A method for obtaining a threshold line for confirming the quantum state of a qubit

Abstract

This invention discloses a method for obtaining a threshold line to confirm the quantum state of a qubit, relating to the field of quantum measurement and control; applied to quantum chips, the method includes obtaining the center points and probability density distribution functions corresponding to two sets of quantum data spatial distributions; wherein the two sets of quantum data are qubit readout signal data when the qubit is in two different determined quantum states; the sum of the integrals of the two probability density distribution functions distributed over a set space is used as a fidelity function, the set space being two spaces divided by a threshold line; the threshold line is the perpendicular line connecting the two center points; the threshold line corresponding to the maximum or minimum value of the fidelity function is determined as the optimal threshold line; the threshold line established according to the method of this invention can provide a more accurate reference for determining unknown quantum states.

Description

[0001] This application is a divisional application filed on April 24, 2019, with application number 201910333092.8, and patent titled "A Method for Obtaining Threshold Lines to Confirm the Quantum State of a Quantum Bit". Technical Field

[0002] This invention belongs to the field of quantum measurement and control, and in particular, it is a method for obtaining a threshold line to confirm the quantum state of a qubit. Background Technology

[0003] Quantum bit information refers to the quantum state described by a quantum bit. The basic quantum states are the |0> state and the |1> state. After a quantum bit is manipulated, its quantum state changes. On a quantum chip, this is reflected in the quantum state described by the quantum bit after the quantum chip is executed, which is the execution result of the quantum chip. This execution result is carried and transmitted by the quantum bit read signal.

[0004] Rapidly analyzing the quantum state of a quantum bit through its readout signal is crucial for understanding the performance of a quantum chip. A previously filed patent provides a method for determining the quantum state of a quantum bit, which includes the following steps: obtaining the distribution patterns of the quantum bit readout signals in an orthogonal plane coordinate system corresponding to two different known quantum states of the quantum bit; obtaining the center positions of the two distribution patterns in the orthogonal plane coordinate system, and determining the perpendicular bisector of the line connecting the two center positions as the threshold dividing line; and using the threshold dividing line as the basis for determining the quantum state of the quantum bit.

[0005] The problem with existing technology is that, ideally, setting the threshold dividing line as the perpendicular bisector of the line connecting the center points of the two distribution patterns can meet the requirements most of the time. However, due to factors such as errors in the preparation of quantum states, the threshold line may contain errors that could affect the reading results of unknown quantum states. Summary of the Invention

[0006] The purpose of this invention is to provide a method for obtaining threshold lines for confirming the quantum state of a qubit, thereby overcoming the shortcomings of the prior art. This method can provide more accurate threshold dividing lines for use in quantum state resolution.

[0007] The technical solution adopted in this invention is as follows:

[0008] A method for obtaining a threshold line to confirm the quantum state of a qubit is applied to a quantum chip. This method obtains the center points and probability density distribution functions corresponding to two sets of quantum data spatial distributions. The two sets of quantum data are qubit readout signal data when the qubit is in two different defined quantum states. The sum of the integrals of the two probability density distribution functions distributed over a set space is used as a fidelity function. The set space consists of two spaces divided by the threshold line. The threshold line is the perpendicular line connecting the two center points. The threshold line corresponding to the maximum or minimum value of the fidelity function is determined as the optimal threshold line.

[0009] Optionally, the quantum bit readout signal data is coordinate point data in an orthogonal plane coordinate system; the two sets of quantum data are two sets of coordinate point data, denoted as the first set. Second set .

[0010] Optionally, acquiring qubit readout signal data when the qubit is in a defined quantum state includes: preparing the qubit into a defined quantum state and repeatedly measuring it to obtain multiple qubit readout signals; and converting each qubit readout signal into qubit readout signal data.

[0011] Optionally, obtaining the center points corresponding to the two sets of quantum data spatial distributions includes: fitting all coordinate points of the two sets of quantum data spatial distributions to obtain the coordinates of the first statistical center point of the corresponding fitted graph. and the first standard deviation Coordinates of the second statistical center point Second standard deviation .

[0012] Optionally, the fitting is a Gaussian fit.

