A method for preparing a high-fidelity two-bit gate
By applying continuous driving and buffer optimization technology with opposite phases in superconducting quantum circuits, the problem of noise suppression of two-bit gates is solved, extending the decoherence time and improving the control accuracy, and achieving a high-fidelity two-bit gate.
Patent Information
- Application Number
- CN202410933209.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-07-12
- Publication Date
- 2024-12-27
- Estimated Expiration
- 2044-07-12
AI Technical Summary
In the Josephson junction-based superconducting quantum circuit, it is difficult to achieve high-fidelity two-bit gate manipulation while maintaining qubit coherence, and the existing methods are sensitive to noise, resulting in qubit decoherence and two-bit gate. The noise control effect is not good.
By applying continuous driving with opposite phases in the decoherence time of the two-bit gate, the noise is suppressed, and the waveform timing block and buffer area are formed, and buffer amplitude calibration optimization is performed before and after interaction, the accumulated phase is eliminated, and the two-bits with high fidelity are achieved. Door.
It effectively extends the decoherence time of superconducting qubits, suppresses noise, and improves the manipulation accuracy and noise resistance of the two-bit gate.
Smart Images
Figure CN118469029B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of quantum bit preparation, and in particular to a method for preparing a high-fidelity two-bit gate. Background Art
[0002] When two quantum bits are coupled, a two-bit entanglement gate can be realized through appropriate control. Entanglement gate refers to a type of quantum gate operation that can produce a two-bit entangled state, which cannot be formed by simply two independent single-bit operations. Among them, the more common two-bit entanglement gate is the swap gate, which has the effect of swapping two-bit single excited states, that is, mapping |01〉 to |10〉, and |10〉 to |01〉. Another type is the controllable entanglement gate, which usually determines different operations on the target bit based on whether the control bit is in the |1〉 state.
[0003] For fault-tolerant quantum computers based on superconducting quantum circuits of Josephson junctions, how to maintain the coherence of quantum bits while still enabling high-fidelity two-bit gate manipulation between any two bits is a key and core issue. This issue includes two dimensions: quantum bit decoherence and two-bit gate manipulation. On the one hand, it is to suppress the dephasing of quantum bits, and on the other hand, it is to achieve noise-insensitive two-bit quantum gates.
[0004] The existing technology is based on an adjustable coupler and a fixed frequency bit architecture. The use of fixed frequency bits results in a loss of flexibility in the control of chip parameters. At the same time, the fine range of fixed frequency parameters leads to higher requirements for the consistency of micro-nano processing, which in turn limits the chip yield, resulting in limited scalability and scale. In addition, although the existing technology mostly uses traditional dynamic decoupling methods such as spin echo to extend the quantum bit dephasing time, most of them have not been integrated into the two-bit gate operation, resulting in the high-fidelity two-bit gate control noise cannot be effectively suppressed. Summary of the invention
[0005] The purpose of the present invention is to solve the shortcomings of the prior art and to propose a high-fidelity two-bit gate preparation method.
[0006] In order to achieve the above object, the present invention adopts the following technical solution: a method for preparing a high-fidelity two-bit gate, comprising the steps of:
[0007] S1: applying two continuously driven suppression noises with opposite phases and half the decoherence time to the two-bit gate within the decoherence time to decouple the quantum system from the environment;
[0008] S2: The two-bit gates interact with each other to form a waveform timing block and an accumulation phase, and buffer areas are respectively set before and after the interaction to form a first buffer area and a second buffer area;
[0009] S3: performing buffer amplitude calibration optimization at the first buffer region and the second buffer region to eliminate the accumulated phase and obtain an optimized two-bit gate.
[0010] As a further description of the above technical solution: in the step S1, it includes:
[0011] S11: When the two-qubit gate has no interaction, the Hamiltonian of a single qubit is determined by the first computational model, and the frequency corresponding to the energy level difference between the qubit ground state |0〉 and the excited state |1〉 is obtained;
[0012] S12: Under the external classical driving field, continuous driving causes the quantum bit to produce two dressed states, and the equivalent Hamiltonian is calculated based on the fluctuation of the quantum bit frequency caused by suppressing noise;
[0013] S13: Calculate the phase error between the two decorated states according to the equivalent Hamiltonian, and cancel it out through echo.
