Reading process state leakage calibration method based on frequency-adjustable quantum bits

Abstract

The invention discloses a reading process state leakage calibration method based on frequency-adjustable quantum bits, and relates to the technical field of quantum computers, quantum bits are prepared to different energy level states and are continuously read, the distribution of classical alternating current signals on an IQ plane is obtained in each reading, and the distribution of the classical alternating current signals on the IQ plane is calculated. According to the distribution, obtaining a probability table of each state of the quantum bits read each time; a reading tensor is defined, and a relation equation between the tensor and the experimental value is listed by using a recursion method; substituting the probability table of each state of the quantum bits into a defined error function, finding out a minimum value point of the error function based on a classical optimization method, and returning to read a tensor; calculating a state leakage rate caused by reading according to the returned reading tensor; according to the reading process state leakage calibration method, state leakage can be continuously measured, the precision is high, and separation errors are resisted.

Description

Technical Field

[0001] The present invention relates to the field of quantum computer technology, and in particular to a method for calibrating state leakage during a reading process based on frequency-adjustable quantum bits. Background Art

[0002] Quantum computers have attracted much attention because they have the ability to solve certain problems far beyond that of classical computers. Using superconducting quantum chips is a popular direction for realizing quantum computing. In superconducting quantum chips, the signal reading of quantum bits is an important part of the quantum chip's operation. Only by converting the quantum signal of the quantum bit into classical information through appropriate methods can we know the state of the quantum bit and perform the next operation.

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

[0004] Since the reading process involves the interaction between photons and quantum bits, there is a probability that the quantum bits will be excited from the 0 and 1 states that can be used for calculation to a higher energy state that cannot be used. This is called state leakage. Therefore, it is necessary to quantitatively measure the extent of quantum bit leakage caused by reading.

[0005] The current measurement methods include tensor method and widely used continuous measurement method, specifically: The tensor method is described in the appendix of 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.

[0006] The paper Bengtsson A et al. Model-Based Optimization of Superconducting Qubit Readout. Phys Rev Lett. 2024 Mar 8;132(10):100603. doi: 10.1103 / PhysRevLett.132.100603. PMID: 38518348 describes the continuous measurement method.

[0007] The tensor method has high accuracy and is not easily affected by separation errors, but it cannot perform continuous measurements, and thus cannot obtain the state of a quantum chip after it has been running for a period of time. The continuous measurement method directly uses the probability of a quantum bit being at a high energy level as state leakage, which can be measured continuously, but has low accuracy and is very susceptible to separation errors. How to find a method that can measure state leakage with high accuracy and continuously is an urgent problem to be solved. Summary of the invention

[0008] Based on the technical problems existing in the background technology, the present invention proposes a state leakage calibration method for the reading process based on frequency-adjustable quantum bits, which can continuously measure state leakage with high accuracy and resist separation errors.

[0009] The present invention proposes a method for calibrating state leakage in a reading process based on frequency-adjustable quantum bits, comprising: 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; Compute the state leakage rate caused by the read based on the returned read tensor.

[0010] Furthermore, 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 by the 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.

[0011] Furthermore, the 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.

[0012] Furthermore, 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.

[0013] Furthermore, based on the classical 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.

[0014] Furthermore, 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.

[0015] Furthermore, when the recursive method is used to list the relationship equations between the reading tensors and the experimental values, 9 probability indicators are obtained for each additional reading, thereby increasing 9 relationship equations.

[0016] Furthermore, the reading process is the same every time.

[0017] Furthermore, the tensor is read as the parameter to be solved, and there are 27 unknowns.