[0013] Optionally, obtaining the probability density distribution functions corresponding to the spatial distributions of the two sets of quantum data includes: based on the coordinates of the first statistical center point. and the first standard deviation Determine the first probability density distribution function of all coordinate points of a set of quantum data in the IQ coordinate system. According to the coordinates of the second statistical center point and the second standard deviation Determine the second probability density distribution function of all coordinate points of another set of quantum data in the IQ coordinate system. .

[0014] Optionally, the first probability density distribution function Second probability density distribution function They are respectively:

[0015] in: ∈ ;

[0016] in: ∈ ;

[0017] The formula for determining the optimal threshold line is:

[0018] （1）。

[0019] Optionally, before obtaining the probability density distribution function, the method further includes: determining a first angle between the line connecting the two center points and any coordinate axis of the coordinate system in which the quantum data spatial distribution is located; rotating and updating the coordinates of the two center points in the coordinate system according to the first angle; and rotating and updating all coordinates of the two sets of quantum data according to the first angle.

[0020] Optionally, the coordinates of the two center points in the coordinate system are rotated and updated according to the first included angle; specifically, this includes: determining the first included angle as the angle between the line connecting the two center points and the I-axis of the IQ coordinate system; the two center points are respectively the coordinates of the first statistical center point. Second statistical center point coordinates Rotate the two center points clockwise according to the first included angle; update the coordinates of the first statistical center point. and the coordinates of the second statistical center point They are respectively , ,in: .

[0021] Optionally, when the updated coordinates of the first statistical center point... and the updated coordinates of the second statistical center point When the vertical axes are equal, the threshold line is a vertical threshold line perpendicular to the I-axis; determining the threshold line corresponding to the maximum or minimum value of the fidelity function is the optimal threshold line, specifically including: when the space to the right of the vertical threshold line is the updated coordinates of the first statistical center point. The space located to the left of the vertical threshold line is the coordinate of the second statistical center point. If the value of the fidelity function is the maximum value, then the threshold line corresponding to the maximum value of the fidelity function is determined as the optimal threshold line; otherwise, the threshold line corresponding to the minimum value of the fidelity function is determined as the optimal threshold line; wherein: the sum of the maximum value of the fidelity function and the minimum value of the fidelity function is 1.

[0022] Optionally, the sine value of the first included angle θ is:

[0023]

[0024] Optionally, the formula for calculating the optimal threshold line can be simplified to the following:

[0025]

[0026] make:

[0027]

[0028] in: The graph of the function is monotonically decreasing and intersects the I-axis, so solving equation (3) can be transformed into solving the following equation:

[0029]

[0030] The solution to equation (4) is a real number solution. Then the optimal threshold line is obtained. The expression is: .

[0031] Compared with existing technologies, this invention prepares two different quantum bit quantum states, namely a first quantum state and a second quantum state, and obtains two sets by performing a large number of repeated read operations. Gaussian fitting is then performed on each set to obtain the coordinates of the first and second statistical center points, their corresponding first and second standard deviations, and the corresponding first and second probability density distribution functions are determined. The resulting threshold line divides the coordinate system into a first space and a second space. The fidelity function is determined based on the sum of the integrals of the first probability density distribution function in the first space and the second probability density distribution function in the second space. When the fidelity function reaches its maximum value, the corresponding threshold line is the optimal threshold line. This invention first obtains quantum states through a large number of repeated read operations. Data on the quantum state of a qubit is obtained, and this data is subjected to Gaussian fitting by a computer. Based on the Gaussian fitting results, the probability density distribution functions are determined. The integral of each probability density distribution function distributed in the corresponding space is used as the fidelity function. When the fidelity function reaches its maximum value, it indicates that the threshold line used to divide the space provides the best fidelity for reading the qubit readout signal on both sides of the threshold line. Since the purpose of establishing the threshold line is to directly determine and obtain the quantum state of the qubit by the relationship between the position of the measurement result in the coordinate system and the threshold line in any subsequent single measurement, the threshold line established in this invention is based on the criterion that the optimal threshold line is the one that makes the fidelity function reach its maximum value. This can provide a more accurate reference for determining unknown quantum states. Attached Figure Description

