CN109406875B - Quantum bit frequency calibration method based on Ramsey interference experiment - Google Patents

Quantum bit frequency calibration method based on Ramsey interference experiment Download PDF

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CN109406875B
CN109406875B CN201811196088.3A CN201811196088A CN109406875B CN 109406875 B CN109406875 B CN 109406875B CN 201811196088 A CN201811196088 A CN 201811196088A CN 109406875 B CN109406875 B CN 109406875B
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qubit
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孔伟成
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Origin Quantum Computing Technology Co Ltd
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Abstract

The present invention belongs toIn the technical field of quantum measurement and control, in particular to a method for carrying out quantum bit frequency calibration based on Ramsey interference experiments, which comprises the steps of carrying out N times of Ramsey interference experiments on quantum bits and recording results obtained according to each time of Ramsey interference experiments
Figure DDA0002594091430000011
Wherein: n is 1,2, … N, based on the N numbers
Figure DDA0002594091430000012
And corresponding
Figure DDA0002594091430000013
Performing linear fitting on the formed coordinate points in an orthogonal plane coordinate system to obtain a fitted linear equation; obtaining f according to the fitted linear equationqThe value is obtained. The precision of the finally obtained quantum bit frequency calibration value is effectively ensured by means of Ramsey interference experiments and data fitting.

