A method for confirming an update of a threshold line of a quantum bit quantum state

Abstract

The application discloses a threshold line updating method for confirming quantum bit quantum state, and relates to the field of quantum measurement and control; the method comprises the following steps: obtaining a third set corresponding to a certain quantum state and an initial threshold line; using the initial threshold line to divide the third set into two clusters, namely a first cluster and a second cluster; obtaining expected coordinates corresponding to the first cluster and the second cluster, namely a first coordinate and a second coordinate; determining a second included angle between a line connecting the first coordinate and the second coordinate and a set coordinate axis of a coordinate system according to the first coordinate and the second coordinate; rotating and updating the first coordinate and the second coordinate according to the second included angle; and determining an updated threshold line according to the initial threshold line and the first coordinate or the second coordinate before and after updating. The application can continuously update the threshold line according to the quantum bit reading accuracy requirement after providing a threshold segmentation line used for quantum state resolution.

Description

[0001] This application is a divisional application filed on April 24, 2019, with application number 201910333096.6, and patent titled "A Method for Updating Threshold Lines for Confirming 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 updating the threshold line for confirming the quantum state of a qubit. Background Technology

[0003] Quantum bit information refers to the quantum state possessed 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 of 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 signals is crucial for understanding the performance of a quantum chip. A patent filed on the same day provides a method for obtaining a threshold line to confirm the quantum state of a quantum bit. This method involves the following steps: preparing the quantum bit into a first quantum state and a second quantum state, and repeatedly measuring each state to obtain coordinate data of multiple quantum bit readout signals in an orthogonal plane coordinate system, denoted as a first set and a second set, respectively; performing Gaussian fitting on the coordinate points of the first and second sets to obtain the coordinates of the first and second statistical center points of the Gaussian fitted graphs for the first and second sets, respectively, and their corresponding first and second standard deviations; determining the first probability density distribution function for the first set and the second probability density distribution function for the second set; determining the fidelity function, and identifying the threshold line corresponding to the maximum or minimum value of the fidelity function as the optimal threshold line.

[0005] Ideally, the threshold line obtained by the above technical solution can meet the high precision requirements in a short time. However, the system used for processing the return signal of the quantum bit will experience performance fluctuations over time, and the performance parameters of the quantum bit itself may also change. At this time, the threshold line can no longer meet the high precision requirements. Summary of the Invention

[0006] The purpose of this invention is to provide a method for updating the threshold line for confirming the quantum state of a qubit, thereby overcoming the shortcomings of the prior art. This method can continuously update the threshold line according to the qubit readout accuracy requirements after the threshold dividing line used for quantum state resolution is provided.

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

[0008] A method for updating a threshold line for confirming the quantum state of a qubit, applied to a quantum chip, includes: obtaining a third set corresponding to a certain quantum state and an initial threshold line; using the initial threshold line to divide the third set into two clusters, namely a first cluster and a second cluster; obtaining the expected coordinates corresponding to the first cluster and the second cluster, namely a first coordinate and a second coordinate; determining a second angle between the line connecting the two and a set coordinate axis of the coordinate system based on the first coordinate and the second coordinate; rotating and updating the first coordinate and the second coordinate by the second angle; and determining an updated threshold line based on the initial threshold line and the first or second coordinate before and after the update.

[0009] Optionally, the line connecting the updated first and second coordinates is parallel to the I-axis.

[0010] Optionally, determining the updated threshold line using the initial threshold line and the first or second coordinates before and after the update includes: the updated threshold line expression is the sum of the set axis coordinates of the updated second coordinates and the initial threshold line expression minus the set axis coordinates of the second coordinates before the update.

[0011] Optionally, obtaining the initial threshold line includes: obtaining the coordinate point data of the read signals of multiple qubits in the first quantum state on an orthogonal plane coordinate system, denoted as the first set R. |0> ; Obtain the coordinate data of the read signals of multiple qubits in the second quantum state on an orthogonal plane coordinate system, denoted as the second set R. |1> Wherein: the first quantum state and the second quantum state are both known quantum states and are distinct from each other; where: the orthogonal plane coordinate system is set as the IQ coordinate system; according to the first set R |0> and the second set R |1> Determine the initial threshold line.

[0012] Optionally, based on the first set R |0> and the second set R |1> Determining the initial threshold line includes: obtaining the first set R |0> and the second set R |1> The corresponding center points and probability density distribution functions are respectively; 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 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 value of the fidelity function is determined as the initial threshold line.