[0032] Figure 1This is a flowchart of a method for obtaining a threshold line to confirm the quantum state of a quantum bit according to an embodiment of the present invention. Detailed Implementation

[0033] The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0034] Combined with appendix Figure 1 This invention provides a method for obtaining a threshold line for confirming the quantum state of a qubit, comprising the following steps:

[0035] The qubits are prepared into a first quantum state and repeatedly measured to obtain the coordinate points of multiple qubit read signals in an orthogonal plane coordinate system, denoted as the first set. The qubits are prepared into a second quantum state and repeatedly measured to obtain the coordinate points of multiple qubit read signals in an orthogonal plane coordinate system, denoted as the second set. Wherein: the first quantum state and the second quantum state are both known quantum states and are distinct from each other; wherein: the orthogonal plane coordinate system is set as the IQ coordinate system; specifically, any quantum state is represented in Hilbert space as follows: Here, |0> and |1> are two orthogonal basis vectors in the Hilbert space, corresponding to the first quantum state and the second quantum state described in this embodiment. Specifically, when the first quantum state is the quantum state |0>, then the second quantum state is |1>; or vice versa.

[0036] Gaussian fitting is performed on all coordinate points in the first set and all coordinate points in the second set to obtain the coordinates of the first statistical center point of the Gaussian fitted graphs for the first set and the second set, respectively. Second statistical center point coordinates The corresponding first standard deviations Second standard deviation Wherein: the IQ coordinate system is used to determine the coordinates of the first statistical center point. and the coordinates of the second statistical center point The straight line dividing the two spaces is denoted as the threshold line, and the threshold line is perpendicular to the coordinates of the first statistical center point. Second statistical center point coordinates The lines connecting the two spaces are denoted as the first space and the second space, respectively.

[0037] Based on the coordinates of the first statistical center point and the first standard deviation Determine the first probability density distribution function of all coordinate points in the first set in the IQ coordinate system. According to the coordinates of the second statistical center point and the second standard deviation Determine the second probability density distribution function of all coordinate points in the second set in the IQ coordinate system. ;

[0038] The fidelity function is determined to be the first probability density distribution function. The integral function in the first space and the second probability density distribution function The sum of integral functions in the second space;

[0039] The threshold line corresponding to the maximum or minimum value of the fidelity function is determined as the optimal threshold line.

[0040] The advantage of this invention lies in that, compared with the prior art, this invention prepares two different quantum states, namely a first quantum state and a second quantum state, and obtains two sets by performing a large number of repeated read operations. Gaussian fitting is then performed on each set to obtain the coordinates of the first and second statistical center points, their corresponding first and second standard deviations, and the corresponding first and second probability density distribution functions are determined. The resulting threshold line divides the coordinate system into a first space and a second space. The fidelity function is determined based on the sum of the integrals of the first probability density distribution function in the first space and the second probability density distribution function in the second space. When the fidelity function reaches its maximum value, the corresponding threshold line is the optimal threshold line. This invention first obtains the values ​​through a large number of repeated read operations. The data of a qubit in a defined quantum state are processed by a computer using Gaussian fitting. Based on the Gaussian fitting results, the probability density distribution functions are determined. The sum of the integrals of each probability density distribution function distributed in its corresponding space is used as the fidelity function. When the fidelity function reaches its maximum value, it indicates that the threshold line used to divide the space provides the best fidelity for reading the qubit readout signal on both sides of the threshold line. Since the purpose of establishing the threshold line is to directly determine and obtain the quantum state of the qubit by the relationship between the position of the measurement result in the coordinate system and the threshold line in any subsequent single measurement, the threshold line established in this invention is based on the criterion that the optimal threshold line is the one that makes the fidelity function reach its maximum value. This provides a more accurate reference for determining unknown quantum states.