[0014] As a further description of the above technical solution: in the step S2, it includes:
[0015] S21: Under the Z pulse, the energy level of the two-bit gate is adjusted to resonant interaction to form the waveform timing block and the accumulation phase;
[0016] S22: applying a square wave of a Z pulse before and after the interaction through a digital-to-analog conversion module, forming the first buffer area and the second buffer area on both sides of the waveform timing block to offset the accumulated phase.
[0017] As a further description of the above technical solution: in the step S3, it includes:
[0018] S31: fixing the time length of the first buffer region, adjusting the voltage amplitude of the second buffer region to 0, preparing the first quantum bit to a superposition state through a rotating gate, and then adjusting the voltage amplitude of the first buffer region;
[0019] S32: adjusting the energy levels of the two qubits to resonate with each other, applying a rotating gate to the second qubit to obtain |01〉, scanning the voltage amplitude of the first buffer region, and selecting the point with the largest probability of |01〉 as the voltage amplitude of the first buffer region;
[0020] S33: Fix the voltage amplitude of the first buffer region, prepare the second quantum bit to a superposition state, apply a rotating gate to the first quantum bit to obtain |10〉, scan the voltage amplitude of the second buffer region, and select the point with the largest probability of |10〉 as the voltage amplitude of the second buffer region.
[0021] As a further description of the above technical solution: the spectrum range for suppressing noise is less than 100 MHz.
[0022] As a further description of the above technical solution: the first calculation model calculates the Hamiltonian of a single quantum bit, and the algorithm formula is as follows:
[0023] ;
[0024] in, is the frequency corresponding to the energy level difference between the quantum bit |1〉 state and |0〉 state, is the quantum bit raising operator, is the reduction operator of the quantum bit, is the driving amplitude, is the driving frequency, is the driving phase, N is the frequency fluctuation of the quantum bit that describes the suppression of noise, is the reduced Planck constant, and t is the time.
[0025] As a further description of the above technical solution: continuous driving causes the quantum bit to produce two dressed states as follows:
[0026] ;
[0027] ;
[0028] If N is less than the drive amplitude , suppressing the noise will not cause the quantum system to transition between the two dressed state energy levels, resulting in a frequency shift between the two dressed states. The equivalent Hamiltonian is:
[0029] ;
[0030] Decoupling quantum systems from their environment.
[0031] As a further description of the above technical solution: the phase error of the equivalent Hamiltonian between the decoherence times [t1, t2] is:
[0032] ;
[0033] By means of echo, the phase of the noise suppression is flipped by π in the middle of [t1, t2], making the decorated state Energy level inversion occurs, making ≈0.
[0034] As a further description of the above technical solution: the energy levels of the two quantum bits are adjusted to a resonant interaction time of: ;
[0035] Where g is the coupling strength between two bits.
[0036] As a further description of the above technical solution: preparing the first quantum bit to a superposition state , adjust the energy levels of the two qubits to resonate and interact for t time to complete the iSWAP gate, and obtain .
[0037] The above technical solution has the following advantages or beneficial effects:
[0038] 1. Use continuous driving with opposite phases for half the duration to suppress noise and extend the dephasing time of superconducting quantum bits. At the same time, in order to correct the phase error caused by deviation from the microwave reference system, a Z pulse buffer area is applied before and after the interaction of the timing waveform blocks to offset it. Combined with the optimization of the two-bit parameter calibration technology, a high-fidelity two-bit gate is obtained experimentally. The noise can be effectively suppressed and the dephasing time can be greatly extended. BRIEF DESCRIPTION OF THE DRAWINGS
[0039] Figure 1 The process of the preparation method proposed by the present invention Figure 1 ;
[0040] Figure 2 The process of the preparation method proposed by the present invention Figure 2 ;
[0041] Figure 3 The process of the preparation method proposed by the present invention Figure 3 ;
[0042] Figure 4 The process of the preparation method proposed by the present invention Figure 4 ;
[0043] Figure 5 A schematic diagram of quantum bit decoupling in the present invention;
[0044] Figure 6 Schematic diagram of quantum bit pulse in the present invention. DETAILED DESCRIPTION
[0045] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. 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 creative work are within the scope of protection of the present invention.
[0046] Reference Figure 1 , an embodiment of the present invention provides: a method for preparing a high-fidelity two-bit gate, comprising the steps of:
[0047] S1: Apply two continuous driving suppression noises with half the decoherence time and opposite phases to the two-bit gate within the decoherence time to decouple the quantum system from the environment;
[0048] S2: interacting the two-bit gates to form a waveform timing block and an accumulation phase, and setting buffer areas before and after the interaction to form a first buffer area and a second buffer area;
[0049] S3: Optimize the buffer amplitude calibration at the first buffer region and the second buffer region to eliminate the accumulated phase and obtain an optimized two-bit gate.
