A calibration method for state leakage in the readout process of frequency-tunable qubits

Abstract

The present invention discloses a calibration method for state leakage in the reading process based on frequency-tunable qubits, which relates to the technical field of quantum computers. The qubits are respectively prepared into different energy level states and continuously read. Each read obtains the distribution of the classical AC signal on the IQ plane, and a probability table of each state of the qubit obtained by each read is obtained according to the distribution; a read tensor is defined, and a relationship equation between the tensor and the experimental value is listed using a recursive method; the probability table of each state of the qubit is substituted into the defined error function, and the minimum value point of the error function is found based on a classical optimization method, and the read tensor is returned; the state leakage rate caused by reading is calculated according to the returned read tensor; this calibration method for state leakage in the reading process can continuously measure state leakage with high precision and resist separation errors.

Description

Technical Field

[0001] The present invention relates to the technical field of quantum computers, and in particular to a method for calibrating the state leakage during the reading process of frequency-tunable qubits. Background Art

[0002] Quantum computers have attracted much attention because they have far more capabilities than classical computers in solving certain problems. Using superconducting quantum chips is a popular direction for realizing quantum computing. In superconducting quantum chips, the signal reading of qubits is an important part during the operation of the quantum chip. Only by converting the quantum signal of the qubit into classical information through a suitable method can we know the state of the qubit and perform the subsequent operations.

[0003] The currently common qubit reading scheme is an indirect measurement method. The main process is as follows: photons are input into the quantum chip. After these photons interact with the qubits, they are output from the quantum chip. After processing, the photons are converted into classical AC signals, and the complex plane of this classical AC signal is called the IQ plane. Ideally, when the qubit is in the 0 state, 1 state, 2 state or other higher energy states, the position of this AC signal on the IQ plane is different, so that the states of the qubits can be distinguished. However, due to the existence of noise, these classical signals will show a Gaussian distribution. When these Gaussian distributions overlap, errors will occur in distinguishing the states of the qubits, and this error is called separation error.

[0004] Since there is an interaction between photons and qubits during the reading process, there is a probability of exciting the qubits from the computable 0 state and 1 state to higher energy states that cannot be used, which is called state leakage. Therefore, it is necessary to quantitatively measure the degree of qubit leakage caused by reading.

[0005] The current measurement methods include the tensor method and the widely used continuous measurement method, specifically:

[0006] The paper "Marques JF et al. All-Microwave Leakage Reduction Units for Quantum Error Correction with Superconducting Transmon Qubits. Phys Rev Lett. 2023 Jun 23;130(25):250602. doi: 10.1103 / PhysRevLett.130.250602. PMID: 37418741" records the tensor method in the appendix of this paper.

[0007] The paper "Model-Based Optimization of Superconducting Qubit Readout" by Bengtsson A et al. in Phys Rev Lett. 2024 Mar 8;132(10):100603. doi: 10.1103 / PhysRevLett.132.100603. PMID: 38518348 records the continuous measurement method.

[0008] The tensor method has high precision and is not easily affected by separation errors. However, the tensor method cannot perform continuous measurement, so the state of the quantum chip after running for a period of time cannot be obtained. The continuous measurement method directly uses the probability of the qubit being in the high-energy level as the state leakage, can perform continuous measurement, but has low precision and is very easily affected by separation errors. How to find a method that can measure the state leakage continuously with high precision is an urgent problem to be solved. Summary of the Invention

[0009] Based on the technical problems existing in the background art, the present invention proposes a method for calibrating the state leakage in the readout process of frequency-tunable qubits, which can continuously measure the state leakage with high precision and resist separation errors.

[0010] A method for calibrating the state leakage in the readout process of frequency-tunable qubits proposed by the present invention includes:

[0011] Prepare the qubits to different energy level states respectively and perform continuous readout. Each readout obtains the distribution of the classical AC signal on the IQ plane, and obtains the probability table of each state of the qubit according to the distribution;

[0012] Define the readout tensor, and use the recursive method to list the relationship equation between the readout tensor and the experimental values;

[0013] Define the error function based on the relationship equation between the readout tensor and the experimental values, substitute the probability table of each state of the qubit into the error function, and return the readout tensor;

[0014] Calculate the state leakage rate caused by the readout according to the returned readout tensor.