[0041] Example 1

[0042] Specifically, in conjunction with the appendix Figure 1 Embodiment 1 of the present invention provides a method for obtaining a threshold line for confirming the quantum state of a qubit, comprising the following steps:

[0043] Step 10: Prepare the qubits into the first quantum state and repeatedly measure them to obtain the coordinate point data of multiple qubit read signals in an orthogonal plane coordinate system, denoted as the first set. The qubits are prepared into a second quantum state and repeatedly measured to obtain the coordinate points of multiple qubit read signals in an orthogonal plane coordinate system, denoted as the second set. Wherein: the first quantum state and the second quantum state are both known quantum states and are different from each other; and the orthogonal plane coordinate system is set as the IQ coordinate system.

[0044] Specifically, the first quantum state can be selected from The second quantum state can be selected from the state quantum state. The quantum state is defined as an orthogonal plane coordinate system, where I is the horizontal axis and Q is the vertical axis.

[0045] Specifically, the first set is denoted as the first set, which involves preparing the qubits into a first quantum state and repeatedly measuring them to obtain the coordinate points of the read signals of multiple qubits in an orthogonal plane coordinate system. The first set is obtained by acquiring and analyzing the quantum bit signal through a quantum bit signal readout device. The data in the first set is stored in the computer, and the same applies to the second set. The data is also stored in the computer;

[0046] Step 20: Perform Gaussian fitting on all coordinate points in the first set and all coordinate points in the second set respectively to obtain the coordinates of the first statistical center point of the Gaussian fitted graphs corresponding to the first set and the second set respectively. Second statistical center point coordinates The corresponding first standard deviations Second standard deviation Wherein: the IQ coordinate system is used to determine the coordinates of the first statistical center point. and the coordinates of the second statistical center point The straight line dividing the two spaces is denoted as the threshold line, and the threshold line is perpendicular to the coordinates of the first statistical center point. Second statistical center point coordinates The lines connecting the two spaces are denoted as the first space and the second space, respectively.

[0047] The Gaussian fitting of all coordinate points in the first set and all coordinate points in the second set is performed by a computer. The computer program then applies the Gaussian fit to the first set. Second set The data in the dataset is subjected to two-dimensional Gaussian fitting to obtain a two-dimensional Gaussian distribution graph, and the coordinates of the first statistical center point of the Gaussian fitting graphs corresponding to the first set and the second set are obtained respectively. Second statistical center point coordinates The corresponding first standard deviations Second standard deviation ;

[0048] Step 30: Based on the coordinates of the first statistical center point and the first standard deviation Determine the first probability density distribution function of all coordinate points in the first set in the IQ coordinate system. According to the coordinates of the second statistical center point and the second standard deviation Determine the second probability density distribution function of all coordinate points in the second set in the IQ coordinate system. ;

[0049] Wherein: the first probability density distribution function Second probability density distribution function They are respectively:

[0050] in: ∈ ;

[0051] in: ∈ ;

[0052] It should be noted that the above formula is the probability density function corresponding to the Gaussian distribution. This formula can be directly derived by fitting the first set and the second set using a computer. However, the first probability density function... Second probability density distribution function The conclusion is not limited to this method.

[0053] Step 40: Determine the fidelity function as the first probability density distribution function. The integral function in the first space and the second probability density distribution function The sum of integral functions in the second space;

[0054] Step 50: Determine the threshold line corresponding to the maximum value of the fidelity function as the optimal threshold line.

[0055] Wherein: the formula for calculating the optimal threshold line is:

[0056] （1）

[0057] By solving the above equation, we can obtain an expression for the optimal threshold line. Since satisfying this equation allows the sum of the fidelity on both sides of the threshold line to reach its maximum value, we can obtain the optimal threshold line required by this invention.

[0058] It should be noted that the statement that the fidelity function takes the maximum or minimum value only refers to the fidelity function taking the maximum or minimum value, where the coordinates of the first statistical center point are... Coordinates of the second statistical center point When on the right, the fidelity function needs to take its maximum value, when the coordinates of the first statistical center point are... Coordinates of the second statistical center point When on the left, the fidelity function needs to take its minimum value.

[0059] Example 2

[0060] It should be noted that, under the premise of satisfying the above two-dimensional double Gaussian distribution statistical model, the current threshold line obtained can be mathematically proven to be related to the coordinates of the first statistical center point. and the coordinates of the second statistical center point vertical.