[0013] Optionally, obtain the first set R |0> and the second set R |1>The corresponding center points include: for the first set R |0> and the second set R |1> Fit the graph to all coordinate points and obtain the coordinates of the first statistical center point (I) of the fitted graph. |0> Q |0> ) and the first standard deviation σ1, the coordinates of the second statistical center point (I) |1> Q |1> ) and the second standard deviation σ2.

[0014] Optionally, the fitting is a Gaussian fit.

[0015] Optionally, obtain the first set R |0> and the second set R |1> The corresponding probability density distribution functions include: based on the coordinates of the first statistical center point (I) |0> Q |0> The first probability density distribution function p(R) of all coordinate points of a set of quantum data in the IQ coordinate system is determined by the first standard deviation σ1. |0> According to the coordinates of the second statistical center point (I) |1> Q |1> The second standard deviation σ² determines the second probability density distribution function p(R) of all coordinate points of another set of quantum data in the IQ coordinate system. |1> ).

[0016] Optionally, the first probability density distribution function p(R) |0> ) and the second probability density distribution function p(R) |1> They are respectively:

[0017] Where: (I, Q)∈R |0> ;

[0018] Where: (I, Q)∈R |1> ;

[0019] The formula for calculating the initial threshold line is:

[0020]

[0021] Optionally, based on the first set R |0> and the second set R |1> Determining the initial threshold line 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.

[0022] Optionally, rotating and updating the coordinates of the two center points in the coordinate system according to the first included angle 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 (I... |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> ); Rotate the two center points clockwise according to the first included angle; Update the coordinates of the first statistical center point (I |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> ) are respectively (I′ |0> Q′ |0> ), (I′ |1> Q′ |1> ), where: Q′ |0> =Q′ |1> .

[0023] Optionally, when the updated coordinates of the first statistical center point (I′) |0> Q′ |0> ) and the updated coordinates of the second statistical center point (I′) |1> Q′ |1> When the vertical axes of the two 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, including: when the space to the right of the vertical threshold line is the updated coordinates of the first statistical center point (I′) |0> Q′ |0> The space where the second statistical center point (I′) is located, to the left of the vertical threshold line, is the coordinate of the second statistical center point. |1> Q′ |1> If the value of the fidelity function is determined to be the maximum value, then the threshold line corresponding to the maximum value of the fidelity function is determined to be the optimal threshold line; otherwise, the threshold line corresponding to the minimum value of the fidelity function is determined to be 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.

[0024] Optionally, the sine value of the first included angle θ is:

[0025]

[0026] Optionally, the formula for calculating the initial threshold line can be simplified to the following:

[0027]

[0028] make:

[0029]

[0030] Wherein: g l′ The graph of the function (I′) is monotonically decreasing and intersects the I-axis, so solving equation (3) can be transformed into solving the following equation:

[0031]

[0032] The solution to equation (4) is a real number solution I′=a. Therefore, the expression for obtaining the optimal threshold line l′ is: I′=a.

[0033] Optionally, obtaining the expected coordinates corresponding to the first cluster and the second cluster includes: averaging all coordinate point data in the first cluster and the second cluster without weights to obtain the corresponding expected coordinates.

[0034] Optionally, after determining the update threshold line using the initial threshold line and the second coordinates before and after the update, the method further includes: setting a termination condition, and repeatedly executing the following steps using the update threshold line as the initial threshold line: dividing the third set into two clusters using the initial threshold line, namely the updated first cluster and the second cluster; counting n = n + 1 times; averaging all coordinate point data in the updated first cluster and the second cluster without weights to obtain the corresponding expected coordinates, namely the first coordinate and the second coordinate; determining the second angle between the line connecting the two coordinates and the set coordinate axis of the coordinate system based on the first coordinate and the second coordinate; rotating and updating the first coordinate and the second coordinate by the second angle; determining the update threshold line using the initial threshold line and the first or second coordinate before and after the update; until the termination condition is reached, stopping the execution, and determining the update threshold line as the desired optimal threshold line.

[0035] Optionally, the setting of the termination condition includes: setting a maximum number of executions N, and stopping execution when n = N, wherein the maximum number of executions N is selected manually.

[0036] Optionally, the setting of the termination condition includes: setting a first threshold, wherein: the first threshold is selected according to the actual required processing precision; 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, execution stops.