Description

Quantum bit frequency calibration method based on Ramsey interference experiment
Technical Field
The invention belongs to the technical field of quantum measurement and control, and particularly relates to a method for carrying out quantum bit frequency calibration based on Ramsey interference experiments.
Background
Quantum computing has the potential to develop far beyond the performance of classical computers in solving specific problems. To implement a quantum computer, a quantum chip containing a sufficient number and quality of qubits is required, and extremely high fidelity operation and reading of the qubits is required. However, the qubit frequency parameter of the qubit fluctuates with the environment, and if such fluctuations are ignored, the fidelity of the operation of the quantum logic gate may be reduced, and the reading efficiency may also be affected. Therefore, the parameters of the quantum chip, especially the qubit frequency parameters, need to be calibrated regularly to ensure that the best performance, i.e., the best execution effect of the quantum algorithm, is exerted stably for a long time.
Generally, the acquisition method of the qubit frequency is to use a spectral measurement experiment. The qubit energy spectrum measurement experiment refers to applying a continuous frequency f to a qubitdThe qubit is caused to transition from the ground state to the excited state by the drive signal, and a read pulse signal is applied to the qubit after the drive signal is ended to obtain an excited state distribution probability P1 (f) of the qubitd) Dependent on the frequency f of the drive signaldThe variation relationship of (a). When the frequency f of the driving signaldAnd qubit frequency f0In close proximity, the qubit can be excited efficiently, resulting in a distribution of excited states P1 (f) for the qubitd) And is increased. And when the driving signal frequency is far away from the actual frequency of the qubit, P1 (f)d) Approaching 0. For the current 4-8GHz bandFor qubits, such as superconducting qubits, a qubit frequency f can be measured by a qubit energy spectrum measurement experiment using a high-performance qubit signal generation system and a high-performance qubit signal reception system0The error of (2) is controlled to be about 1 MHz.
Quantum bit frequency f obtained by existing energy spectrum measurement experiment0The error of (1) cannot meet the requirement of the frequency precision of the quantum bit at 1MHz, and the check requirement of the frequency of the quantum bit cannot be realized.
Disclosure of Invention
The invention aims to provide a method for calibrating a quantum bit frequency based on Ramsey interference experiments, which aims to overcome the defects in the prior art and can realize accurate calibration of the quantum bit frequency.
The technical scheme adopted by the invention is as follows:
a method for carrying out quantum bit frequency calibration based on Ramsey interference experiments comprises the following steps:
performing Ramsey interference experiments on the quantum bits for N times, and recording the Ramsey interference experiments obtained according to the result of each Ramsey interference experiment
Figure GDA0002594091420000021
Wherein: n is 1,2, … N,
Figure GDA0002594091420000022
the carrier frequency of the microwave pulse signal corresponding to the pi/2 quantum logic gate operation adopted by the nth Ramsey interference experiment,
Figure GDA0002594091420000023
the oscillation frequency of the quantum bit obtained from the nth Ramsey interference experiment, and
Figure GDA0002594091420000024
fqis the qubit frequency, N being a positive integer greater than 1;
according to N number of
Figure GDA0002594091420000026
And corresponding
Figure GDA0002594091420000025
Performing linear fitting on the formed coordinate points in an orthogonal plane coordinate system to obtain a fitted linear equation;
obtaining f according to the fitted linear equationqThe value is obtained.
The method for calibrating the qubit frequency based on the Ramsey interference experiment as described above, wherein preferably, the nth Ramsey interference experiment specifically includes:
applying two time intervals tau to qubits m timesmAnd obtaining two time intervals tau each time the qubit is appliedmAfter the two pi/2 quantum logic gates are operated, the probability P of the distribution of the excited state of the qubitfd(τm) (ii) a Wherein, taumA time interval for two pi/2 quantum logic gate operations applied to the qubit for the mth time, m being a positive integer greater than 1;
from P obtained for each measurementfd(τm) And τmTo carry out
Figure GDA0002594091420000029
Fitting a function to obtain
Figure GDA0002594091420000028
Wherein:
Figure GDA0002594091420000027
carrier frequency f of microwave pulse signal corresponding to pi/2 quantum logic gate operation adopted by nth Ramsey interference experiment0For oscillating frequency of qubits, T0And A and B are fitting coefficients.
The method for calibrating the qubit frequency based on the Ramsey interference experiment as described above, wherein preferably, the qubit frequency f is obtained when N Ramsey interference experiments are performed on the qubitqRemain unchanged.
Compared with the prior art, the invention carries out Ramsey interference experiments on the quantum bits for N times and records the result of each Ramsey interference experimentObtained
Figure GDA00025940914200000210
Then according to N
Figure GDA00025940914200000211
And corresponding
Figure GDA00025940914200000212
Performing linear fitting on the formed coordinate points in an orthogonal plane coordinate system to obtain a fitted linear equation; obtaining f according to the fitted linear equationqThe value is obtained. In the process, each Ramsey interference experiment can provide the precision of the quantum bit frequency, and on the basis, the result of each Ramsey interference experiment is further utilized to perform data fitting to reduce the experimental error, so that the finally obtained quantum bit frequency calibration value is effectively ensured.
Drawings
Fig. 1 is a flowchart of a method for performing a quantum bit frequency calibration based on a Ramsey interference experiment according to an embodiment of the present invention.
Detailed Description
The embodiments described below with reference to the drawings are illustrative only and should not be construed as limiting the invention.
Ramsey interferometry refers to the process of applying two pi/2 quantum logic gate operations to a qubit, separated by a time interval tau, while applying a read pulse to the qubit after a second pi/2 quantum logic gate operation to obtain the excited state distribution P1 (tau) of the qubit and varying the time interval tau to obtain P1 (tau).
The result of a typical Ramsey interferometric experiment is that P1(τ) is a mathematical model that satisfies exponential oscillation decay over time interval τ as follows:
Figure GDA0002594091420000031