[0061] The proof process is as follows:

[0062] Given:

[0063]

[0064]

[0065]

[0066] Let's assume that the final optimal threshold line is expressed as follows in the IQ coordinate system:

[0067] ,in ， ，

[0068] Obtain the angle φ between the optimal threshold line and the I-axis. Rotate all coordinate point data from the first and second sets clockwise by the angle φ around the origin in the IQ coordinate system. The updated coordinates of the first statistical center point... and the coordinates of the second statistical center point Recorded as , The expression for the optimal threshold line after rotation becomes Q = -c, and we assume that in the space Q ≤ -c... Where φ can be obtained by solving the following equation:

[0069] At this point, the space divided by Q=-c and the corresponding formula for calculating the fidelity are:

[0070]

[0071] Since the optimal threshold line is a straight line that maximizes fidelity, that is:

[0072]

[0073] That is:

[0074]

[0075] in:

[0076]

[0077]

[0078] The optimization method for the maximum value of the multivariate function g(a,b,c) is as follows: In this problem, the maximum value must exist, so we only need to solve for all the stationary points and then find the maximum value point among the stationary points.

[0079] Under constraints , , The stationary points can be solved using the Lagrange multiplier method:

[0080]

[0081] Where λ is an auxiliary parameter, that is:

[0082]

[0083]

[0084]

[0085] From the above system of equations, we can deduce that the stationary points satisfy: .

[0086] because The coordinates of the first statistical center point and the coordinates of the second statistical center point slope of the line , It is the slope of the optimal threshold line. That is Therefore, it is concluded that the optimal threshold line must be perpendicular to the line connecting the coordinates of the first and second statistical center points, thus concluding the proof.

[0087] Based on the above facts, the present invention also provides another embodiment, which, based on embodiment 1, further includes the following step before step 30:

[0088] Step 22: Based on the coordinates of the first statistical center point and the coordinates of the second statistical center point Determine the first angle between the line connecting the two and any coordinate axis of the IQ coordinate system;

[0089] Step 24: Rotate according to the first included angle and update the coordinates of the first statistical center point. and the coordinates of the second statistical center point ;

[0090] Step 26: Rotate according to the first included angle and update all coordinate points in the first set and all coordinate points in the second set.

[0091] By adopting the technical solution described above, this embodiment obtains the first included angle, then rotates and updates the coordinates of the first statistical center point based on the first included angle. and the coordinates of the second statistical center point The purpose of this rotation operation is to reduce the degrees of freedom of the fidelity function, thereby facilitating the calculation of the maximum and minimum values ​​of the fidelity function later.

[0092] Furthermore, the first included angle θ is the coordinate of the first statistical center point. and the coordinates of the second statistical center point The angle between the line connecting the two and the I-axis of the IQ coordinate system is used to rotate the coordinates of the first statistical center point clockwise based on the first angle θ. and the coordinates of the second statistical center point and all coordinate points in the first set and all coordinate points in the second set, wherein: the updated coordinates of the first statistical center point and the coordinates of the second statistical center point They are respectively , ,and By performing a rotation operation, the updated coordinates of the first statistical center point are obtained. Second statistical center point coordinates The Q components are equal, thus making the optimal threshold line parallel to the Q axis.

[0093] Preferably, the first included angle θ can be obtained by calculating the following formula:

[0094]

[0095] It should be noted that the method for obtaining the first included angle θ includes, but is not limited to, the methods described above.

[0096] Furthermore, the formula for calculating the optimal threshold line is:

[0097] （1）

[0098] The following transformations can be performed:

[0099] (2a)

[0100] Among them: considering the actual physical meaning Then equation (2a) becomes:

[0101]

[0102] make:

[0103]

[0104] in: The graph of the function is monotonically decreasing and intersects the I-axis. Therefore, according to the properties of integrals, solving equation (3) can be transformed into solving the following equation:

[0105]

[0106] The solution to equation (4) is a real number solution. Then the first threshold line is obtained. The expression is .

