Method for preparing high-fidelity two-qubit gate

Abstract

A method for preparing a high-fidelity two-qubit gate, comprising: within a decoherence time, applying two consecutively-driven suppression noises on a two-qubit gate, the suppression noises each lasting half the decoherence time and having opposite phases, to decouple a quantum system from an environment (s1); enabling interaction of the two-qubit gate to form a waveform timing block and an accumulated phase, and respectively configuring a buffer region before the interaction and configuring a buffer region after the interaction to form a first buffer region and a second buffer region (s2); and performing buffer amplitude calibration optimization at the first buffer region and the second buffer region to eliminate the accumulated phase, so as to obtain an optimized two-qubit gate (s3).

Description

A method for preparing a high-fidelity two-bit gate Technical Field

[0001] This invention relates to the field of quantum bit preparation, and more particularly to a method for preparing a high-fidelity two-qubit gate. Background Technology

[0002] When two qubits are coupled, a two-qubit entanglement gate can be implemented through appropriate control. Entanglement gates refer to a class of quantum gate operations that can generate two-qubit entangled states, operations that cannot be achieved through simple single-qubit operations. One common type of two-qubit entanglement gate is the swap gate, which swaps the two single-excitation states, mapping |01> to |10> and |10> to |01>. Another type is the controllable entanglement gate, which typically determines the operation performed on the target qubit based on whether the control qubit is in the |1> state.

[0003] For fault-tolerant quantum computers based on Josephson junction superconducting quantum circuits, a key and core problem is how to maintain the coherence of qubits while still enabling high-fidelity two-qubit gate manipulation between any two qubits. This problem involves two dimensions: qubit decoherence and two-qubit gate manipulation. On the one hand, it involves suppressing qubit dephase, and on the other hand, it involves realizing noise-insensitive two-qubit quantum gates.

[0004] Existing technologies are based on tunable couplers and fixed-frequency bit architectures. The use of fixed-frequency bits results in a loss of flexibility in controlling chip parameters. Furthermore, the fine range of fixed-frequency parameters places higher demands on the consistency of micro / nano fabrication, thus limiting chip yield and consequently limiting scalability and mass production. In addition, although existing technologies often employ traditional dynamic decoupling methods such as spin echo to extend the dephase time of qubits, most of these methods are not integrated into two-qubit gate operations, resulting in the inability to effectively suppress high-fidelity two-qubit gate manipulation noise. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a high-fidelity two-bit gate preparation method.

[0006] To achieve the above objectives, the present invention employs the following technical solution: a high-fidelity two-bit gate preparation method, comprising the following steps:

[0007] S1: Apply two consecutive, phase-opposite driving suppression noises, each half the decoherence time, to the two-qubit gate during the decoherence time to decouple the quantum system from the environment;

[0008] S2: The two bit gates interact to form a waveform timing block and an accumulated phase, and buffer regions are set before and after the interaction to form a first buffer region and a second buffer region.

[0009] S3: Perform buffer amplitude calibration optimization in the first buffer region and the second buffer region to eliminate the accumulated phase and obtain the optimized two-bit gate.

[0010] As a further description of the above technical solution: step S1 includes:

[0011] S11: When there is no interaction between the two qubit gates, the Hamiltonian of a single qubit is determined by the first computational model, and the frequency corresponding to the energy level difference between the ground state |0〉 and the excited state |1〉 of the qubit is obtained;

[0012] S12: Under the external classical driving field, continuous driving causes the qubit to generate two decorated states. The equivalent Hamiltonian is calculated based on the fluctuation of the qubit frequency caused by suppressing noise.

[0013] S13: Calculate the phase error between the two adorned states based on the equivalent Hamiltonian, and cancel it out by echo.

[0014] As a further description of the above technical solution: step S2 includes:

[0015] S21: Under the Z pulse, the energy levels of the two-bit gate resonate and interact to form the waveform timing block and the accumulated phase;

[0016] S22: A square wave of a Z-pulse is applied before and after the interaction by a digital-to-analog converter module, forming the first buffer region and the second buffer region on both sides of the waveform timing block to cancel the accumulated phase.

[0017] As a further description of the above technical solution: step S3 includes:

[0018] S31: Fix the time length of the first buffer region, adjust the voltage amplitude of the second buffer region to 0, and after preparing the first quantum bit into a superposition state through the rotating gate, adjust the voltage amplitude of the first buffer region.