[0018] The advantages of the state leakage calibration method for the reading process based on frequency-adjustable quantum bits provided by the present invention are: the state leakage calibration method for the reading process based on frequency-adjustable quantum bits provided in the structure of the present invention is based on the recursive tensor method, measures the quantum bit state leakage caused by the reading process, combines the advantages of the tensor method and the continuous measurement method and improves them, can continuously measure state leakage, resist separation errors, have higher accuracy, and do not significantly increase the amount of information processing operations. BRIEF DESCRIPTION OF THE DRAWINGS

[0019] Figure 1 It is a schematic diagram of the process of the present invention; Figure 2 Schematic diagram of the circuit used in the experiment; Figure 3 Schematic diagram of IQ plane distribution and separation error; Figure 4 Representing intentions for probability distributions; Figure 5 Schematic diagram comparing the measurement accuracy of the recursive tensor method with the existing tensor method. DETAILED DESCRIPTION

[0020] Below, the technical solution of the present invention is described in detail through specific embodiments. Many specific details are set forth in the following description to facilitate a full understanding of 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 violating the connotation of the present invention. Therefore, the present invention is not limited to the specific implementation disclosed below.

[0021] like Figures 1 to 5 As shown, the present invention proposes a method for calibrating state leakage in a reading process based on frequency-adjustable quantum bits, comprising the following steps: S1. Prepare the quantum bits to different energy levels and read them continuously. Each reading obtains the distribution of the classical AC signal on the IQ plane. According to the distribution, a probability table of each state of the quantum bit is obtained each time. The probability table can be obtained by using existing methods.

[0022] S2. define a reading tensor and use a recursive method to list the relationship equation between the tensor and the experimental value; In this embodiment, the quantum bits are prepared to the states 0, 1, and 2 respectively as an example to define the read tensor The state of the quantum bit before one round of reading is The status read is , the state of the bit after reading is The probability of each state can be 0, 1 or high energy level 2, so there are actually 27 unknowns in reading the tensor, and the reading tensor is the parameter that needs to be solved. Define the probability index obtained by the experiment The state of the initial prepared quantum bit is , No. The quantum bit state read out The probability of and Each round of reading can obtain 9 probability indicators. Since the reading process of each round is the same, there is no need to distinguish the read tensors according to the number of reading rounds. By definition, the following formula is obtained: ; ; ......; in, To indicate that the state of the quantum bit before one round of reading is When the status is read , the state of the quantum bit after reading is probability; The state of the quantum bit before one round of reading is When the status is read , the state of the quantum bit after reading is probability; The state of the quantum bit before one round of reading is When the status is read , the state of the quantum bit after reading is probability; The state of the initial prepared quantum bit is When the quantum bit state is read for the first time probability; The state of the initial prepared quantum bit is When the second reading is made, the quantum bit state is probability.

[0023] Replace the read tensor in the probability index formula of the second read with the probability index of the first read, and you can get a new formula for the second read: ; This is a recursive formula, which is easy to extend directly to the The recursive formula for reads: ; in, The state of the initial prepared quantum bit is At that time, The quantum bit state read out probability.

[0024] S3. Substitute the probability table of each state of the quantum bit into the defined error function, find the minimum point of the error function based on the classical optimization method, and return the read tensor; In S2, each additional reading will obtain 9 probability indicators, thus adding 9 equations. Since there are only 27 unknowns, the classic optimization method is used to calculate the minimum difference between the reading tensor and the experimental data. Define the error function: ; in, The state of the initially prepared quantum bit is At that time, The quantum bit state read out The probability of The state of the initially prepared quantum bit is At that time, The quantum bit state read out 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 one 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 one round of reading is When the status is read , the state of the quantum bit after reading is probability.

[0025] Finding with classical optimization algorithms The minimum point of the experiment can return the read tensor closest to the experiment Since the number of unknowns is fixed at 27 and the equations obtained at each reading use actual experimental data to reduce the amount of calculation, the amount of calculation does not increase significantly with the increase in the number of readings.

[0026] S4. Calculate the state leakage rate caused by reading based on the returned read tensor : ; 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.

[0027] According to steps S1 to S4, for a quantum bit that needs to be calibrated and read to cause state leakage, the quantum bit is prepared to different quantum states, and multiple rounds of reading experiments are performed to obtain the IQ plane distribution of each round of reading. According to the IQ plane distribution, a probability distribution table (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 point of the error function and return the found read tensor . The final state leakage rate is calculated 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.