[0107] In particular, if = Therefore, the expression for the current threshold line is:

[0108] 。

[0109] Through the above embodiments, by rotating the current threshold line, the original threshold line is transformed into a straight line perpendicular to the Q axis, i.e., the first threshold line. This greatly simplifies the difficulty of solving the original equation (1) and improves the efficiency of obtaining the threshold line.

[0110] Example 3

[0111] It should be noted that repeatedly acquiring the data after analyzing the qubit read signal when the qubit is in the |0> state or the |1> state will result in different statistical data, leading to different coordinates of the first statistical center point of its two-dimensional double Gaussian distribution graph. and the coordinates of the second statistical center point It will fluctuate and change, but the distance between the two center coordinates, that is... First, the noise level remains unchanged; second, the noise level of the system does not change significantly and can still be approximated as... and Finally, the distribution of the qubit readout results in the iq coordinate system still follows a two-dimensional bigaussian statistical distribution. Under the premise that the above three conditions hold true, we can still use the same rotation transformation method as in Example 2 to transform the theoretical threshold line into a solution for a single variable, i.e.: In the form of. Furthermore, given that the above three conditions hold true, it can be mathematically proven that, It is a constant, and its value is only equal to... , as well as That is, the optimal threshold line The difference between the x-coordinate and the desired x-coordinate is a constant c.

[0112] The proof process is as follows:

[0113] It is known that the threshold line is perpendicular to the line connecting the coordinates of the center point. Furthermore, after the rotation operation, the following condition is met:

[0114]

[0115] Then if the coordinates of the first statistical center point are... and the coordinates of the second statistical center point The fluctuation and change are equivalent to needing to solve for the following:

[0116]

[0117] And due to It remains unchanged, therefore after the rotation transformation, we still have:

[0118]

[0119] Furthermore, since the purpose of rotation transformation is to make the line connecting the coordinates of the center point parallel to the I-axis, that is, to make... ,therefore:

[0120]

[0121] That is .

[0122] Compare the coordinates of the first statistical center point respectively and the coordinates of the second statistical center point The calculation process of equation (4) before and after the change of floating:

[0123] (Formula a)

[0124] (Formula b)

[0125] As can be seen from equations (a) and (b), the two equations, except for and Aside from the differences, the rest are completely identical (Note: Considering the actual constraint that the threshold line lies between the coordinates of the two center points, the sign does not affect the solution process and conclusion), therefore, there should be a solution of exactly the same form: .

[0126] The proof is complete.

[0127] Based on the above facts, and combined with the K-means clustering method in machine learning, this invention further proposes a method for obtaining a more reliable and updated threshold line;

[0128] The basic idea of ​​k-means clustering is to initialize k distinct centroids. Then iterate through the two different steps until convergence. Step one: Each training sample is assigned to the nearest centroid. The cluster represented by i. Step two, each center point The update is for all training samples in cluster i. The mean.

[0129] Therefore, based on Example 2, after obtaining the expression for the optimal threshold line, the following steps are also included:

[0130] Step 60: Repeatedly acquire the coordinate data of multiple coordinate points of the qubit read signal in the orthogonal plane coordinate system when the qubit is in a certain quantum state, and denote it as the third set;

[0131] Wherein: the repeated acquisition of multiple coordinate points of the qubit readout signal corresponding to a certain quantum state in an orthogonal plane coordinate system, denoted as the third set, refers to preparing a certain qubit to a certain quantum state, regardless of whether it is unknown, and repeatedly acquiring multiple coordinate points of the corresponding qubit readout signal in an orthogonal plane coordinate system, denoted as the third set. ;

[0132] Step 70: Rotate and update all coordinate point data in the third set according to the first included angle;

[0133] The purpose of rotating and updating all coordinate point data in the third set according to the first included angle θ is to make the third set... The data in the dataset is consistent with both the first and second sets.