[0015] Further, the relationship equation between the readout tensor and the experimental values is as follows:

[0016] ;

[0017] where the experimentally obtained probability index represents that the state of the initially prepared qubit is when the The state of the qubit read in the second read The probability of reading the tensor Indicates that the state of the qubit before a round of reading is When the read state is After reading, the state of the qubit is The probability of For the state of the initially prepared qubit being When the The state of the qubit read in the second read The probability of

[0018] Furthermore, the error function Is defined as follows:

[0019] ;

[0020] Among them, Indicates that the state of the initially prepared qubit is When the The state of the qubit read in the second read The probability of Is the total number of reads, Indicates that the state of the initially prepared qubit is When the The state of the qubit read in the second read The probability of Indicates that the state of the initially prepared qubit is When the state of the qubit read in the first read is The probability of Indicates that the state of the qubit before a round of reading is When the read state is After reading, the state of the qubit is The probability of For the state of the qubit before a round of reading being When the read state is After reading, the state of the qubit is The probability of

[0021] Furthermore, find the minimum point of the error function based on the classical optimization method, and use the minimum point as the read tensor closest to the experiment, and return the read tensor.

[0022] Furthermore, among the minimum points of the error function found based on the classical optimization method, find the minimum point of the error function through the minimize function in the scipy package of the python software.

[0023] Further, when the qubits are respectively prepared in the 0, 1, and 2 states, the state leakage rate is calculated as follows:

[0024] ;

[0025] where is the probability that when the state of the qubit before a round of reading is 0, the read state is and the state of the qubit after reading is 2, and is the probability that when the state of the qubit before a round of reading is 1, the read state is and the state of the qubit after reading is 2.

[0026] Further, when using the recursive method to list the relationship equations between the read tensor and the experimental values, 9 probability indicators are obtained for each additional reading, thereby increasing 9 relationship equations.

[0027] Further, each reading process is the same.

[0028] Further, the read tensor, as a parameter to be solved, has 27 unknowns.

[0029] The advantages of a method for calibrating the state leakage during the reading process of frequency-tunable qubits provided by the present invention are as follows: The method for calibrating the state leakage during the reading process of frequency-tunable qubits provided in the structure of the present invention, based on the recursive tensor method, measures the state leakage of qubits caused by the reading process, combines and improves the advantages of the tensor method and the continuous measurement method, can continuously measure the state leakage, resist separation errors, has higher precision, and does not significantly increase the computational amount of information processing. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a schematic flow chart of the present invention;

[0031] Figure 2 is a schematic diagram of the circuit used in the experiment;

[0032] Figure 3 is a schematic diagram of the IQ plane distribution and separation error;

[0033] Figure 4 is a schematic diagram of the probability distribution representation;

[0034] Figure 5 is a schematic diagram comparing the measurement accuracy of the recursive tensor method with the existing tensor method. DETAILED DESCRIPTION OF THE INVENTION

[0035] Next, the technical solutions of the present invention will be described in detail through specific embodiments. Many specific details are set forth in the following description in order to fully understand the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without departing from the connotation of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed below.

[0036] As Figures 1 to 5 shown, a method for calibrating the state leakage during the reading process of frequency-tunable qubits proposed by the present invention includes the following steps:

[0037] S1. Prepare the qubits into different energy level states respectively and perform continuous readings. Each reading obtains the distribution of the classical AC signal on the IQ plane, and a probability table of each state of the qubit is obtained according to the distribution; for the acquisition of the probability table, the existing method can be used.

[0038] S2. Define the reading tensor and use the recursive method to list the relationship equation between the tensor and the experimental values;

[0039] In this embodiment, taking the preparation of the qubits into states 0, 1, and 2 respectively as an example, the reading tensor is defined as the probability that the state of the qubit before a round of reading is , the state read is , and the state of the qubit after reading is . Each state can take 0, 1, or the high energy level 2. Therefore, the reading tensor actually has 27 unknowns, and the reading tensor is the parameter to be solved. Define the experimentally obtained probability index as the probability that the initial state of the prepared qubit is , and the state of the qubit read at the th reading is . Therefore, with the different values of and , 9 probability indexes can be obtained in each round of reading. Since the reading process in each round is the same, it is not necessary to distinguish the reading tensor according to the number of reading rounds. Through definition, there are the following formulas:

[0040] ;

[0041] ; ......;

[0043] Among them, represents the probability that when the state of the qubit before a round of reading is , the state read is , and the state of the qubit after reading is ; When the state of the qubit before a round of readout is the state read is and the state of the qubit after readout is the probability; When the state of the qubit before a round of readout is the state read is and the state of the qubit after readout is the probability; When the state of the initially prepared qubit is the probability that the state of the qubit read for the first time is ; When the state of the initially prepared qubit is the probability that the state of the qubit read for the second time is .

[0044] By substituting the readout tensor in the probability index formula for the second readout with the probability index of the first time, a new formula for the second readout can be obtained:

[0045] ;

[0046] This is a recurrence formula, which is relatively easy to directly generalize to the recurrence formula for the th readout:

[0047] ;

[0048] where is the probability that when the state of the initially prepared qubit is the state of the qubit read at the th readout is .