[0037] Compared with existing technologies, this invention obtains the coordinate point data of multiple qubit readout signals in an orthogonal plane coordinate system when the qubit is in a first quantum state and a second quantum state, respectively, denoted as the first set and the second set. Based on the original data, i.e., the first set and the second set, a first threshold line for analytical resolution of the qubit readout signals is first determined. Then, the coordinate point data of multiple qubit readout signals in an orthogonal plane coordinate system corresponding to a certain quantum state are repeatedly obtained, denoted as the third set. The third set at this time is used as the data basis for obtaining the updated threshold line. The first threshold line is used as the initial threshold line. The third set is divided into two clusters using the initial threshold line, namely the first cluster and the second cluster, counted n=1 times; root The updated threshold line is determined based on the initial threshold line, the first cluster, and the second cluster; the updated threshold line is used as the initial threshold line to return to the execution step: the third set is divided into two clusters using the initial threshold line, namely the first cluster and the second cluster, counted n = n + 1 times; until the set termination condition is reached, the execution stops and the updated threshold line is determined to be the optimal threshold line to be obtained. Through the steps of the above technical solution, after obtaining the first threshold line from the original data, the third set is repeatedly obtained as needed, and the updated threshold line is obtained again using the data of the third set and the first threshold line. Since the updated threshold line is obtained based on the latest data of the third set, it can be guaranteed that the updated threshold line will be more accurate than the first threshold line. Attached Figure Description

[0038] Figure 1 This is a flowchart of a method for updating a threshold line to confirm the quantum state of a qubit according to an embodiment of the present invention. Detailed Implementation

[0039] 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.

[0040] Combined with appendix Figure 1 This invention provides a method for updating a threshold line for confirming the quantum state of a qubit, comprising the following steps:

[0041] We obtain the coordinate data of the read signals of multiple qubits in the first quantum state on an orthogonal plane coordinate system, denoted as the first set R. |0> ; Obtain the coordinate data of the read signals of multiple qubits in the second quantum state on an orthogonal plane coordinate system, denoted as the second set R. |1> Wherein: the first quantum state and the second quantum state are both known quantum states and are different from each other; wherein: the orthogonal plane coordinate system is set as the I-Q coordinate system;

[0042] According to the first set R |0> and the second set R |1> Determine the first threshold line;

[0043] The coordinate points corresponding to the read signals of multiple qubits when a qubit is in a certain quantum state are obtained on an orthogonal plane coordinate system and are denoted as the third set.

[0044] Use the first threshold line as the initial threshold line and set the termination condition;

[0045] The third set is divided into two clusters using the initial threshold line, namely the first cluster and the second cluster, counted n=1 times;

[0046] The updated threshold line is determined based on the initial threshold line, the first cluster, and the second cluster;

[0047] The following steps are repeated using the updated threshold line as the initial threshold line: the third set is divided into two clusters using the initial threshold line, namely the first cluster and the second cluster, for n = n + 1 times;

[0048] Execution stops when the termination condition is met, and the updated threshold line is determined to be the optimal threshold line that needs to be obtained.

[0049] The third quantum state can be divided into two clusters by the initial threshold line, where the first quantum state is the |0> state and the second quantum state is the |1> state, and a certain quantum state can be determined to be a mixture of the first quantum state and the second quantum state.

[0050] The advantage of this invention lies in that, compared with the prior art, this invention obtains the coordinate point data of multiple qubit read signals in an orthogonal plane coordinate system when the qubit is in a first quantum state and a second quantum state, respectively, denoted as a first set and a second set. The first set corresponds to a large number of qubit read signals when the qubit is in the first quantum state, and the second set corresponds to a large number of qubit read signals when the qubit is in the second quantum state. The data of the first set and the second set are used as the original data. Based on the original data, a first threshold line for the first quantum state and the second quantum state is first determined. Then, the coordinate point data of multiple qubit read signals in an orthogonal plane coordinate system corresponding to a certain quantum state of the qubit is repeatedly obtained, denoted as a third set. The third set at this time is used as the data basis for the updated threshold line to be obtained. The first threshold line is used as the initial threshold line. The third set is divided into two clusters, namely the first cluster and the second cluster, counted n=1 times; the updated threshold line is determined based on the initial threshold line, the first cluster, and the second cluster; the updated threshold line is used as the initial threshold line to return to the execution step: using the initial threshold line to divide the third set into two clusters, namely the first cluster and the second cluster, counted n=n+1 times; until the set termination condition is reached, the execution stops and the updated threshold line is determined to be the optimal threshold line to be obtained. Through the steps of the above technical solution, after obtaining the first threshold line from the original data, the third set is repeatedly obtained as needed, and the next updated threshold line is obtained by using the data of the third set and the previously calculated updated threshold line. Since the updated threshold line is obtained based on the latest data of the third set, it can be guaranteed that the updated threshold line will be more accurate than the first threshold line.

