Taylor expansion of the longitudinal field of the Hamiltonian after applying two beams of transverse field microwave driving and one beam of longitudinal field microwave driving in S2 is obtained:

[0011]

[0012] Transfer this Hamiltonian into the microwave reference frame, and the Hamiltonian becomes

[0013]

[0014]

[0015] Select the vertical field frequency as ω φ =Δ d1d2 =ω d1 -ω d2 , discarding the oscillatory term, we can obtain the final Hamiltonian

[0016]

[0017] At this time, there are five degrees of freedom in the Hamiltonian that can be controlled

[0018]

[0019] S4. Based on S3, the transverse field and the longitudinal field are added simultaneously to increase the controllable degree of freedom, thereby realizing the quantum gate.

[0020] Preferably, S1 also includes partial diagonalization of the Hamiltonian of two qubits and a quantum coupler, which can obtain a more practical form:

[0021]

[0022] Preferably, the effective coupling J(Φ) is obtained by direct coupling g 1c g 2c and the inverse of the detuning between the quantum bit and the quantum coupler Decision, for

[0023] Preferably, in S3 and Physically, this is the shift in quantum bit frequency caused by applying a longitudinal field, and calibration compensation is performed by calibrating the bit frequency shift in subsequent experiments.

[0024] The technical effects and advantages of the present invention include applying a transverse field to a quantum bit while applying a longitudinal field to a quantum coupler, thereby increasing the adjustable degrees of freedom of the Hamiltonian to realize a quantum gate. This expands the field of superconducting quantum computing and provides a way to realize quantum gates or quantum unitary operations. This provides a feasible solution for large-scale quantum computing, increases the degrees of freedom in the use of the Hamiltonian, and, when combined with numerical methods, can realize quantum unitary operations that were not directly achievable with previous solutions. The quantum gate time achieved is faster than that of traditional solutions. With a 4 MHz longitudinal field coupling, a CNOT gate can be realized in 250 ns, reducing errors caused by decoherence mechanisms. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 Schematic diagram of an applicable model of the present invention;

[0026] Figure 2 This is a schematic diagram of the present invention applying two transverse field drives and one longitudinal field drive at the same time;

[0027] Figure 3 Schematic diagram of parameter requirements for realizing CNOT gate in numerical solution of the present invention;

[0028] Figure 4 Schematic diagram of two transverse field microwave beams and one longitudinal field driving beam of the present invention;

[0029] Figure 5 Schematic diagram of the evolution of CNOT gates in different initial states of the present invention;

[0030] Figure 6 This is a system block diagram of the present invention. DETAILED DESCRIPTION

[0031] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0032] The present invention provides Figures 1-6 The method for realizing quantum gates based on the physical model of quantum couplers is shown in .

[0033] like Figure 1 As shown in the first figure, there is a direct coupling g between the left quantum bit 1 (Qubit1) and the middle quantum coupler (Coupler) 1c , there is a direct coupling g between the right qubit 2 (Qubit2) and the middle quantum coupler (Coupler) 2c Here the Hamiltonian of the two-qubit and one-qubit coupler model can be written as

[0034]

[0035] Performing Schrieffer-Wolff transformation (a matrix partial diagonalization method) can get a more practical form

[0036]

[0037] in and are the Pauli operators of qubit 1 and qubit 2 and the quantum coupler, and is the first quantum bit's raise and lower operator, and is the raise and lower operator for the second qubit, and is the raising and lowering operator of the quantum coupler, ω1, ω2 and ω c is the eigenfrequency of the two qubits and the quantum coupler, J(Φ) is the effective coupling between the two qubits, and the effective coupling is given by the direct coupling g 1c g 2c and the inverse of the detuning between the quantum bit and the quantum coupler Decision, for