[0049] S3. Substitute the probability table of each state of the qubit into the defined error function, find the minimum point of the error function based on the classical optimization method, and return the readout tensor;

[0050] In S2, each additional readout will obtain 9 probability indices, thus increasing 9 equations. Since there are only 27 unknowns, the classical optimization method is used to calculate the minimum difference between the readout tensor and the experimental data. Define the error function:

[0051] ;

[0052] where represents the probability that when the state of the initially prepared qubit is the state of the qubit read at the th readout is , Indicates the probability that when the initial prepared state of the qubit is , the state of the qubit read at the -th read is . Indicates the probability that when the initial prepared state of the qubit is , the state of the qubit read at the 1st read is . Indicates the probability that when the state of the qubit before a round of reading is , the state read is , and the state of the qubit after reading is . Is the probability that when the state of the qubit before a round of reading is , the state read is , and the state of the qubit after reading is .

[0053] Using a classical optimization algorithm to find the minimum value point can return the read tensor that is closest to the experiment. Since the number of unknowns is fixed at 27, and the equations obtained in each read use actual experimental data to reduce the computational amount, the computational amount does not increase significantly as the number of reads increases.

[0054] S4. Calculate the state leakage rate caused by reading according to the returned read tensor :

[0055] ;

[0056] where is the probability that when the state of the qubit before a round of reading is 0, the state read is , and the state of the qubit after reading is 2, is the probability that when the state of the qubit before a round of reading is 1, the state read is , and the state of the qubit after reading is 2.

[0057] According to steps S1 to S4, for a qubit that needs to calibrate the state leakage caused by reading, prepare the qubit into different quantum states, perform multiple rounds of reading experiments, and obtain the IQ plane distribution of each round of reading. Obtain a probability distribution table according to this IQ plane distribution (such as Figure 4 ). Substitute the data in the probability distribution table into the error function. Use the minimize function in the scipy package of the python software to find the minimum value point of the error function and return the found read tensor Calculate the final state leakage rate based on the read tensor, where the minimize function is used to find the minimum value of a given function, and the scipy package is for scientific computing.

[0058] According to steps S1 to S4, through the read process state leakage calibration method provided in this embodiment, the advantages of the tensor method and the continuous measurement method can be integrated. It can measure the state leakage caused by multiple rounds of reading, can resist separation errors, and at the same time, due to the ability to perform continuous measurement, the measurement accuracy is greatly improved compared with the tensor method (the standard deviation is only 22% of the original), as Figure 5 shown.

[0059] Experiment 1: Test whether the recursive tensor method can perform multi-round measurements;

[0060] The IQ ball test of multi-round reading was carried out on 17 qubits, that is, the classical AC signal after preparing the qubits to different states in the background technology. When the reading intensity is increased, it can be clearly seen that the 1 state in part of the IQ plane is excited to the 2 state. The recursive tensor method was used to test the continuous reading situation and compared with the IQ of multi-round reading, and the two were completely consistent. It can be confirmed that the recursive tensor method can be used to test multi-round reading both theoretically and experimentally.

[0061] Experiment 2: Test whether the recursive tensor method can reduce errors;

[0062] A comparative test of the tensor method and the recursive tensor method was carried out on the selected 17 qubits. The selected number of reading rounds is 8. Theoretically, as the number of reading rounds increases, the error of the recursive tensor method will become smaller. When the number of rounds is equal to 8, the state leakage of 17 qubits is serially tested, and the processed data is as Figure 5 shown. It can be confirmed both theoretically and experimentally that the recursive tensor method can reduce the calibration error of reading state leakage. Five repeated experiments were carried out. In the five experiments, the data of the recursive tensor method had a lower standard deviation than the tensor method. The specific standard deviation transformation is shown in Table 1 below;

[0063] Table 1

[0064]

[0065] In Table 1, taking the worst experiment of the recursive tensor method as an example, the recursive tensor method can reduce the standard deviation to less than 22% of the original. The experimental results meet the expectations.

[0066] Experiment 3: Test whether the recursive tensor method can resist separation errors:

[0067] In theory, when the read fidelity of the recursive tensor method is above 75% (equivalent to a separation error within 0.25), it is not easily interfered by separation errors. To check whether it can resist separation errors, 17 qubits were selected, and the attenuator on the read microwave line was manually increased. This does not affect the true value of the read state leakage, but will gradually increase the separation error of the read. With other conditions remaining the same, for each additional set of attenuators, the recursive tensor method was used serially to test the state leakage caused by each read. The average leakage rate and read separation error are shown in Table 2 below;

[0068] Table 2

[0069]

[0070] As can be seen from Table 2, when the separation error is less than 0.25, as the separation error increases, the average state leakage obtained by testing with the recursive tensor method remains basically unchanged, that is, the recursive tensor method can resist separation errors. And all current experiments do not involve cases where the separation error is outside 0.25 (which means the performance of the quantum computer is very poor and the computer can hardly be used). Therefore, in the normal usage state, the recursive tensor method can better resist separation errors.