[0051] Example 1

[0052] Specifically, in conjunction with the appendix Figure 1 Embodiment 1 of the present invention provides a method for updating a threshold line to confirm the quantum state of a qubit, comprising the following steps:

[0053] Step 10: Obtain the coordinate data of the read signals of multiple qubits in the first quantum state on the orthogonal plane coordinate system, denoted as the first set R. |0> ; Obtain the coordinate data of the read signals of multiple qubits in the second quantum state on an orthogonal plane coordinate system, denoted as the second set R. |1>Wherein: the first quantum state and the second quantum state are both two fundamental quantum states, and the fundamental quantum state is defined according to the identifier of any quantum state in Hilbert space ψ = a|0> + b|1>, where |0> and |1> are two orthogonal basis vectors in Hilbert space, corresponding to two fundamental quantum states, and a and b are the vibration amplitudes corresponding to the two fundamental quantum states, wherein: the orthogonal plane coordinate system is set as the I-Q coordinate system;

[0054] In specific settings, the first quantum state can be the |0> state, and the second quantum state can be the |1> state, or the exact opposite. In this embodiment, the first quantum state is preferably |0> and the second quantum state is preferably |1>. The orthogonal plane coordinate system is set as the I-Q coordinate system, where I is the horizontal axis and Q is the vertical axis.

[0055] Specifically, the qubits are prepared into a first quantum state and repeatedly measured to obtain the coordinate point data of multiple qubit read signals in an orthogonal plane coordinate system, denoted as the first set R. |0> In this process, the quantum state of the quantum bit is read through a quantum bit signal reading device to obtain the quantum bit reading signal. Then, the quantum bit reading signal is processed by a data processing device, such as an FPGA-based data processing chip or a computer, to obtain coordinate point data. The set of coordinate point data is the first set, which is then obtained as the first set R. |0> Data can be stored in the computer's data storage area for later use, or it can be directly used for the next step of processing. The specific choice depends on the pre-defined data processing flow of the data processing equipment. Similarly, the second set R... | Perform the same treatment as before;

[0056] Step 20: Based on the first set R |0> and the second set R |1> Determine the first threshold line;

[0057] According to the first set R |0> and the second set R |1> Determining the first threshold line specifically includes the following steps:

[0058] Step 201: 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 (I) of the Gaussian fitted graphs corresponding to the first set and the second set respectively. |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1>), corresponding to the first standard deviation σ1 and the second standard deviation σ2, respectively; wherein: the IQ coordinate system is used to represent the coordinates of the first statistical center point (I |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> 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 (I). |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> The lines connecting the two spaces are denoted as the first space and the second space, respectively.

[0059] 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 R. |0> The second set R |0> The data in the dataset are subjected to two-dimensional Gaussian fitting to obtain a two-dimensional Gaussian distribution graph, and the coordinates of the first statistical center point (I) of the Gaussian fitting graphs corresponding to the first set and the second set are obtained respectively. |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> ), corresponding to the first standard deviation σ1 and the second standard deviation σ2, respectively;

[0060] Step 202: Based on the coordinates of the first statistical center point (I) |0> Q |0> The first probability density distribution function p(R) of all coordinate points in the first set in the IQ coordinate system is determined by the first standard deviation σ1 and the first probability density distribution function p(R). |0> According to the coordinates of the second statistical center point (I) |1> Q |1> The second probability density distribution function p(R) of all coordinate points in the second set in the IQ coordinate system is determined by the second standard deviation σ². |1> );

[0061] Specifically, the first probability density distribution function p(R) |0> ) and the second probability density distribution function p(R) |1> They are respectively:

[0062] Where: (I, Q)∈R |0> ;

[0063] Where: (I, Q)∈R |1> ;

[0064] It should be noted that the above formula is the probability density function corresponding to the Gaussian distribution. This formula can be directly derived after fitting the first and second sets using a computer. However, the first probability density function p(R) is different. |0> ) and the second probability density distribution function p(R) |1> The results are not limited to this method.