[0050] In this embodiment, noise is suppressed by continuous driving with opposite phases for half the duration, and the suppressed noise is a continuous timing pulse signal, which prolongs the dephasing time of the superconducting quantum bit. At the same time, in order to correct the phase error caused by deviation from the microwave reference system, a Z pulse buffer area is applied before and after the interaction of the timing waveform blocks to offset it. Combined with the two-bit parameter calibration technology optimization, a high-fidelity two-bit gate is obtained experimentally, the noise can be effectively suppressed, and the dephasing time can be greatly extended.
[0051] Reference Figure 2 , in step S1, comprising:
[0052] S11: When the two-qubit gate has no interaction, the Hamiltonian of a single qubit is determined by the first computational model, and the frequency corresponding to the energy level difference between the qubit ground state |0〉 and the excited state |1〉 is obtained;
[0053] S12: Under the external classical driving field, continuous driving causes the quantum bit to produce two dressed states, and the equivalent Hamiltonian is calculated based on the fluctuation of the quantum bit frequency caused by suppressing noise;
[0054] S13: Based on the equivalent Hamiltonian, the phase error between the two decorated states is calculated and offset by echo.
[0055] The inventors found in their research that for superconducting quantum bits, the main source of dephasing is low-frequency noise whose intensity is inversely proportional to the frequency, generally called Noise. This type of noise causes the phase of the quantum state to decay in the form of a Gaussian function over time, with the decay time scale being In traditional experiments, It is usually calibrated using a free-evolution Ramsey interferometer experiment.
[0056] In this embodiment, in order to extend the dephasing time of the superconducting quantum bit, we cleverly designed the pulse sequence to connect the two The time between pulses is The free evolution of is replaced by a continuous drive with an intermediate anti-phase, such as Figure 5 As shown, the interaction term has an effect on the quantum system over a period of time. The average value of the effect produced is zero, that is, , making it have a better suppression effect on the dephasing dominated by higher-frequency noise. The equivalent result is that the quantum system is "decoupled" from the external environment and the noise is "suppressed".
[0057] certainly, This is an ideal situation. In non-ideal situations, the noise suppression is distributed in various spectrum bands. The above method is often only effective for suppressing noise in a part of the spectrum range (less than 100MHz), and cannot completely offset all the effects. For example, for the energy relaxation process of quantum bits that have energy exchange processes with the external environment, the noise frequency is very high and the bandwidth is very narrow, so this method is difficult to work. On the contrary, the main factors that affect the dephasing of superconducting quantum bits are Low-frequency noise, and there is no energy exchange with the external environment in this process. This method often has a better effect. Compared with the free evolution in the Ramsey interference experiment, it increases the dephasing time by about an order of magnitude.
[0058] In the case of no interaction between quantum bits, the specific principle of using continuous drive to suppress noise is as follows: Under the action of the external classical driving field, the Hamiltonian of a single quantum bit can be expressed as:
[0059] ;
[0060] in, is the frequency corresponding to the energy level difference between the quantum bit |1〉 state and |0〉 state, is the quantum bit raising operator, is the reduction operator of the quantum bit, is the driving amplitude, is the driving frequency, is the driving phase, N is the frequency fluctuation of the quantum bit that describes the suppression of noise, is the reduced Planck constant, and t is the time.
[0061] Assume that the drive frequency , at the quantum bit frequency In the rotating reference frame, the Hamiltonian can be simplified to:
[0062] ;
[0063] Continuous driving causes the quantum bit to produce two dressed states as follows:
[0064] ;
[0065] ;
[0066] The energy level difference between them is . In a decorative state is the new basis vector, the Hamiltonian can be re-expressed as:
[0067] ;
[0068] Assume that the suppression noise is a low-frequency noise with a very long correlation length, much larger than the system dynamics time scale. , then, relative to the Rabi oscillation caused by the drive, its effect can be regarded as an adiabatic process. At the same time, if N is smaller than the amplitude of the drive , suppressing noise will not cause the quantum system to transition between the two dressed state energy levels. The final effect is a frequency shift between the dressed states, and the equivalent Hamiltonian is:
[0069] ;
[0070] The above formula shows that the equivalent coupling between the quantum bit and the environment under the effect of the driven suppression noise is Compared with the undriven is reduced, and the suppressed noise of the microwave drive applied to the qubit causes the qubit to be decoupled from the external environment.
