A phase calibration method for coupling strength of two-dimensional quantum bit array

Abstract

The present invention relates to a method for calibrating the phase of the coupling strength of a two-dimensional quantum bit array. The method applies a DC bias signal to an adjustable coupler between all adjacent quantum bits, applies an additional parameter modulation waveform, and the parameter modulation waveform has been individually calibrated for frequency and amplitude, detection microwaves and readout microwave signals, measures the effective energy spectrum structure of the quantum bit system, then applies a new flux control signal of the changed parameter modulation phase, continues to measure the corresponding energy spectrum structure, and finally obtains a corresponding image of the phase of the unilateral coupling strength of the array and the energy spectrum structure of the system, and then finds the corresponding compensation phase according to the required energy spectrum structure. The present invention only needs to measure energy spectrum information, and has low requirements for reading fidelity; does not need to measure dynamic information, and has low requirements for microwave drive crosstalk. The detection microwave can be applied from the driving line or transmission line of the quantum bit, and has wider applicability to different samples; does not need to measure the phase by indirect means such as quantum state tomography, and is easy to implement.

Description

Technical Field

[0001] The present invention relates to the field of quantum computing technology, and in particular to a phase calibration method for coupling strength of a two-dimensional quantum bit array. Background Art

[0002] With the emergence of new sample architectures and the improvement of micro-nano processing technology, we are already in the era of Noisy Intermediate-Scale Quantum (NISQ). At present, superconducting quantum bits are usually arranged in a two-dimensional array. The connected quantum bits are connected by adjustable couplers to achieve complete shutdown of the coupling strength, which is conducive to the convenient implementation of high-fidelity single-bit gates and two-bit gates on large-scale samples. Such samples can be used to demonstrate some quantum algorithms with quantum superiority. Digital quantum simulation decomposes the evolution of the system under study into a series of quantum gate circuits, which requires high fidelity of parallel single-bit gates and parallel multi-bit gates. Before achieving fault-tolerant quantum computing, realizing analog quantum simulation on NISQ samples is also a hot research direction in the field of quantum information, which helps us verify and explore scientific problems in fields such as condensed matter physics and high-energy physics that are difficult to touch under current experimental conditions. Analog quantum simulation requires mapping the Hamiltonian of the system to be studied to the physical quantum bit, and constructing an accurate Hamiltonian by adjusting the coupling strength, applying microwaves and flux control fields. Phase calibration in two-dimensional quantum bit arrays is very important for both digital and analog quantum simulations.

[0003] The phase deviation of the coupling strength in a two-dimensional quantum bit array comes from the delay in the control signal line and the nonlinearity of the quantum bit or adjustable coupler frequency as a function of the magnetic flux change. If the phase is not calibrated, performing two-bit gates at the same time will result in additional phase offsets, and the Hamiltonian constructed using the coupling strength will deviate from the original Hamiltonian. Usually, phase calibration requires quantum state tomography to convert the phase of the coupling strength into the phase of the quantum bit, which is then read out. However, this solution is cumbersome for multi-qubit systems and relies on the fidelity of the gate operation.

[0004] Currently, the number of quantum bits is increasing, and the requirements for manipulation accuracy are also getting higher and higher, which poses a huge challenge to phase calibration technology. Summary of the invention

[0005] In view of the problems existing in the prior art, the present invention provides a phase calibration method for the coupling strength of a two-dimensional quantum bit array.

[0006] The technical implementation of the present invention is as follows: a phase calibration method for coupling strength of a two-dimensional quantum bit array, the method comprising the following steps:

[0007] S1. Apply a DC bias signal to the Z line of the adjustable coupler on each side of the two-dimensional quantum bit array to generate a magnetic flux, so that the frequencies of all quantum bits and adjustable couplers meet the following conditions:

[0008] The difference between the frequency of the qubit and the frequency of the tunable coupler connected to it is greater than the coupling strength between them;

[0009] The frequency difference between the two qubits on the same edge is smaller than the frequency difference between the qubit and the tunable coupler;