[0065] Step 203: Determine the fidelity function as the first probability density distribution function p(R). |0> The integral function in the first space and the second probability density distribution function p(R) |1 The sum of integral functions in the second space;

[0066] Step 204: Determine the threshold line corresponding to the maximum value of the fidelity function as the optimal threshold line.

[0067] Wherein: the formula for calculating the optimal threshold line is:

[0068]

[0069] Where: A in the formula is the first space, and B is the second space.

[0070] By solving the above equation, we can obtain the expression for the first threshold line, i.e. 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.

[0071] It should be noted that the fidelity function taking its maximum or minimum value only refers to the fidelity function taking its maximum or minimum value, wherein, when the coordinates of the first statistical center point (I) |0> Q |0> ) is located at the coordinates of the second statistical center point (I) |1> Q |1> When the coordinates of the first statistical center point (I) are on the right, the fidelity function needs to take its maximum value. |0> Q |0> ) is located at the coordinates of the second statistical center point (I) |1> Q |1> When the left side is ), the fidelity function needs to take its minimum value.

[0072] 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 necessarily be related to the coordinates of the first statistical center point (I). |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1>)vertical;

[0073] The proof process is as follows:

[0074] Given:

[0075]

[0076]

[0077]

[0078] Let's assume that the final optimal threshold line is expressed as follows in the IQ coordinate system:

[0079] aI + bQ + c = 0, where ab ≠ 0, b ≥ 0, a 2 +b 2 =1

[0080] 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 an angle φ around the origin in the IQ coordinate system. The updated coordinates of the first statistical center point (I...) |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> ) is denoted as (I |0>，new Q |0>，new ), (I |1>，new Q |1>，new The expression for the optimal threshold line after rotation becomes Q = -c, and we assume that it is in the space Q ≤ -c; where φ can be obtained by solving the following equation:

[0081]

[0082] At this point, the space divided by Q = -c and the corresponding formula for calculating the fidelity are:

[0083]

[0084] The optimal threshold line is a straight line that maximizes fidelity, i.e.:

[0085]

[0086] That is:

[0087]

[0088] in:

[0089]

[0090]

[0091] The optimization method for maximizing the multivariate function g(a, b, c) is as follows: Since the maximum value must exist in this problem, we only need to solve for all stationary points and then find the maximum value point among the stationary points.

[0092] Under the constraints ab≠0, b≥0, a 2 +b 2 When the value is 1, the stationary point can be solved using the Lagrange multiplier method:

[0093]

[0094] Where λ is an auxiliary parameter. That is:

[0095]

[0096]

[0097]

[0098] From the above system of equations, we can deduce that the stationary point satisfies: (Q |0> -Q |1> )a=(I |0> -I |1> b. And The coordinates of the first statistical center point (I) |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> The slope k of the connecting line o1 , The slope k of the optimal threshold line l That is, k o1 k l =-1, thus proving that the optimal threshold line must be perpendicular to the line connecting the coordinates of the first and second statistical center points, and the proof ends.

[0099] Specifically, based on the above important facts, in the actual processing, in order to facilitate the solution of the threshold line, we usually adopt a method to simplify the degrees of freedom. Before step 202, the following steps are also included:

[0100] Step 2011: Based on the coordinates of the first statistical center point (I) |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> Determine the first angle between the line connecting the two and any coordinate axis of the IQ coordinate system;

[0101] Step 2012: Rotate and update the coordinates of the first statistical center point (I) according to the first included angle. |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> );

[0102] Step 2013: Rotate according to the first included angle and update all coordinate points in the first set and all coordinate points in the second set.

[0103] By employing the technical solution described above, the first included angle is obtained, and then the coordinates of the first statistical center point (I) are rotated and updated based on the first included angle. |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> 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.

[0104] Specifically, the first included angle θ is determined as the coordinates of the first statistical center point (I). |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> 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 (I) clockwise according to the first angle θ. |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> ) 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 (I |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> ) are respectively (I′ |0> Q′ |0> ), (I′ |1> Q′ |1> ), while Q′ |0> =Q′ |1> Through rotation operations, the updated coordinates of the first statistical center point (I′) are obtained. |0> Q′ |0> ) and the coordinates of the second statistical center point (I′) |1> Q′ |1> The Q component of ) is equal, and the threshold line obtained above must be at the same coordinate as the first statistical center point (I).|0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> By making the line perpendicular to the Q-axis, the above steps can be used to make the optimal threshold line parallel to the Q-axis, thus reducing the computational difficulty.