[0038] Our solution is to apply transverse field microwave Ω1(t)cos(ω d1 t), applying transverse field microwave Ω2(t)cos(ω d2 t) and applying a longitudinal field drive Φ(t)=Θ+δcos(ω Φ t). The schematic diagram is as follows Figure 2 ,Ω1(t) and Ω2(t) are the amplitudes of the transverse field microwaves, ω d1 and ω d2 is the transverse field microwave frequency, δ and ω φ are the amplitude and frequency of the longitudinal field drive, ω c (Θ) represents the eigenfrequency of the idle bias point when no longitudinal field is applied. In the field of superconducting quantum computing, applying a transverse field means applying XY direction drive, and applying a longitudinal field means that the Z direction is controlled. The two transverse field microwave drives increase the Hamiltonian. The longitudinal field drive changes the eigenfrequency ω of the quantum coupler. c (Φ(t))=ω c (Θ+δcos(ω φ t)), after applying two beams of transverse field microwave driving and one beam of longitudinal field microwave driving, the Hamiltonian can be written as

[0039]

[0040] We perform Taylor expansion on the longitudinal field

[0041]

[0042] in and Physically, this is the shift in the frequency of the quantum bit caused by the application of the longitudinal field, which needs to be calibrated and compensated by the Ramsey method in subsequent experiments. When this Hamiltonian is transferred to the microwave reference frame, the Hamiltonian becomes

[0043]

[0044] Select the vertical field frequency as ω φ =Δ d1d2 =ω d1 -ω d2 , discarding the oscillatory term, we can obtain the final Hamiltonian

[0045]

[0046] At this time, there are five degrees of freedom in the Hamiltonian that can be controlled

[0047]

[0048] Δ1 and Δ2 can be controlled by adjusting the frequencies of the two transverse field microwave beams, Ω1 and Ω2 can be controlled by adjusting the amplitudes of the two transverse field microwave beams, and g can be controlled by adjusting the amplitude of the longitudinal field.

[0049] By applying both transverse and longitudinal fields simultaneously, we increase the controllable degrees of freedom. Through analytical or numerical methods, we can achieve quantum gates or unitary operations that were previously impossible with either transverse or longitudinal field alone, such as the two-qubit controlled flip-flop gate (CNOT gate) and quantum Fourier transform (QFT).

[0050] Specific embodiment: Taking the parameters of the CNOT gate of the numerical solution as an example, its implementation parameters are as follows Figure 3 As shown, Δ1 and Δ2 represent the detuning size of the transverse field microwave required for quantum bit 1 and quantum bit 2, Ω1 and Ω2 represent the amplitude of the required transverse field microwave, and g represents the amplitude of the required longitudinal field. The implementation parameters are obtained by solving the Schrödinger equation using the gradient descent algorithm. Compared with the traditional scheme, the process of implementing the CNOT gate is to first add the quantum bit transverse field, then the quantum coupler longitudinal field, and then the quantum bit transverse field. Figure 4 As shown in the figure, a CNOT gate with a 4 MHz vertical field requires at least 300 ns, while our solution is more than 50 ns faster. Figure 3 To meet the requirements of the CNOT gate parameter range, we choose the microwave frequency of the first microwave beam to be 5.2568 GHz, with a fixed detuning of -6 MHz, and the microwave frequency of the second microwave beam to be 5.1283 GHz, with a fixed detuning of -6 MHz, and the longitudinal field frequency to be 128.46 MHz, which is a resonant longitudinal field without detuning. By adding two actual transverse field microwaves and one longitudinal field drive to two quantum bits and a quantum coupler respectively, we can achieve Figure 3 The required parameter range allows us to realize CNOT gate operation on our model within 250 ns, which is not directly achievable by conventional methods. The actual applied transverse field microwave and longitudinal field pulses are as follows: Figure 5 As shown, Figure 5 The horizontal axis is time and the vertical axis is amplitude.

[0051] In the field of superconducting quantum computing, the unitary matrix that controls the flip gate is as follows. The physical process implemented is that when the first quantum bit is in the |0> state, the second quantum bit does not flip the quantum state. When the first quantum bit is in the |1> state, the second quantum bit flips the quantum state.