in the above formula, A and B are fitting coefficients, T0Is the decoherence time of a qubit, fdIs piCarrier frequency, f of microwave pulse signal corresponding to/2 quantum logic gate operation0Is the oscillation frequency of the qubit, and f0With the true frequency f of the qubitqCarrier frequency f of pi/2 quantum logic gate operationdSatisfies the following conditions:
f0(fd)＝|fq-fd|
in conclusion we have reached another important conclusion: results of Ramsey interferometric experiments, i.e. P1The oscillation frequency of the (tau) curve is equal to the difference between the carrier frequency of the operation of the quantum logic gate and the actual frequency of the qubit, so that the Ramsey interference experiment can be used for accurately obtaining the actual frequency of the qubit in addition to the decoherence time of the qubit.
But still cannot directly realize the calibration of the frequency of the quantum bit by Ramsey interference experiments. This is due to the fact that the Ramsey experiment gives P1(τ) mathematical model expressions for exponential oscillation decay need to be obtained by mathematical fitting, and the accuracy of the mathematical fitting depends on P1(τ) accuracy of the raw data, thus fitting the resulting oscillation frequency f0And often inaccurate. In order to solve the problem and simultaneously realize the calibration of the qubit frequency by using the Ramsey interference experiment, an embodiment of the present application provides a method for calibrating the qubit frequency based on the Ramsey interference experiment, wherein the calibration method includes the following steps:
step S1:
performing Ramsey interference experiments on the quantum bits for N times, and recording the Ramsey interference experiments obtained according to the result of each Ramsey interference experiment
Figure GDA0002594091420000044
n＝1,2,…N，
Figure GDA0002594091420000043
The carrier frequency of the microwave pulse signal corresponding to the pi/2 quantum logic gate operation adopted by the nth Ramsey interference experiment,
Figure GDA0002594091420000045
the oscillation frequency of the qubit obtained for each Ramsey interference experiment, an
Figure GDA0002594091420000041
fqIs the qubit frequency, N being a positive integer greater than 1;
step S2: according to N number of
Figure GDA0002594091420000046
And corresponding
Figure GDA0002594091420000047
Performing linear fitting on the formed coordinate points in an orthogonal plane coordinate system to obtain a fitted linear equation;
step S3:
obtaining f according to the fitted linear equationqThe value is obtained.
In the implementation, through steps S1 to S3, Ramsey interference experiments are performed on the quantum bits for N times, and the Ramsey interference experiments obtained according to the results of each Ramsey interference experiment are recorded
Figure GDA0002594091420000048
Then according to N
Figure GDA0002594091420000049
And corresponding
Figure GDA0002594091420000042
Performing linear fitting on the formed coordinate points in an orthogonal plane coordinate system to obtain a fitted linear equation; obtaining f according to the fitted linear equationqThe value is obtained. In the process, each Ramsey interference experiment can provide the precision of the quantum bit frequency, on the basis, data fitting is further performed by using the result of each Ramsey interference experiment to reduce experimental errors, and the precision of the finally obtained quantum bit frequency calibration value is effectively ensured by means of the Ramsey interference experiment and the data fitting in the whole process.
As a preferred technical solution of this embodiment, the nth Ramsey interference experiment specifically includes:
(1) applying two time intervals tau to qubits m timesmAnd obtaining two time intervals tau each time the qubit is appliedmAfter the two pi/2 quantum logic gates are operated, the probability P of the distribution of the excited state of the qubitfd(τm) (ii) a Wherein, taumA time interval for two pi/2 quantum logic gate operations applied to the qubit for the mth time, m being a positive integer greater than 1;
(2) from P obtained for each measurementfd(τm) And τmTo carry out
Figure GDA00025940914200000410
Fitting a function to obtain
Figure GDA00025940914200000411
Wherein:
Figure GDA00025940914200000412
carrier frequency f of microwave pulse signal corresponding to pi/2 quantum logic gate operation adopted by nth Ramsey interference experiment0For oscillating frequency of qubits, T0And A and B are fitting coefficients.
The present embodiment will be described with reference to specific implementation processes, specifically:
a series of Ramsey interference experiments are carried out on the qubits, namely N times in the above embodiment, each time changing the carrier frequency f of the operation of the quantum logic gated(i.e., the carrier frequency of each quantum logic gate operation employed is
Figure GDA0002594091420000051
) Thereby obtaining a plurality of P1(τ) curves from each of which the oscillation frequency f can be obtained by fitting0(fd) (i.e. the
Figure GDA0002594091420000052
). It is clear that the qubit true frequency can be obtained due to the duration of the series of Ramsey interference experiments (typically not more than 1 hour)Considering the accuracy to be unchanged, the oscillation frequency f obtained by Ramsey interference experiment0(i.e. the
Figure GDA0002594091420000053
) The carrier frequency f necessarily operating with the quantum logic gatedIs varied and the relationship of the variation is f0(fd)＝|fq-fd|
Namely:
Figure GDA0002594091420000054
thus, f obtained by multiple Ramsey interference experiments0(fd) The curve is fitted by the expression, so that the real frequency f of the quantum bit can be accurately obtainedq. F is obtained by Ramsey interference experiment fitting0Change fdRepeating Ramsey interference to obtain f0(fd) (i.e. the
Figure GDA0002594091420000055
) And fitting again to obtain fqThe method can improve the precision of the actual frequency of the qubit to the level of 10kHz, and fully meets the requirement of people on the accurate actual frequency of the qubit. And the precision of the actual frequency of the quantum bit is further improved, and the integral improvement of the whole system is relied on to obtain P with smaller noise1The (τ) curve.
The above method is applicable to all cases where the qubit real frequency is almost constant during the series of Ramsey interference experiments (typically not more than 1 hour), especially in cases where there may be a slow time drift in the qubit real frequency (e.g. 1MHz for 1 day). The method can effectively realize the periodical recalibration of the actual frequency of the qubit.
The construction, features and functions of the present invention are described in detail in the embodiments illustrated in the drawings, which are only preferred embodiments of the present invention, but the present invention is not limited by the drawings, and all equivalent embodiments modified or changed according to the idea of the present invention should fall within the protection scope of the present invention without departing from the spirit of the present invention covered by the description and the drawings.