[0134] Step 80: Set the optimal threshold line As the initial threshold line, set the termination condition;

[0135] Step 90: Use the initial threshold line to divide the third set into two clusters, namely the first cluster and the second cluster, counted n=1 times;

[0136] Specifically, using the initial threshold line Will Divided into two clusters and Counted times n=1;

[0137] Step 100: Perform an unweighted average of all coordinate point data in the first cluster and the second cluster to obtain the corresponding expected coordinates, namely the first coordinate and the second coordinate. Determine the second angle between the line connecting the first and second coordinates and any coordinate axis of the IQ coordinate system. Rotate and update all coordinate point data, the first coordinate, and the second coordinate in the first and second clusters by the second angle, wherein: the line connecting the updated first and second coordinates is parallel to the I-axis; wherein the third quantum state can be divided into two clusters by the initial threshold line, wherein the first quantum state is... The second quantum state is A state can be determined to be a mixture of the first and second quantum states.

[0138] Specifically, clustering and Each sample coordinate is averaged without weight to obtain the corresponding expected coordinate. as well as ;

[0139] Obtaining a second angle The second angle The sine value is:

[0140]

[0141] Clustering and All sample coordinates, the first coordinate, and the second coordinate are rotated clockwise around the origin in the IQ coordinate system by an angle. The purpose is to utilize the important property that the difference between the x-coordinate of the optimal threshold line and the desired coordinate is constant for subsequent calculations;

[0142] Step 110: Determine the update threshold line based on the initial threshold line and the second coordinates before and after the update, wherein: the expression of the update threshold line is the sum of the I-axis coordinate of the updated second coordinate and the expression of the initial threshold line minus the I-axis coordinate of the second coordinate before the update;

[0143] Specifically: At this point, obtain the update threshold line. Right now It will satisfy the following formula:

[0144] Where: c and d are both constants.

[0145]

[0146] Step 110, Right now Return to the execution step as the new initial threshold: Using the initial threshold as... Divided into two clusters and The number of times is n = n + 1;

[0147] Step 120: Stop execution until the termination condition is met, and determine the updated threshold line to be the required threshold line.

[0148] The above steps utilize the core idea of ​​the K-means clustering algorithm. A threshold line is used to divide a large cluster into two smaller clusters. The rotation angle is determined based on the expected coordinates of the two smaller clusters, and the large cluster is rotated clockwise. Then, the threshold line is redefined, and the large cluster is divided into two smaller clusters again. This process is repeated until the termination condition is met. It can be predicted that as the number of divisions increases, the distance between the expected center coordinates of the smaller clusters after being redefined by the new threshold line and the expected center coordinates of the smaller clusters after being divided by the previous threshold line will become smaller and smaller, that is, it will become more and more convergent. This indicates that the updated threshold line will get closer and closer to the theoretical threshold division line, that is, it will become more and more accurate.

[0149] Furthermore, step 80, setting the termination condition, specifically includes:

[0150] A maximum number of executions N is set. When n=N, execution stops. The maximum number of executions N is selected manually and can be determined based on the actual required running time. This allows for effective control of the execution time.

[0151] Furthermore, step 80, setting the termination condition, specifically includes:

[0152] Set a first threshold, wherein: the first threshold is selected according to the actual required processing precision;

[0153] Execution stops when the maximum value of the distance between the first coordinates before and after the update and the distance between the second coordinates before and after the update is less than the first threshold.

[0154] Specifically, set a first threshold. Wherein: the first threshold Select based on the actual required processing precision; when When that happens, execution will stop.

[0155] Among them, the first threshold Determined manually, its physical meaning is that the distance between the expected center coordinates of the small clusters after the new threshold line re-segmentation and the expected center coordinates of the small clusters after the previous threshold line segmentation is less than the first threshold. When the time is reached, execution stops, meaning the final threshold line will meet this accuracy requirement.

[0156] The above description, based on the embodiments shown in the figures, details the structure, features, and effects of the present invention. The above description is only a preferred embodiment of the present invention, but the present invention is not limited to the scope of implementation shown in the figures. Any changes made in accordance with the concept of the present invention, or equivalent embodiments modified to have equivalent changes, that do not exceed the spirit covered by the specification and figures, should be within the protection scope of the present invention.