[0105] Specifically, the formula for calculating the optimal threshold line is:

[0106]

[0107] The following transformations can be performed:

[0108]

[0109] Where: considering the actual physical meaning of P1-P3>0, then equation (2) becomes:

[0110]

[0111] make:

[0112]

[0113] Wherein: g l′ The graph of the function (I′) 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:

[0114]

[0115] The solution to equation (5) is a real number solution I′=a, and the expression for the first threshold line l′ is I′=a.

[0116] Specifically, if σ1 = σ2, then the expression for the current threshold line is:

[0117]

[0118] Through the above steps, the original threshold line is transformed into a straight line perpendicular to the Q axis, i.e., the first threshold line, by rotation operation. This greatly simplifies the difficulty of solving the original equation (1) and improves the efficiency of obtaining the threshold line.

[0119] Step 30: Obtain the coordinate data of the multiple qubit read signals corresponding to a certain quantum state in the orthogonal plane coordinate system, and denote it as the third set;

[0120] Specifically, the quantum state of the qubit does not need to be determined. The coordinate data corresponding to the read signals of all qubits are used as a third set, which is then compared with the first set R. |0>and the second set R |1> Similarly, it is also stored in the computer for further processing;

[0121] Step 40: Use the optimal threshold line, i.e. the first threshold line, as the initial threshold line and set the termination condition;

[0122] Specifically, in order to obtain an updated threshold line, an initial threshold line is required. In this scheme, the optimal threshold line obtained in the aforementioned steps, i.e., the first threshold line, is used as the initial threshold line.

[0123] Step 50: 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;

[0124] Step 60: Determine the updated threshold line based on the initial threshold line, the first cluster, and the second cluster;

[0125] It should be noted that the k-means clustering method from machine learning is used here. Its basic idea is to initialize k distinct centroids {μ}. (1) , ..., μ (k) Then iterate through the two different steps until convergence. Step one: Each training sample is assigned to the nearest centroid μ. (i) The cluster represented by i. Step two, for each center point μ (i) The update is for all training samples x in cluster i. (j) The mean.

[0126] 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 (I) of its two-dimensional double Gaussian distribution graph. |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> The distance between the two center coordinates will fluctuate, but the distance between the two center coordinates will remain constant. First, the noise level of the system remains unchanged; second, the noise level of the system does not change much and can still be approximated as σ1 and σ2. Finally, the distribution of the qubit readout results in the iq coordinate system still follows a two-dimensional bi-Gaussian statistical distribution. Under the premise that the above three conditions are met, 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.:

[0127]

[0128] In the form of. Furthermore, under the premise that the above three conditions hold, it can be mathematically proven that I′-I′ |0> It is a constant, and its value is only equal to... σ1 and σ2 are related, that is, the difference between the x-coordinate of the optimal threshold line l and the expected coordinate is a constant c.

[0129] The proof process is as follows:

[0130] 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:

[0131]

[0132] Then if the coordinates of the first statistical center point (I) |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> The fluctuation and change are equivalent to needing to solve for the following:

[0133]

[0134] And due to It remains unchanged, therefore after the rotation transformation, we still have:

[0135]

[0136] 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 Q′ |0> -Q′ |1> =Q″ |0> -Q″ |1> =0, therefore:

[0137]

[0138] That is, |I′ |0> -I′ |1> |=|I″ |0> -I″ |1> |=m.

[0139] Compare the coordinates of the first statistical center point (I) respectively |0> Q |0> ) and the coordinates of the second statistical center point (I) |1> Q |1> The calculation process of equation (4) before and after the change is as follows:

[0140]

[0141]

[0142] As can be seen from equations (a) and (b), the two equations, except for I′ |0> and I″ |0>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: I′-I′ |0> =I″-I″ |0> .

[0143] The proof is complete.