[0071] At the same time, the phase error of the equivalent Hamiltonian between the decoherence times [t1, t2] is:
[0072] ;
[0073] It is worth noting that compared with the case without driving, the phase error accumulated during the evolution process is The value of is independent of the sign direction of the suppressed noise N, which enables further cancellation of the phase error by means of an echo: in the middle of the decoherence time [t1, t2], the phase of the external drive is flipped by π, so that the decorated state Energy level flip occurs. In this case, the accumulated phase error can be expressed as:
[0074]
[0075] At this point, define Assume N 2 The means of the first and second half are and , then:
[0076]
[0077] For the suppression noise that changes slowly over time, that is, , the phase error accumulated in the first and second half can be almost completely offset, making the phase error ≈0, thus using dynamic decoupling to suppress noise and extend the dephasing time of the superconducting quantum bit.
[0078] Reference Figure 3 and Figure 6 , in step S2, including:
[0079] S21: Under the Z pulse, the energy level of the two-bit gate is adjusted to resonant interaction, forming waveform timing blocks and accumulation phases;
[0080] S22: Applying a square wave of a Z pulse before and after the interaction through a digital-to-analog conversion module to form a first buffer area and a second buffer area on both sides of the waveform timing block to offset the accumulated phase.
[0081] In this embodiment, in order to obtain a two-qubit entangled gate, such as an iSWAP gate, the energy levels of the two qubits need to be adjusted to resonant interaction by a Z pulse, and the result is , where g is the coupling strength between the two bits, so that |01〉 is completely converted into |10〉. However, when the quantum bits interact with each other, they have actually deviated from the original microwave reference frame, that is, the two quantum bits belong to different microwave reference frames, which will accumulate the dynamical phase.
[0082] Therefore, in this process, the phase is accumulated due to the different rotation speeds of the two microwave reference frames. Thus, in order to prepare a complete two-bit entangled gate, the corresponding waveform timing block adds a Z pulse buffer area before and after the interaction to offset the phase generated by the above reasons.
[0083] The buffer area is a square wave that is maintained for a certain period of time and is completed by the digital-to-analog conversion module DAC. The DAC outputs this waveform before and after the interaction in the waveform timing block to form the first buffer area and the second buffer area to offset the accumulated phase.
[0084] Reference Figure 4 , in step S3, including:
[0085] S31: fixing the time length of the first buffer region, adjusting the voltage amplitude of the second buffer region to 0, preparing the first quantum bit to a superposition state through a rotating gate, and then adjusting the voltage amplitude of the first buffer region;
[0086] S32: adjusting the energy levels of the two qubits to resonate with each other, applying a rotating gate to the second qubit to obtain |01〉, scanning the voltage amplitude of the first buffer region, and selecting the point with the largest probability of |01〉 as the voltage amplitude of the first buffer region;
[0087] S33: Fix the voltage amplitude of the first buffer region, prepare the second quantum bit to a superposition state, apply a rotating gate to the first quantum bit to obtain |10〉, scan the voltage amplitude of the second buffer region, and select the point with the largest probability of |10〉 as the voltage amplitude of the second buffer region.
[0088] In this embodiment, in order to correct various phase errors caused by deviation from the microwave reference system, it is necessary to perform buffer amplitude calibration optimization. For the optimization of the first buffer region amplitude, first fix its time length (5-10ns). , 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, and the first quantum bit is prepared to the superposition state through the rotation gate (R gate, microwave reference frame coordinates are [0, π / 2]) , then change the voltage amplitude of the first buffer region, and then adjust the energy levels of the first qubit and the second qubit to resonate and interact for a period of time to complete the iSWAP gate. If the iSWAP gate has no errors, we get Finally, a rotation gate (R gate, microwave reference frame coordinates are [π / 2, π / 2]) is applied to the second qubit to obtain |01〉. Therefore, scanning the voltage amplitude of the first buffer region will observe oscillations between |00〉 and |01〉. When it can offset part of the phase error, the probability of |01〉 will be maximized.
[0089] At the same time, if there are multiple qubits, after the first qubit is calibrated and before the second qubit, another phase will be accumulated for the same reason. , for correction 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 quantum bit is prepared to a superposition state through a rotating gate (R gate, microwave reference frame coordinates are [0, π / 2]), and finally the first quantum bit is rotated by a rotating gate (R gate, microwave reference frame coordinates are [0, π / 2]) to scan the voltage amplitude of the second buffer region. In this way, oscillations between |00〉 and |10〉 are observed. The point with the maximum probability of |10〉 is selected as the voltage amplitude of the second buffer region, and parameter optimization is completed, so that a high-fidelity two-bit gate is obtained experimentally, laying the foundation for a universal quantum logic gate.