[0010] S2: Apply parameter modulation waveform to the Z line of the adjustable coupler on each side to realize effective coupling of quantum bits, calibrate the parameter modulation frequency and fit the Rabi frequency for different parameter modulation amplitudes, and obtain a mapping relationship table between the Rabi frequency and the parameter modulation amplitude and frequency;

[0011] S3, applying four parameter modulation waveforms to the Z lines of the adjustable couplers on the four sides of the two-dimensional quantum bit array at the same time, coupling the four quantum bits together at the same time, applying the energy spectrum of the detection microwave detection system within the time range of the parameter modulation waveform, and reading out with a single-tone readout microwave;

[0012] S4. Using frequency division multiplexing technology, readout microwaves are applied to the four quantum bits at the same time, and four voltage signals are read out using multi-tone readout microwaves;

[0013] S5. By calibrating the effective coupling strength induced by parameter modulation on the four edges to the same value, the relationship between the energy spectrum structure of the entire system and the phase of parameter modulation is directly measured, and the phase of the two-dimensional quantum bit array is calibrated according to the theoretical model.

[0014] As a preferred solution of the present invention, in S1, the DC bias signal is a signal whose amplitude has been calibrated separately.

[0015] As a preferred embodiment of the present invention, in S1, the lower limit of the frequency difference between the two quantum bits on the same edge is not less than 100 MHz, and the upper limit is 300 MHz, and the upper limit is determined by the bandwidth of the filter and arbitrary waveform generator on the experimental circuit.

[0016] As a preferred solution of the present invention, in S2, any quantum bit on each edge realizes the X-gate of the quantum bit through a microwave pulse to prepare the first excited state of the quantum bit.

[0017] As a preferred solution of the present invention, in S2, the spectrum of the parameter modulation waveform is:

[0018] As a preferred embodiment of the present invention, the parameter modulation waveform is applied to the Z line, and the magnetic flux generated by the signal on the Z line is

[0019] As a preferred solution of the present invention, in S2, the parameter modulation frequency point corresponding to the minimum Rabi frequency is used as the calibrated frequency corresponding to the parameter modulation amplitude.

[0020] As a preferred solution of the present invention, in S2, the spectrum of the parameter modulation waveform is:

[0021] As a preferred embodiment of the present invention, the parameter modulation waveform is applied to the Z line, and the magnetic flux generated by the signal on the Z line is

[0022] As a preferred embodiment of the present invention, in S3, the detection microwave frequency scanning range is determined according to the selected Rabi frequency and the eigenfrequency before the quantum bit coupling, and four eigenstates of the single excitation subspace are obtained to determine the effective energy spectrum of the system after coupling.

[0023] As a preferred solution of the present invention, in S4, the best of the four readout voltage signals is selected according to the read fidelity.

[0024] As a preferred embodiment of the present invention, in S5, the theoretical model is: λ is the solution of the eigenvalue equation used to solve the eigenvalue of the effective Hamiltonian of the system. λ has 4 solutions, which correspond to the effective energy spectrum of the system.

[0025] Beneficial Effects

[0026] 1. The present invention only needs to measure effective energy spectrum information, and has low requirements on reading fidelity;

[0027] 2. The present invention does not require the measurement of dynamic information, and has low requirements for microwave driven crosstalk. The detection microwave can be applied from the driving line or transmission line of the quantum bit, which is more applicable to different samples;

[0028] 3. The present invention does not require indirect means such as quantum state tomography to measure the phase, and is easy to implement; BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is a flowchart of the steps of the method of the present invention;

[0030] Figure 2 Schematic diagram of the architecture of a two-dimensional quantum bit array;

[0031] Figure 3 This is a single-side calibration timing diagram;

[0032] Figure 4 It is the vacuum Rabi diagram and the diagram of vacuum Rabi changing with parameter modulation frequency;

[0033] Figure 5 It is the timing diagram of the energy spectrum of the measurement system;

[0034] Figure 6 This is the phase change diagram of the system energy spectrum as the parameter modulation changes. DETAILED DESCRIPTION

[0035] As an embodiment of the present invention, Figure 1-6 As shown, the specific embodiment of the method is as follows:

[0036] S1: The two-dimensional quantum bit array is composed of four quantum bits Q1, Q2, Q3, Q4 and four adjustable couplers C1, C2, C3, C4 (see Figure 2 ), C1 is coupled to Q1 and Q2 through capacitance; Q1 and Q2 are also coupled to each other through capacitance. Each side of the two-dimensional quantum bit array is an adjustable coupler that is coupled to two quantum bits through capacitance. The coupling strength between the adjustable coupler and one quantum bit is 80MHz. The coupling strength between the two quantum bits is 5MHz through capacitance. The quantum bit frequency f Qi and adjustable coupler frequency f Ci The external magnetic flux Φ i To change this, we apply a DC bias signal to their own flux control circuit (called the Z line). To generate magnetic flux The frequencies of all qubits and adjustable couplers meet the following conditions: Condition 1: The absolute value of the frequency difference between the qubit and the adjustable coupler connected to it is 800MHz, which is ten times the coupling strength between them of 80MHz; Condition 2: The frequency difference of the qubits on the same side of the array is between 100MHz and 300MHz, and the lower limit should not be lower than 100MHz, but the upper limit can be appropriately changed. The upper limit is determined by the bandwidth of the filter and arbitrary waveform generator on the experimental circuit. A higher frequency instrument can reach 500MHz, for example, but it should not be close to the frequency difference of 800MHz between the qubit and the adjustable coupler. The f of the two-dimensional qubit array Q1 =5.72GHz, f Q2 =5.53GHz, f Q3 =5.67GHz, f Q4 =5.50GHz. C1 =f C2 =f C3 =f C4 =6.5GHz satisfies the above two conditions.

[0037] S2: Implement the X-gate of quantum bit Q1 through microwave pulses. After completing the X-gate, the first excited state of quantum bit Q1 can be prepared. Figure 3 As shown, after the X gate of Q1 is the Z line parameter modulation signal of C1, so the Z line signal is the DC bias signal of S1. Based on this, we additionally apply a parameter modulation waveform to the Z line of the adjustable coupler C1 This step is to apply an AC current signal Give the flux control line, so that such a periodically changing flux can be generated The total magnetic flux generated by the signal applied to the Z line of C1 is

[0038] The duration of the parameter modulation signal is t, and the microwave signal (called the readout signal) used to detect the state of the quantum bit follows the parameter modulation signal. By continuously changing the length of the parameter modulation waveform t from 0 to 1.0μs, with one point every 10ns, the readout signal is used to measure the occupancy number P1 / P2 of the quantum bit Q1 or quantum bit Q2 in the first excited state, and the image of the change of P1 / P2 with t is obtained, which is called the vacuum Rabi image. Among them, P1 or P2 changes with the period of t, the amplitude is A, the center value is B, and the change frequency is ω, which is called the oscillation frequency. P1(t)=Acos(ωt)+B,P2(t)=Acos(ωt+π)+b.

[0039] For example: If decoherence is not considered, and the frequency of parameter modulation is exactly equal to the frequency difference between Q1 and Q2, and the excited state of Q1 is prepared, then A = 0.5, B = 0.5. If the excited state of Q2 is prepared at the beginning, then A = -0.5, B = 0.5. Note that only one qubit needs to be prepared.

[0040] Further, in the appropriate parameter modulation frequency range, that is, near the frequency difference between Q1 and Q2, plus or minus 10MHz, change the parameter modulation frequency, and select a frequency point every 0.2MHz. Because we don’t know what the frequency difference between Q1 and Q2 is after parameter modulation is applied, we need to scan a range (for example, f Q1 =5.72GHz, f Q2 =5.53GHz, the frequency difference without parameter modulation is 190MHz, then the parameter modulation frequency needs to be changed from 180MHz to 200MHz, and a frequency point is selected every 0.2MHz), and a vacuum Rabi image is measured at each frequency point (variable time t, measure P1 or P2 as t changes). Fit the oscillation frequency for each vacuum Rabi image, and use the parameter modulation frequency point corresponding to the minimum oscillation frequency (called Rabi frequency) as the parameter modulation amplitude δ C1The corresponding calibrated frequencies are different for different amplitudes, because the amplitude of parameter modulation will cause the frequency of the quantum bit to move, such as Figure 4 As shown, the first two figures show the change of P1 / P2 with the evolution time t, and the third figure shows the calibration parameter modulation frequency. However, the scanning range is only 187MHz to 191MHz, and a point is selected every 1MHz. C1 The larger the value, the larger the Rabi frequency. Therefore, the modulation amplitude of the variable parameter is further calibrated. C1 From 0 to 0.15Φ0, there is a point every 0.01Φ0, where Φ0=h / 2e is the magnetic flux quantum, h is the Planck constant, and e is the electron charge. All amplitudes are calibrated, and the mapping relationship table between Rabi frequency and parameter modulation frequency and amplitude is obtained to complete the unilateral calibration.