[0019] S32: The energy levels of the two qubits are tuned to resonate and interact. A rotation gate is applied to the second qubit to obtain |01>. The voltage amplitude of the first buffer region is scanned, and the point with the highest probability of |01> is selected as the voltage amplitude of the first buffer region.

[0020] S33: Fix the voltage amplitude of the first buffer region, prepare the second qubit into a superposition state, apply a rotation gate to the first qubit to obtain |10>, scan the voltage amplitude of the second buffer region, and select the point that maximizes the probability of |10> as the voltage amplitude of the second buffer region.

[0021] As a further description of the above technical solution: the frequency range of the noise suppression is less than 100MHz.

[0022] As a further description of the above technical solution: the first computational model calculates the Hamiltonian of a single qubit, and the algorithm formula is as follows:

[0023] Where, ω 10 The frequency corresponding to the energy level difference between the |1> and |0> states of a quantum bit. For the qubit, the raise operator, Ω is the descent operator for the qubit, ω is the driving amplitude, and ω is the descent operator for the qubit. d For the driving frequency, The driving phase is N, which describes the fluctuation of the quantum bit frequency caused by noise suppression. is the reduced Planck constant.

[0024] As a further description of the above technical solution: continuous driving causes the qubit to generate two decorated states as follows:

[0025] If N is less than the driving amplitude Ω, suppressing noise will not cause the quantum system to transition between the two decorated state energy levels, resulting in a frequency shift between the two decorated states. The equivalent Hamiltonian is:

[0026] Decouple quantum systems from their environment.

[0027] As a further description of the above technical solution: the phase error of the equivalent Hamiltonian between the decoherence times [t1, t2] is:

[0028] By using echoes, the phase of the noise-suppressing state is flipped π in the middle of [t1, t2], causing the energy level of the decorated state {|+>,|->} to reverse, making ε≈0.

[0029] As a further description of the above technical solution: the resonant interaction time of the energy levels of the two qubits is: t=π / 2g;

[0030] Where g represents the coupling strength between the two bits.

[0031] As a further description of the above technical solution: the first quantum bit is prepared into a superposition state. After tuning the resonant interaction of the two qubit energy levels for time t, the iSWAP gate is completed, resulting in...

[0032] The above technical solution has the following advantages or beneficial effects:

[0033] 1. Noise is suppressed by continuous driving with half of the time and opposite phase, and the dephase time of the superconducting quantum bit is extended. At the same time, in order to correct the phase error caused by deviation from the microwave reference frame, a Z-pulse buffer region is applied before and after the interaction of the time-series waveform blocks to cancel it out. Combined with the two-bit parameter calibration technique for optimization, a high-fidelity two-bit gate is obtained in the experiment, the noise can be effectively suppressed, and the dephase time can be greatly extended. Attached Figure Description

[0034] Figure 1 is a flowchart of the preparation method proposed in this invention;

[0035] Figure 2 is a flowchart of the preparation method proposed in this invention;

[0036] Figure 3 is a flowchart of the preparation method proposed in this invention;

[0037] Figure 4 is a flowchart of the preparation method proposed in this invention;

[0038] Figure 5 is a schematic diagram of quantum bit decoupling in this invention;

[0039] Figure 6 is a schematic diagram of the quantum bit pulse in this invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Referring to Figure 1, one embodiment of the present invention provides a method for preparing a high-fidelity two-bit gate, comprising the following steps:

[0042] S1: Apply two consecutive, phase-opposite driving noises, each half the decoherence time, to the two-qubit gate during the decoherence time to decouple the quantum system from the environment;

[0043] S2: Interact with the two bit gates to form a waveform timing block and an accumulated phase, and set buffer regions before and after the interaction to form a first buffer region and a second buffer region.

[0044] S3: Perform buffer amplitude calibration optimization in the first and second buffer regions to eliminate accumulated phase and obtain the optimized two-bit gate.

[0045] In this embodiment, continuous driving with opposite phases for half the duration is used to suppress noise. The noise suppression is a continuous time-series pulse signal, which prolongs the dephase time of the superconducting quantum bit. At the same time, in order to correct the phase error caused by deviation from the microwave reference frame, a Z-pulse buffer region is applied before and after the interaction of the time-series waveform blocks to cancel it out. Combined with the two-bit parameter calibration technique for optimization, a high-fidelity two-bit gate is obtained experimentally, the noise can be effectively suppressed, and the dephase time can be greatly extended.