[0090] 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, it is still possible for those skilled in the art to modify the technical solutions described in the aforementioned embodiments or to 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 protection scope of the present invention.
Claims
1. A method for preparing a high-fidelity two-bit gate, characterized in that: Includes steps: S1: applying two continuously driven suppression noises with half the decoherence time and opposite phases to the two-bit gate within the decoherence time to decouple the quantum system from the environment; S2: The two-bit gates interact with each other to form a waveform timing block and an accumulation phase, and buffer areas are respectively set before and after the interaction to form a first buffer area and a second buffer area; S3: performing buffer amplitude calibration optimization at the first buffer region and the second buffer region to eliminate the accumulated phase and obtain an optimized two-bit gate; In the step S3, it includes: S31: fixing the time length of the first buffer region, adjusting the voltage amplitude of the second buffer region to 0, preparing the first quantum bit to a superposition state through a rotating gate, and then adjusting the voltage amplitude of the first buffer region; S32: adjusting the energy levels of the two qubits to resonate with each other, applying a rotating gate to the second qubit to obtain |01〉, scanning the voltage amplitude of the first buffer region, and selecting the point with the largest probability of |01〉 as the voltage amplitude of the first buffer region; S33: Fix the voltage amplitude of the first buffer region, prepare the second quantum bit to a superposition state, apply a rotating gate to the first quantum bit to obtain |10〉, scan the voltage amplitude of the second buffer region, and select the point with the largest probability of |10〉 as the voltage amplitude of the second buffer region.
2. The preparation method according to claim 1, characterized in that: In the step S1, it includes: S11: When the two-qubit gate has no interaction, the Hamiltonian of a single qubit is determined by the first computational model, and the frequency corresponding to the energy level difference between the qubit ground state |0〉 and the excited state |1〉 is obtained; S12: Under the external classical driving field, continuous driving causes the quantum bit to produce two dressed states, and the equivalent Hamiltonian is calculated based on the fluctuation of the quantum bit frequency caused by suppressing noise; S13: Calculate the phase error between the two decorated states according to the equivalent Hamiltonian, and cancel it out through echo.
3. The preparation method according to claim 1, characterized in that: In the step S2, it includes: S21: Under the Z pulse, the energy level of the two-bit gate is adjusted to resonant interaction to form the waveform timing block and the accumulation phase; S22: applying a square wave of a Z pulse before and after the interaction through a digital-to-analog conversion module, forming the first buffer area and the second buffer area on both sides of the waveform timing block to offset the accumulated phase.
4. The preparation method according to claim 1, characterized in that: The frequency spectrum range of the noise suppression is less than 100 MHz.
5. The preparation method according to claim 2, characterized in that: The first calculation model calculates the Hamiltonian of a single quantum bit, and the algorithm formula is as follows: ； in, is the frequency corresponding to the energy level difference between the quantum bit |1〉 state and |0〉 state, is the quantum bit raising operator, is the reduction operator of the quantum bit, is the driving amplitude, is the driving frequency, is the driving phase, N is the frequency fluctuation of the quantum bit that describes the suppression of noise, is the reduced Planck constant.
6. The preparation method according to claim 2, characterized in that: Continuous driving causes the quantum bit to produce two dressed states as follows: ； ； If N is less than the drive amplitude , suppressing the noise will not cause the quantum system to transition between the two dressed state energy levels, resulting in a frequency shift between the two dressed states. The equivalent Hamiltonian is: ； Decoupling quantum systems from their environment.
7. The preparation method according to claim 2, characterized in that: The phase error of the equivalent Hamiltonian between the decoherence times [t1, t2] is: ； By means of echo, the phase of the noise suppression is flipped by π in the middle of [t1, t2], making the decorated state Energy level inversion occurs, causing ≈0.
8. The preparation method according to claim 3, characterized in that: The energy levels of the two qubits are adjusted to a resonant interaction time of: ; Where g is the coupling strength between two bits.
9. The preparation method according to claim 1, characterized in that: Putting the first qubit into superposition , adjust the energy levels of the two qubits to resonate and interact for t time to complete the iSWAP gate, and obtain .