[0041] S3: After all four sides are calibrated, select the Rabi frequency 2Ω, for example 5MHz. According to the mapping table of S2, we can know the amplitude and frequency of the parameter modulation waveform on the Z line of the adjustable coupler of each side. The system is initially in the state where all quantum bits are 0, and four parameter modulation waveforms are applied at the same time, with a waveform time of 12μs. The four quantum bits are coupled together at the same time, and the energy spectrum of each quantum bit is split into 4 frequencies, corresponding to the eigenvalues ​​of the system. Figure 5 As shown, within the time range of the parameter modulation waveform, a certain frequency f is applied drive The detection microwave has a detection microwave time of 10μs. In terms of timing, the center position of the detection microwave is aligned with the center position of the parameter modulation, that is, the detection microwave starts 1μs after the parameter modulation starts, and the parameter modulation ends 1μs after the detection microwave ends. Following the parameter modulation waveform is the readout microwave, which is used to read the state of the quantum bit Q1. The measured voltage signal V reflects the state of the quantum bit. For example, the signal obtained by the readout microwave is 1mV, corresponding to the quantum bit in state 0; the signal obtained is 3mV, corresponding to the quantum bit in state 1; the signal obtained is between 1mV and 3mV, corresponding to the quantum bit in a superposition state or mixed state of state 0 and state 1. Under the action of the detection microwave, the quantum bit can only be in state 0 or a mixed state after the detection microwave ends. We constantly change the frequency f of the detection microwave. drive When the detection microwave frequency is the same as a certain eigenfrequency of the system, after the detection microwave ends, the entire quantum system is in a mixed state. When the detection microwave frequency is not the same as any eigenfrequency of the system, the system is still in the 0 state. When the detection microwave frequency is near a certain eigenfrequency, the signal V obtained by reading the microwave varies with the detection microwave frequency f driveA peak will appear in the curve of the change. According to the selected Rabi frequency of 5MHz and the eigenfrequency of 5.72GHz before the coupling of the quantum bit Q1, the scanning range of the detection microwave frequency is determined: 5.71GHz to 5.73GHz, and four eigenstates of the single excitation subspace are obtained to determine the effective energy spectrum of the system after coupling.

[0042] S4: Using frequency division multiplexing technology, four qubit readout microwaves are applied simultaneously to obtain four voltage signals, which respectively reflect the states of the four qubits. The single-tone readout microwave of S3 is replaced by a multi-tone readout microwave to repeat S3, and the best of the four readout voltage signals is selected based on the reading fidelity.

[0043] S5: Change the initial phase of a certain parameter modulation waveform The variation range is 0-2pi, and the structure of the effective energy spectrum changes with the phase, passing through the energy level structure of different numbers of degenerate points in sequence. According to the formula This formula is the eigenvalue equation for solving the following effective Hamiltonian. The following matrix is ​​the effective Hamiltonian. The difference between the system's eigenfrequency and the original Q1 eigenfrequency of 5.72 GHz is the four solutions to the equation, the sum of the phases of the four coupling intensities. Determines the energy level structure, When , there are three eigenvalues, the middle eigenvalue has double degeneracy, the maximum and minimum frequencies of these four energy levels have no degeneracy, and the middle frequencies have double mergers. When , there are two eigenvalues, each of which is doubly degenerate, and only two frequencies can be detected at the four energy levels. The effective energy level can see four frequencies, but the relative position will vary. Changes. Figure 6 As shown, the changes The energy spectrum of the measuring system is at the black dashed line, which is calibrated to location.