Claims (2)

1. A method for carrying out quantum bit frequency calibration based on Ramsey interference experiments is characterized by comprising the following steps:
performing Ramsey interference experiments on the quantum bits for N times, and recording the Ramsey interference experiments obtained according to the result of each Ramsey interference experiment
Figure FDA0002594091410000011
Wherein: n is 1,2, … N; wherein:
Figure FDA0002594091410000012
the carrier frequency of the microwave pulse signal corresponding to the pi/2 quantum logic gate operation adopted by the nth Ramsey interference experiment,
Figure FDA0002594091410000013
the oscillation frequency of the quantum bit obtained from the nth Ramsey interference experiment, and
Figure FDA0002594091410000014
fqis the qubit frequency, N being a positive integer greater than 1;
according to N number of
Figure FDA0002594091410000015
And corresponding
Figure FDA0002594091410000016
Performing linear fitting on the formed coordinate points in an orthogonal plane coordinate system to obtain a fitted linear equation;
obtaining f according to the fitted linear equationqThe value is obtained.
2. The method for performing quantum bit frequency calibration based on Ramsey interference experiments according to claim 1, wherein the nth Ramsey interference experiment specifically comprises:
applying two time intervals tau to qubits m timesmAnd obtaining two time intervals tau each time the qubit is appliedmAfter the two pi/2 quantum logic gates are operated, the probability P of the distribution of the excited state of the qubitfd(τm) (ii) a Wherein, taumA time interval for two pi/2 quantum logic gate operations applied to the qubit for the mth time, m being a positive integer greater than 1;
from P obtained for each measurementfd(τm) And τmTo carry out
Figure FDA0002594091410000017
Fitting a function to obtain
Figure FDA0002594091410000018
Wherein:
Figure FDA0002594091410000019
carrier frequency f of microwave pulse signal corresponding to pi/2 quantum logic gate operation adopted by nth Ramsey interference experiment0For oscillating frequency of qubits, T0And A and B are fitting coefficients.
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