[0144] Based on the above facts, and combined with the aforementioned K-means clustering method, the specific steps for solving the update threshold line include:

[0145] Unweighted averages are applied to all coordinate point data in the first cluster and the second cluster to obtain corresponding expected coordinates, namely the first coordinate and the second coordinate. The second angle between the line connecting the first coordinate and the second coordinate and any coordinate axis of the IQ coordinate system is determined based on the first coordinate and the second coordinate. All coordinate point data, the first coordinate and the second coordinate in the first cluster and the second cluster are rotated and updated by the second angle, wherein: the line connecting the updated first coordinate and the second coordinate is parallel to the I axis.

[0146] Specifically, clustering and Each sample coordinate is averaged without weight to obtain the corresponding expected coordinate. as well as

[0147] Obtain the second angle θ′, where the sine value of the second angle θ′ is:

[0148]

[0149] Clustering and All sample coordinates, the first coordinate, and the second coordinate are rotated clockwise by an angle θ′ around the origin in the IQ coordinate system. The purpose is to utilize the important property that the difference between the abscissa of the optimal threshold line and the desired coordinate is constant for subsequent calculations.

[0150] Specifically: at this point, the update threshold line l1 is obtained. The following formula will be satisfied:

[0151] Where: c and d are both constants.

[0152]

[0153] Step 70: Repeat the following steps using the updated threshold line as the initial threshold line: use the initial threshold line to divide the third set into two clusters, namely the first cluster and the second cluster, for n = n + 1 times;

[0154] Similar to the calculation steps described above, by continuously obtaining updated threshold lines, it is foreseeable that the distance between the first center and the second center corresponding to the first cluster and the second cluster before and after the update will become smaller and smaller, that is, the performance will become more and more convergent. At this time, the corresponding updated threshold lines will also be more accurate than the previous threshold lines.

[0155] Step 80: Stop execution until the termination condition is met, and determine the updated threshold line as the optimal threshold line to be obtained.

[0156] Since the threshold line will be continuously refreshed, we can obtain a relatively more accurate threshold line by using the termination condition set in the previous steps, within a limited number of iterations.

[0157] 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.

[0158] Preferably, in step 40, the optimal threshold line, i.e., the first threshold line, is used as the initial threshold line, and a termination condition is set; the termination condition specifically includes:

[0159] 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.

[0160] Preferably, in step 40, the optimal threshold line, i.e., the first threshold line, is used as the initial threshold line, and a termination condition is set; the setting of the termination condition specifically includes:

[0161] Set a first threshold, wherein: the first threshold is selected according to the actual required processing precision;

[0162] 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.

[0163] Specifically, a first threshold ∈ is set, where: the first threshold ∈ is selected according to the actual required processing precision; when

[0164]

[0165] When that happens, execution will stop.

[0166] The first threshold ∈ is determined manually. Its physical meaning is that when the distance between the expected center coordinates of the small clusters after the new threshold line is re-segmented and the expected center coordinates of the small clusters after the previous threshold line is segmented is less than the first threshold ∈, the execution stops. That is, the final threshold line will meet this accuracy requirement.

[0167] 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 confirming an update of a threshold line of a quantum bit quantum state, applied to a quantum chip, characterized in that, The method comprises the following steps: obtaining a third set corresponding to a certain quantum state in an I-Q coordinate system and an initial threshold line; using the initial threshold line to divide the third set into two clusters, i.e., a first cluster and a second cluster; obtaining expected coordinates corresponding to the first cluster and the second cluster, i.e., a first coordinate and a second coordinate, respectively, determining a second angle between a line connecting the first coordinate and the second coordinate and a set coordinate axis of the coordinate system according to the first coordinate and the second coordinate, rotating and updating the first coordinate and the second coordinate according to the second angle, and making the line connecting the updated first coordinate and the second coordinate parallel to the I-axis; determining an updated threshold line according to the initial threshold line and the first coordinate or the second coordinate before and after the update; the expression of the updated threshold line is the sum of the set axis coordinate of the updated second coordinate and the expression of the initial threshold line minus the same set axis coordinate of the second coordinate before the update.

2. The method of claim 1, wherein, The step of obtaining the initial threshold line comprises the following steps: Obtain coordinate point data corresponding to the plurality of qubit reading signals respectively in the I-Q coordinate system when the quantum bit is in the first quantum state, denoted as a first set Obtain coordinate point data corresponding to the plurality of qubit reading signals respectively in the I-Q coordinate system when the quantum bit is in the second quantum state, denoted as a second set ; wherein: the first quantum state and the second quantum state are known quantum states and different from each other; determine an initial threshold line according to the first set and the second set .