[0044]

[0045] Explanation of λ: The effective Hamiltonian of the system is

[0046]

[0047] This is a 4 by 4 matrix. Let the eigenvalue be λ and the eigenvector be ψ. ψ is a vector with 1 row and 4 columns. The eigenvalue and eigenvector satisfy the following formula: Hψ=λψ

[0048] So (H-λI)ψ=0, where I is the 4 by 4 identity matrix;

[0049] According to Cramer's rule for solving linear equations, ψ has a non-zero solution only when |H-λI|=0, and |A| refers to the determinant of the A matrix;

[0050] Eigen equation:

[0051] The implementation modes of the present invention are described in detail above in conjunction with the embodiments / drawings, but the present invention is not limited to the above-mentioned implementation modes. For ordinary technicians in this technical field, after knowing the contents recorded in the present invention, they can make several equivalent changes and substitutions thereto without departing from the principle of the present invention, and these equivalent changes and substitutions should also be regarded as belonging to the protection scope of the present invention.

Claims

1. A phase calibration method for coupling strength of a two-dimensional quantum bit array, characterized in that: The phase calibration method comprises the following steps: S1. Apply a DC bias signal to the Z line of the adjustable coupler on each side of the two-dimensional quantum bit array to generate a magnetic flux, so that the frequencies of all quantum bits and adjustable couplers meet the following conditions: The difference between the frequency of the qubit and the frequency of the tunable coupler connected to it is greater than the coupling strength between them; The frequency difference between the two qubits on the same edge is smaller than the frequency difference between the qubit and the tunable coupler; S2: Apply a parameter modulation waveform to the Z line of the adjustable coupler on each side to achieve effective coupling of quantum bits, calibrate the parameter modulation frequency for different parameter modulation amplitudes and fit the Rabi frequency, and obtain a mapping relationship table between the Rabi frequency and the parameter modulation amplitude and frequency; S3, applying four parameter modulation waveforms to the Z lines of the adjustable couplers on the four sides of the two-dimensional quantum bit array at the same time, coupling the four quantum bits together at the same time, applying the energy spectrum of the detection microwave detection system within the time range of the parameter modulation waveform, and reading out the microwaves with a single tone readout; S4. Using frequency division multiplexing technology, readout microwaves are applied to the four quantum bits at the same time, and four voltage signals are read out using multi-tone readout microwaves; S5. By calibrating the effective coupling strength induced by parameter modulation on the four edges to the same value, the relationship between the energy spectrum structure of the entire system and the phase of parameter modulation is directly measured, and the phase of the two-dimensional quantum bit array is calibrated according to the theoretical model.

2. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S1, the DC bias signal is a signal whose amplitude has been calibrated separately.

3. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S1, the lower limit of the frequency difference between the two quantum bits on the same edge is not less than 100 MHz, and the upper limit is 300 MHz, and the upper limit is determined by the bandwidth of the filter and arbitrary waveform generator on the experimental circuit.

4. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S2, any quantum bit on each edge realizes the X-gate of the quantum bit through microwave pulses to prepare the first excited state of the quantum bit.

5. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S2, the parameter modulation frequency point corresponding to the minimum Rabi frequency is used as the calibrated frequency corresponding to the parameter modulation amplitude.

6. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S2, the spectrum of the parameter modulation waveform is:

7. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 6, characterized in that: The parameter modulation waveform is applied to the Z line, and the magnetic flux generated by the signal on the Z line is 8. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S3, the frequency scanning range of the detection microwave is determined according to the selected Rabi frequency and the eigenfrequency of the quantum bit before coupling, and the four eigenstates of the single excitation subspace are obtained to determine the effective energy spectrum of the system after coupling.

9. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S4, the best of the four readout voltage signals is selected based on read fidelity.

10. A phase calibration method for coupling strength of a two-dimensional quantum bit array according to claim 1, characterized in that: In S5, the theoretical model is described:

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