[0046] Referring to Figure 2, step S1 includes:

[0047] S11: When there is no interaction between the two qubit gates, the Hamiltonian of a single qubit is determined by the first computational model, and the frequency corresponding to the energy level difference between the ground state |0〉 and the excited state |1〉 of the qubit is obtained;

[0048] S12: Under the external classical driving field, continuous driving causes the qubit to generate two decorated states. The equivalent Hamiltonian is calculated based on the fluctuation of the qubit frequency caused by suppressing noise.

[0049] S13: Calculate the phase error between the two decorated states based on the equivalent Hamiltonian and cancel it out by echo.

[0050] The inventors discovered in their research that for superconducting qubits, the main source of phase dephase is low-frequency noise, whose intensity is inversely proportional to its frequency, generally referred to as 1 / f noise. This type of noise causes the phase of the quantum state to decay over time in the form of a Gaussian function, with the decay timescale being... Indication. In traditional experiments The Ramsey interferometer experiment, which involves free evolution, is generally used for calibration.

[0051] In this embodiment, to extend the dephase time of the superconducting qubit, we cleverly designed a pulse sequence to replace the free evolution of duration τ between two π / 2 pulses in the Ramsey interference experiment with a continuous drive with an intermediate antiphase, as shown in Figure 5. This makes the average effect of the interaction term on the quantum system |Ψ> zero over a certain period of time, i.e., H int The value is approximately 0, which makes it more effective at suppressing dephase caused by higher frequency noise. The equivalent result is that the quantum system is "decoupled" from the external environment, and the noise is "suppressed".

[0052] Of course, H int≈0 represents the ideal situation. In non-ideal cases, noise suppression is distributed across various spectral bands. The methods described above are often only effective for noise suppression within a certain spectral range (requiring less than 100MHz), and cannot completely eliminate all effects. For example, for the energy relaxation process of a qubit that involves energy exchange with the external environment, the noise frequency is very high and the bandwidth is very narrow, making this method ineffective. Conversely, the dephase of superconducting qubits is mainly affected by 1 / f low-frequency noise, and this process does not involve energy exchange with the external environment. This method often achieves better results, improving the dephase time by about an order of magnitude compared to free evolution in the Ramsey interferometer experiment.

[0053] The specific principle of noise suppression using continuous driving when qubits do not interact is as follows: Under the influence of an external classical driving field, the Hamiltonian of a single qubit can be expressed as:

[0054] Where, ω 10 The frequency corresponding to the energy level difference between the |1> and |0> states of a quantum bit. For the qubit, the raise operator, Ω is the descent operator for the qubit, ω is the driving amplitude, and ω is the descent operator for the qubit. d For the driving frequency, The driving phase is N, which describes the fluctuation of the quantum bit frequency caused by noise suppression. is the reduced Planck constant.

[0055] Assume the driving frequency ω d =ω 10 At the quantum bit frequency ω 10 In a rotating reference frame, the Hamiltonian can be simplified to:

[0056] Continuous driving caused the qubit to produce two decorated states as follows:

[0057] The energy level difference between them is With the adorned states {|+>,|->} as new basis vectors, the Hamiltonian It can be rephrased as:

[0058] Assuming the suppressed noise is a low-frequency noise with a very long correlation length, much larger than the system dynamics timescale Ω. -1 Therefore, the effect of the Rabi oscillation caused by the driving force can be considered an adiabatic process. Meanwhile, if N is less than the driving amplitude Ω, noise suppression will not cause the quantum system to transition between the two decorated state energy levels; the final effect is a frequency shift between the decorated states, with the equivalent Hamiltonian being:

[0059] The above equation shows that, under the noise suppression effect of the drive, the equivalent coupling between the quantum bit and the environment is: Compared to the undriven The reduction is due to the microwave-driven noise suppression applied to the qubit, which causes the qubit to decouple from the external environment.