3. The method of claim 2, wherein, determining an initial threshold line, comprising: and the second set determining an initial threshold line, comprising: obtaining the first set and the second set respectively corresponding center points and probability density distribution functions; taking the sum of integrals of two probability density distribution functions distributed on a set space as a fidelity function, the set space being two spaces divided by the threshold line, and the threshold line being a vertical line of a line connecting two center points; determining the threshold line corresponding to the maximum value of the fidelity function as the initial threshold line.

4. The method according to claim 2 or 3, characterized in that, obtaining the first set and the second set corresponding center points, respectively, comprising: fitting all coordinate points of the first set and the second set respectively to obtain the first statistical center point coordinate and the first standard deviation of the corresponding fitting graph, the second statistical center point coordinate and the second standard deviation .

5. The method of claim 4, wherein, The fitting is Gaussian fitting.

6. The method of claim 4, wherein, obtaining the first set and the second set corresponding probability density distribution functions, respectively, comprising: 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 of claim 6, wherein, the first probability density distribution function and the second probability density distribution function are respectively: wherein: ∈ ; wherein: ∈ ; The evaluation formula of the initial threshold line is: （1）。 8. The method of claim 3, wherein, determining the initial threshold line further comprises: and the second set determining the initial threshold line further comprises: determining a first angle between a line connecting two center points and any coordinate axis of a coordinate system in which quantum data is distributed; rotating and updating the coordinate points of the two center points in the coordinate system according to the first angle; rotating and updating all coordinates of the two sets of quantum data according to the first angle.

9. The method of claim 8, wherein, The step of rotating and updating the coordinate points of the two center points in the coordinate system according to the first angle comprises the following steps: determining the first included angle as an included angle between a line connecting the two center points and an I-axis of an I-Q coordinate system; the two center points are respectively a first statistical center point coordinate and a second statistical center point coordinate ; clockwise rotating the two center points according to the first angle; updating the first statistical center point coordinate and the second statistical center point coordinate are respectively , wherein .

10. The method of claim 9, wherein, when the longitudinal axis of the updated first statistical center point coordinate and the longitudinal axis of the updated second statistical center point coordinate are equal, the threshold line is a vertical threshold line of the vertical I-axis; determining the threshold line corresponding to the maximum value of the fidelity function as the optimal threshold line comprises the following steps: When the space located at the right side of the vertical threshold line is the updated first statistical center point coordinate When the space located at the left side of the vertical threshold line is the second statistical center point coordinate If the space located at the right side of the vertical threshold line is the updated first statistical center point coordinate, 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 of claim 8 or 9, wherein, the evaluation formula of the initial threshold line is transformed into the following formula by simplification: let wherein: The function graph of is monotonically decreasing and intersects the I-axis, then solving equation (3) can be converted to solving the following equation: The solution of formula (4) is a real solution The optimal threshold line is obtained The expression is: .

13. The method of claim 1, wherein, The step of obtaining the expected coordinates corresponding to the first cluster and the second cluster comprises the following steps: non-weightedly averaging all coordinate point data in the first cluster and the second cluster respectively to obtain the corresponding expected coordinates.

14. The method of claim 13, wherein, After determining the updated threshold line according to the initial threshold line and the second coordinate before and after the update, the method further comprises the following steps: setting a termination condition, and repeatedly executing the following steps with the updated threshold line as the initial threshold line: using the initial threshold line to divide the third set into two clusters, i.e., an updated first cluster and a second cluster; counting n = n + 1; non-weightedly averaging all coordinate point data in the updated first cluster and the second cluster respectively to obtain the corresponding expected coordinates, i.e., a first coordinate and a second coordinate, respectively, determining a second angle between a line connecting the first coordinate and the second coordinate and a set coordinate axis of the coordinate system according to the first coordinate and the second coordinate, and rotating and updating the first coordinate and the second coordinate according to the second angle; determining an updated threshold line according to the initial threshold line and the first coordinate or the second coordinate before and after the update; stopping execution until the termination condition is reached, and determining the updated threshold line as the optimal threshold line required to be obtained.

15. The method of claim 14, wherein, The setting of the termination condition comprises the following steps: A maximum execution number N is set, and when n=N, the execution is stopped, wherein the maximum execution number N is artificially selected.

16. The method of claim 14, wherein, The termination condition is set, including: A first threshold is set, wherein the first threshold is selected according to the actual required processing accuracy; 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, the execution is stopped.

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