Claims

1. A method for obtaining a threshold line to confirm the quantum state of a qubit, applied to a quantum chip, characterized in that, The center point and probability density distribution function corresponding to the spatial distribution of two sets of quantum data are obtained respectively; wherein, the two sets of quantum data are the quantum bit read signal data when the quantum bit is in two different defined quantum states; The sum of the integrals of the two probability density distribution functions distributed over a set space is used as the fidelity function. The set space is the two spaces divided by a threshold line. The threshold line is the perpendicular line connecting the two center points. The threshold line corresponding to the maximum or minimum value of the fidelity function is determined as the optimal threshold line.

2. The method according to claim 1, characterized in that, The quantum bit readout signal data is coordinate point data on an orthogonal plane coordinate system; The two sets of quantum data are two sets of coordinate point data, denoted as the first set. Second set .

3. The method according to claim 2, characterized in that, Obtaining the qubit readout signal data when the qubit is in a defined quantum state includes: The qubits are prepared into a defined quantum state and repeatedly measured to obtain multiple qubit read signals; each qubit read signal is converted into a qubit read signal data.

4. The method according to claim 2, characterized in that, The process of obtaining the center points corresponding to the spatial distributions of the two sets of quantum data includes: By fitting all coordinate points of the spatial distribution of the two sets of quantum data, the coordinates of the first statistical center point of the corresponding fitted graph are obtained. and the first standard deviation Coordinates of the second statistical center point Second standard deviation .

5. The method according to claim 4, characterized in that, The fitting is a Gaussian fit.

6. The method according to claim 4, characterized in that, The process of obtaining the probability density distribution functions corresponding to the spatial distributions of the two sets of quantum data includes: Based on the coordinates of the first statistical center point and the first standard deviation Determine the first probability density distribution function of all coordinate points of a set of quantum data in the IQ coordinate system. According to the coordinates of the second statistical center point and the second standard deviation Determine the second probability density distribution function of all coordinate points of another set of quantum data in the IQ coordinate system. .

7. The method according to claim 6, characterized in that, The first probability density distribution function Second probability density distribution function They are respectively: in: ∈ ; in: ∈ ; The formula for determining the optimal threshold line is: （1）。 8. The method according to claim 2, characterized in that, Before obtaining the probability density distribution function, the following steps are also included: Determine the first angle between the line connecting the two center points and any coordinate axis of the coordinate system in which the quantum data space is located; Rotate and update the coordinates of the two center points in the coordinate system according to the first included angle; Rotate and update all coordinates of the two sets of quantum data according to the first included angle.

9. The method according to claim 8, characterized in that, Rotate and update the coordinates of the two center points in the coordinate system according to the first included angle; specifically including: The first included angle is defined as the angle between the line connecting the two center points and the I-axis of the IQ coordinate system; the two center points are respectively the coordinates of the first statistical center point. Second statistical center point coordinates ; Rotate the two center points clockwise according to the first included angle; Update the coordinates of the first statistical center point and the coordinates of the second statistical center point They are respectively , ,in: .

10. The method according to claim 9, characterized in that, When the updated coordinates of the first statistical center point and the updated coordinates of the second statistical center point When the vertical axes are equal, the threshold line is a vertical threshold line perpendicular to the I-axis; Determining the threshold line corresponding to the extreme value of the fidelity function as the optimal threshold line specifically includes: When the space to the right of the vertical threshold line is the updated coordinate of the first statistical center point. The space located to the left of the vertical threshold line is the coordinate of the second statistical center point. If the value of the fidelity function is the maximum value, then the threshold line corresponding to the maximum value of the fidelity function is determined as the optimal threshold line; otherwise, the threshold line corresponding to the minimum value of the fidelity function is determined as the optimal threshold line; wherein: the sum of the maximum value of the fidelity function and the minimum value of the fidelity function is 1.

11. The method according to claim 8 or 9, characterized in that, The sine of the first included angle θ is:

12. The method according to claim 8 or 9, characterized in that, The formula for determining the optimal threshold line is simplified to the following: make: in: The graph of the function is monotonically decreasing and intersects the I-axis, so solving equation (3) can be transformed into solving the following equation: The solution to equation (4) is a real number solution. Then the optimal threshold line is obtained. The expression is: .

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