[0060] Meanwhile, the phase error of the equivalent Hamiltonian between decoherence times [t1, t2] is:

[0061] It is worth noting that, compared to the case without driving, the value of the phase error ∈ accumulated during evolution is independent of the sign direction of the suppressed noise N. This allows for further cancellation of the phase error through echo: in the middle of the decoherence time [t1, t2], the externally driven phase is flipped by π, causing the adorned states {|+>,|->} to undergo energy level flipping. In this case, the accumulated phase error can be expressed as:

[0062] At this point, we define T = t2 - t1. Assume N... 2 The mean values ​​of the first half and the second half are respectively and Then we have:

[0063] For noise suppression that varies slowly over time, i.e. The phase errors accumulated in the first and second halves can be almost completely canceled out, making the phase error ∈≈0. This allows for the use of dynamic decoupling to suppress noise and extend the dephase time of the superconducting quantum bit.

[0064] Referring to Figures 3 and 6, step S2 includes:

[0065] S21: Under the Z pulse, the energy levels of the two-bit gate resonate and interact, forming waveform timing blocks and accumulated phases;

[0066] S22: A square wave of Z pulse is applied before and after the interaction by the digital-to-analog conversion module, forming a first buffer region and a second buffer region on both sides of the waveform timing block to cancel the accumulated phase.

[0067] In this embodiment, to obtain a two-qubit entangled gate, such as the iSWAP gate, it is necessary to use a Z-pulse to resonate and interact the energy levels of the two qubits to obtain t. iSWAP=π / 2g, where g is the coupling strength between the two bits, so that |01〉 is completely transformed into |10〉. However, when the qubits interact, they have actually deviated from the original microwave reference frame, that is, the two qubits belong to different microwave reference frames, which will accumulate dynamic phase.

[0068] Therefore, phase accumulates during this process due to the different rotational speeds of the two microwave reference frames. Thus, in order to prepare a complete two-bit entangled gate, a Z-pulse buffer region is added to the corresponding waveform timing block before and after the interaction to cancel the phase caused by the above reasons.

[0069] The buffer region is a square wave that is maintained for a certain period of time. This is accomplished by the digital-to-analog converter (DAC). The DAC outputs this waveform before and after the interaction in the waveform timing block, forming the first buffer region and the second buffer region to cancel out the accumulated phase.

[0070] Referring to Figure 4, step S3 includes:

[0071] S31: Fix the time length of the first buffer region, adjust the voltage amplitude of the second buffer region to 0, prepare the first quantum bit into the superposition state through the rotating gate, and then adjust the voltage amplitude of the first buffer region.

[0072] S32: The energy levels of the two qubits are tuned to resonate and interact. A rotation gate is applied to the second qubit to obtain |01>. The voltage amplitude of the first buffer region is scanned, and the point with the highest probability of |01> is selected as the voltage amplitude of the first buffer region.

[0073] S33: Fix the voltage amplitude of the first buffer region, prepare the second qubit into a superposition state, apply a rotation gate to the first qubit to obtain |10>, scan the voltage amplitude of the second buffer region, and select the point that maximizes the probability of |10> as the voltage amplitude of the second buffer region.

[0074] In this embodiment, buffer amplitude calibration optimization is required to correct various phase errors caused by deviations from the microwave reference frame. For the optimization of the amplitude in the first buffer region, its time length (5-10 ns) is first fixed. The voltage amplitude of the first buffer region needs to be corrected. First, the voltage amplitude of the second buffer region is fixed to 0. Then, the first qubit is prepared into a superposition state through a rotating gate (R gate, with microwave reference coordinates [0, π / 2]). Then, the voltage amplitude of the first buffer region is varied, and the energy levels of the first and second qubits are tuned to interact resonantly for a period of time to complete the iSWAP gate. If the iSWAP gate is error-free, the result is obtained. Finally, a rotation gate (R-gate, with microwave reference coordinates [π / 2, π / 2]) is applied to the second qubit to obtain |01>. Therefore, scanning the voltage amplitude of the first buffer region will reveal oscillations between |00> and |01>. When these oscillations can cancel out some of the phase errors, the probability of |01> will be maximized.

[0075] At the same time, if there are multiple qubits, after the calibration of the first qubit is completed but before the calibration of the second qubit, another phase will accumulate for the same reason. To correct The second buffer region needs to be corrected. First, the amplitude of the first buffer region is fixed to the voltage amplitude that maximizes the probability of |01>. The second qubit is prepared into a superposition state using a rotation gate (R-gate, microwave reference coordinates [0, π / 2]). Finally, the first qubit is rotated using a rotation gate (R-gate, microwave reference coordinates [0, π / 2]) to scan the voltage amplitude of the second buffer region. This will observe oscillations between |00> and |10>. The point that maximizes the probability of |10> is selected as the voltage amplitude of the second buffer region, completing parameter optimization and resulting in a high-fidelity two-qubit gate experimentally, laying the foundation for universal quantum logic gates.