[0052]

[0053] After applying a transverse field to both qubits and a longitudinal field to a quantum coupler simultaneously, we obtained the results of the CNOT gate. For the four initial states |00>, |01>, |10>, and |11>, according to the evolution rules of the CNOT gate, the initial state |00> should return to the state |00> after the CNOT gate evolves. Except for the |00> state, the final state layout numbers of the other three states should be 0. Figure 6 The first sub-graph is the evolution of the initial state |00>, where the horizontal axis is time 250ns and the vertical axis is the layout number of each quantum state. The same is true for the second sub-graph |01> state. When the initial state is |10>, after evolving through the CNOT gate, the final state will reach the |11> state, which is consistent with the definition of the CNOT gate that the first quantum bit is |1> and the second quantum state is flipped, which is the evolution trajectory shown in the third sub-graph. When the initial state is |11>, after evolving through the CNOT gate, the final state reaches the |10> state, which verifies that our method can simultaneously apply transverse and vertical fields to the model of two quantum bits and one quantum coupler (CNOT gate time 250ns), thereby realizing the CNOT gate scheme that the traditional scheme requires to add transverse and vertical fields successively (CNOT gate time more than 300ns), indicating the feasibility of adding transverse and vertical fields at the same time and achieving quantum superiority. The evolution results are shown as follows. Figure 6 shown.

[0054] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions described in the aforementioned embodiments or make equivalent substitutions for some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for realizing a quantum gate based on a physical model containing a quantum coupler, characterized in that: It includes at least two quantum bits and a quantum coupler, and the specific steps are as follows: S1. The quantum coupler placed between the two qubits has a direct coupling with one of the qubits g. 1C , there is a direct coupling g with another qubit 2C , the Hamiltonian of two qubits and a quantum coupler is written as: in and are the Pauli operators of qubit 1 and qubit 2 and the quantum coupler, and is the first quantum bit's raise and lower operator, and is the raise and lower operator for the second qubit, and is the raising and lowering operator of the quantum coupler, ω1, ω2 and ω c is the eigenfrequency of the two qubits and the quantum coupler, J(Φ) is the effective coupling between the two qubits; S2, at the same time, apply transverse field microwave Ω1(t)cos(ω d1 t), applying transverse field microwave Ω2(t)cos(ω d2 t) and applying a longitudinal field drive Φ(t)=Θ+δcos(ω Φ t), after applying two beams of transverse field microwave driving and one beam of longitudinal field microwave driving, the Hamiltonian can be written as S3. Taylor expansion of the longitudinal field of the Hamiltonian after applying two beams of transverse field microwave driving and one beam of longitudinal field microwave driving in S2 is obtained: Transfer this Hamiltonian into the microwave reference frame, and the Hamiltonian becomes Select the vertical field frequency as ω φ =Δ d1d2 =ω d1 -ω d2 , discarding the oscillatory term, we can obtain the final Hamiltonian At this time, there are five degrees of freedom in the Hamiltonian that can be controlled S4. Based on S3, the transverse field and the longitudinal field are added simultaneously to increase the controllable degree of freedom, thereby realizing the quantum gate.

2. The method for realizing a quantum gate based on a physical model containing a quantum coupler according to claim 1, characterized in that: S1 also includes a partial diagonalization of the Hamiltonian of two qubits and a quantum coupler, which can be used to obtain a more practical form:

3. The method for realizing a quantum gate based on a physical model containing a quantum coupler according to claim 1, characterized in that: The effective coupling J(Φ) is determined by the direct coupling g 1c g 2c and the inverse of the detuning between the quantum bit and the quantum coupler Decision, for 4. The method for realizing a quantum gate based on a physical model containing a quantum coupler according to claim 1, characterized in that: S3 and Physically, this is the shift in quantum bit frequency caused by applying a longitudinal field, which is compensated by calibrating the bit frequency in subsequent experiments.

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