[0028] According to steps S1 to S4, the reading process state leakage calibration method provided by this embodiment can combine the advantages of the tensor method and the continuous measurement method. It can measure the state leakage caused by multiple rounds of reading, resist separation errors, and because it can perform continuous measurement, the measurement accuracy is greatly improved compared with the tensor method (the standard deviation is only 22% of the original), such as Figure 5 shown.

[0029] Experiment 1: Test whether the recursive tensor method can perform multiple rounds of measurements; The IQ ball test of multiple rounds of reading was performed on 17 qubits, that is, the classical AC signal after the qubits were prepared to different states in the background technology. When the reading intensity was enhanced, it was obvious that the 1 state in some IQ planes was excited to the 2 state. The recursive tensor method was used to test the continuous reading situation and compare the IQ of multiple rounds of reading. The two are completely consistent. It can be confirmed that the recursive tensor method can be tested for multiple rounds of reading both theoretically and experimentally.

[0030] Experiment 2: Test whether the recursive tensor method can reduce the error; The tensor method and the recursive tensor method were compared on the 17 selected qubits. The number of reading rounds selected was 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 tested serially. The processed data is as follows Figure 5 As shown. It can be confirmed from both theory and experiment that the recursive tensor method can reduce the calibration error of read state leakage. Five repeated experiments were conducted. In all 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; Table 1

[0031] In Table 1, the worst performance of the recursive tensor method is shown in the experiment. The recursive tensor method can reduce the standard deviation to less than 22% of the original value. The experimental results are in line with expectations.

[0032] Experiment 3: Test whether the recursive tensor method can resist separation errors: Theoretically, the recursive tensor method is not easily disturbed by separation errors when the reading fidelity is above 75% (approximately equal to the separation error within 0.25). In order to check whether it can resist separation errors. 17 quantum bits were selected, and the attenuators on the reading microwave line were manually added. This does not affect the true value of the read state leakage, but will gradually increase the read separation error. The other conditions remain the same. Each time a set of attenuators is added, the recursive tensor method is used serially to test the state leakage caused by the read. The average leakage rate and read separation error are shown in Table 2 below; Table 2

[0033] 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 the recursive tensor method test remains basically unchanged, that is, the recursive tensor method can resist separation errors. However, all current experiments will not use the case where the separation error is beyond 0.25 (which means that the performance of the quantum computer is very poor and the computer is almost unusable), so under normal use, the recursive tensor method can resist separation errors well.

[0034] Experiment 4: Test the computation time of the recursive tensor method; This section only has qualitative analysis. Since the recursive tensor method has only 27 variables, which is the same as the tensor method, it is inferred that there is no significant difference in the optimization time, which may increase slightly due to the increase in the number of equations. There is no quantitative theoretical result because the optimization time of the classical optimization algorithm is not fixed and can only be tested through experiments.

[0035] 17 qubits and 20 test data sets were selected. The results of the first two rounds of reading were used to test the state leakage using the tensor method. The results of all 20 rounds of reading were used to test the state leakage using the recursive tensor method. The number of repeated calculations was 100,000. The specific time is shown in Table 3. Table 3

[0036] As can be seen from Table 3, the experimental results are in line with expectations. The data calculation time of the recursive tensor method is not significantly improved compared with the tensor method (an average increase of 1.53%, which is basically no effect), that is, the recursive tensor method does not significantly increase the amount of information processing operations.

[0037] Experimental conclusion: The recursive tensor method can combine the advantages of the tensor method and the continuous measurement method. It can measure the state leakage caused by multiple rounds of reading, resist separation errors, and because it can perform continuous measurements, the measurement accuracy is greatly improved compared to the tensor method (the maximum measured standard deviation is only 22% of the original).

[0038] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can make equivalent replacements or changes according to the technical scheme and inventive concept of the present invention within the technical scope disclosed by the present invention, which should 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; Compute the state leakage rate caused by the read based on the returned read tensor.

2. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 1, characterized in that: 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 by the 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.

3. 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.

4. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 2, 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.

5. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 4, 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.

6. 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.

7. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 2, 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.

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

9. The method for calibrating state leakage during reading process based on frequency-adjustable quantum bits according to claim 7, characterized in that: Read the tensor as the parameter to be solved, there are 27 unknowns.

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