[0071] Experiment 4: Test the calculation duration of the recursive tensor method;

[0072] This part only has qualitative analysis. Since there are only 27 variables in the recursive tensor method, the same as the tensor method, it is inferred that there is no obvious difference in the optimization duration, and it may increase slightly due to the increase in the number of equations. There is no quantitative theoretical result because the optimization duration of the classical optimization algorithm is not fixed and can only be verified through experiments.

[0073] 17 qubits were selected, 20 groups of test data were selected. The results of the first two rounds of reads were used to test the state leakage with the tensor method, and the results of all 20 rounds of reads were used to test the state leakage with the recursive tensor method. The number of repeated calculations was 100,000 times. The specific time used is shown in Table 3;

[0074] Table 3

[0075]

[0076] As can be seen from Table 3, the experimental results meet the expectations. The data calculation duration of the recursive tensor method has no obvious improvement compared with the tensor method (the average increase is 1.53%, which has basically no impact), that is, the recursive tensor method does not significantly increase the amount of computation for information processing.

[0077] Experimental conclusion: The recursive tensor method can integrate the advantages of the tensor method and the continuous measurement method. It can measure the state leakage caused by multiple rounds of readings, can resist separation errors, and at the same time, due to the ability to perform continuous measurements, the measurement accuracy has been greatly improved compared with the tensor method (the measured standard deviation is at most only 22% of the original).

[0078] The above are only the preferred specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention, according to the technical solution and inventive concept of the present invention, making equivalent replacements or changes, shall be covered by the protection scope of the present invention.

Claims

1. A method for calibrating state leakage during reading based on frequency-adjustable quantum bits, characterized in that: include: The qubits are prepared to different energy levels and read continuously, and the distribution of the classical AC signal on the IQ plane is obtained each time the qubits are read, and a probability table of each state of the qubit is obtained each time the qubits are read according to the distribution; Define the read tensor and use the recursive method to list the relationship equation between the read tensor and the experimental value; Define the error function based on the relationship equation between the read tensor and the experimental value, substitute the probability table of each state of the quantum bit into the error function, and return the read tensor; Calculate the state leakage rate caused by reading based on the returned read tensor; The relationship equation between the read tensor and the experimental value is as follows: ； Among them, the probability index obtained by the experiment The state of the initially prepared quantum bit is At that time, The quantum bit state read out The probability of reading the tensor Indicates that the state of the quantum bit before a round of reading is When the status is read , the state of the quantum bit after reading is The probability of The state of the initial prepared quantum bit is At that time, The quantum bit state read by the probability.

2. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 1, characterized in that: Error function The definition is as follows: ； in, The state of the initially prepared quantum bit is At that time, The quantum bit state read by the The probability of is the total number of reads, The state of the initially prepared quantum bit is At that time, The quantum bit state read by the The probability of The state of the initially prepared quantum bit is When the quantum bit state is read for the first time The probability of Indicates that the state of the quantum bit before a round of reading is When the status is read , the state of the quantum bit after reading is The probability of The state of the quantum bit before a round of reading is When the status is read , the state of the quantum bit after reading is probability.

3. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 1, characterized in that: Based on the classical optimization method, the minimum point of the error function is found, the minimum point is used as the read tensor closest to the experiment, and the read tensor is returned.

4. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 3, characterized in that: Based on the classic optimization method, the minimum point of the error function is found, and the minimum point of the error function is found through the minimize function in the scipy package of the python software.

5. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 1, characterized in that: When the quantum bit is prepared to the 0, 1, and 2 states respectively, the state leakage rate The calculation formula is as follows: ； in, When the state of the quantum bit before one round of reading is 0, the state read is , the probability that the state of the qubit is 2 after reading, When the state of the quantum bit before one round of reading is 1, the state read is , the probability that the state of the quantum bit is 2 after reading.

6. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 1, characterized in that: When using a recursive method to list the relationship equations between the reading tensors and the experimental values, each additional reading obtains 9 probability indicators, thereby adding 9 relationship equations.

7. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 6, characterized in that: The reading process is the same every time.

8. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 6, characterized in that: Read the tensor as the parameter to be solved, there are 27 unknowns.

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