[0076] Finally, it should be noted that the above description 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 foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for preparing a high-fidelity two-bit gate, characterized in that, Including the following steps: S1: Apply two consecutive, phase-opposite driving suppression noises, each half the decoherence time, to the two-qubit gate during the decoherence time to decouple the quantum system from the environment; S2: The two bit gates interact to form a waveform timing block and an accumulated phase, and buffer regions are set before and after the interaction to form a first buffer region and a second buffer region. S3: Perform buffer amplitude calibration optimization in the first buffer region and the second buffer region to eliminate the accumulated phase and obtain the optimized two-bit gate.

2. The preparation method according to claim 1, characterized in that: Step S1 includes: S11: When there is no interaction between the two qubit gates, the Hamiltonian of a single qubit is determined by the first computational model, and the frequency corresponding to the energy level difference between the ground state |0〉 and the excited state |1〉 of the qubit is obtained; S12: Under the external classical driving field, continuous driving causes the qubit to generate two decorated states. The equivalent Hamiltonian is calculated based on the fluctuation of the qubit frequency caused by suppressing noise. S13: Calculate the phase error between the two adorned states based on the equivalent Hamiltonian, and cancel it out by echo.

3. The preparation method according to claim 1, characterized in that: Step S2 includes: S21: Under the Z pulse, the energy levels of the two-bit gate resonate and interact to form the waveform timing block and the accumulated phase; S22: A square wave of a Z-pulse is applied before and after the interaction by a digital-to-analog converter module, forming the first buffer region and the second buffer region on both sides of the waveform timing block to cancel the accumulated phase.

4. The preparation method according to claim 1, characterized in that: Step S3 includes: S31: Fix the time length of the first buffer region, adjust the voltage amplitude of the second buffer region to 0, and after preparing the first quantum bit into a superposition state through the rotating gate, adjust the voltage amplitude of the first buffer region. S32: The energy levels of the two qubits are tuned to resonate and interact. A rotation gate is applied to the second qubit to obtain |01>. The voltage amplitude of the first buffer region is scanned, and the point with the highest probability of |01> is selected as the voltage amplitude of the first buffer region. S33: Fix the voltage amplitude of the first buffer region, prepare the second qubit into a superposition state, apply a rotation gate to the first qubit to obtain |10>, scan the voltage amplitude of the second buffer region, and select the point that maximizes the probability of |10> as the voltage amplitude of the second buffer region.

5. The preparation method according to claim 1, characterized in that: The frequency range for noise suppression is less than 100MHz.

6. The preparation method according to claim 2, characterized in that: The first computational model calculates the Hamiltonian of a single qubit, and the algorithm formula is as follows: Where, ω 10 The frequency corresponding to the energy level difference between the |1> and |0> states of a quantum bit. For the qubit, the raise operator, Ω is the descent operator for the qubit, ω is the driving amplitude, and ω is the descent operator for the qubit. d For the driving frequency, The driving phase is N, which describes the fluctuation of the quantum bit frequency caused by noise suppression. is the reduced Planck constant.

7. The preparation method according to claim 2, characterized in that: Continuous driving causes the qubit to generate two decorated states as follows: If N is less than the driving amplitude Ω, suppressing noise will not cause the quantum system to transition between the two decorated state energy levels, resulting in a frequency shift between the two decorated states. The equivalent Hamiltonian is: Decouple quantum systems from their environment.

8. The preparation method according to claim 2, characterized in that: The phase error of the equivalent Hamiltonian between decoherence times [t1, t2] is: By using echoes, the phase of the noise-suppressing state is flipped π in the middle of [t1, t2], causing the energy level of the decorated state {|+>,|->} to reverse, making ε≈0.

9. The preparation method according to claim 3, characterized in that: The time for the resonance interaction of the energy levels of the two qubits is: t = π / 2g; Where g represents the coupling strength between the two bits.

10. The preparation method according to claim 4, characterized in that: The first quantum bit is prepared into a superposition state. After tuning the resonant interaction of the two qubit energy levels for time t, the iSWAP gate is completed, resulting in...

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