CN111860550B - Acquisition method for confirming threshold line of quantum state of quantum bit - Google Patents
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Abstract
The invention discloses an acquisition method of a threshold line for confirming a quantum state of a quantum bit, and relates to the field of quantum measurement and control; preparing quantum bits into a first quantum state and a second quantum state, respectively carrying out repeated measurement on the first quantum state and the second quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, respectively recording the coordinate point data as a first set and a second set, respectively carrying out Gaussian fitting on the coordinate points of the first set and the second set to obtain a first statistical center point coordinate and a second statistical center point coordinate of a Gaussian fitting graph corresponding to the first set and the second set respectively, and respectively corresponding to a first standard deviation and a second standard deviation; determining a first probability density distribution function in the first set and a second probability density distribution function in the second set respectively; determining a fidelity function, and determining a threshold line corresponding to the fidelity function when the fidelity function takes the maximum value as an optimal threshold line; the threshold line established according to the method can provide more accurate reference for the determination of the unknown quantum state.
Description
Technical Field
The invention belongs to the field of quantum measurement and control, and particularly relates to an acquisition method for a threshold line for confirming a quantum state of a quantum bit.
Background
The quantum bit information refers to a quantum state of the quantum bit, the basic quantum states are a state |0> and a state |1>, after the quantum bit is operated, the quantum state of the quantum bit is changed, and on the quantum chip, the execution result of the quantum state of the quantum bit, namely the quantum chip, is reflected after the quantum chip is executed, and the execution result is carried and transmitted by a quantum bit reading signal.
The analysis of the quantum state of the quantum bit by the rapid analysis of the read signal of the quantum bit is a key work for knowing the execution performance of the quantum chip, and in the patent applied before, a method for determining the quantum state of the quantum bit is provided, which comprises the following steps: acquiring distribution patterns of corresponding quantum bit reading signals in an orthogonal plane coordinate system when the quantum bits are in two different known quantum states; acquiring the central positions of two distribution patterns in an orthogonal plane coordinate system, and determining the perpendicular bisectors of connecting lines of the two central positions as threshold dividing lines; and taking the threshold dividing line as a basis for judging the quantum state of the quantum bit.
The problem in the prior art is that in an ideal situation, the arrangement of taking the perpendicular bisector of the connecting line of the central points of two distribution patterns as the threshold dividing line can meet the requirements in most of the time, but due to the factors such as the preparation error of the quantum state, the threshold line has an error which can influence the reading result of the unknown quantum state.
Disclosure of Invention
The invention aims to provide a method for acquiring a threshold line for confirming a quantum state of a quantum bit, which solves the defects in the prior art and can provide a more accurate threshold dividing line for quantum state resolution.
The technical scheme adopted by the invention is as follows:
an acquisition method for confirming a threshold line of a qubit quantum state is applied to a quantum chip and comprises the following steps:
preparing the quantum bits into a first quantum state, repeatedly measuring the first quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a first set R |0> The method comprises the steps of carrying out a first treatment on the surface of the Preparing the quantum bits into a second quantum state, repeatedly measuring the second quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a second set R |1> Wherein: the first quantum state and the second quantum state are known quantum states and are different from each other, wherein: the orthogonal plane coordinate system is set as an I-Q coordinate system;
respectively performing Gaussian fitting on all coordinate points in the first set and all coordinate points in the second set to obtain first statistical center point coordinates (I |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) First standard deviation sigma respectively corresponding to 1 And a second standard deviation sigma 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein: for use in the I-Q coordinate system for locating the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) A straight line divided in two spaces is denoted as a threshold line, and the threshold line is perpendicular to the first statistical center point coordinate (I |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) Is connected with the connecting line of the (a); the two spaces are respectively marked as a first space and a second space;
according to the first statistical center point coordinates (I |0> ，Q |0> ) And the first standard deviation sigma 1 Determining a first probability density distribution function p (R) of all coordinate points in the first set in an I-Q coordinate system |0> ) According to the second statistical center point coordinates (I |1> ，Q |1> ) And the second standard deviation sigma 2 Determining a second probability density distribution function of all coordinate points in the second set in the I-Q coordinate system p (R |1> )；
Determining a fidelity function as said first probability density distribution function p (R |0> ) An integral function in the first space and the second probability density distribution function p (R |1> ) A sum of integral functions in the second space;
and determining the corresponding threshold line as the optimal threshold line when the fidelity function takes the maximum value.
Further, the first probability density distribution function p (R |0> ) And a second probability density distribution function p (R |1> ) The method comprises the following steps of:
The evaluation formula of the optimal threshold line is as follows:
further, the first statistical center point coordinate (I |0> ，Q |0> ) And the first standard deviation sigma 1 Determining a first probability density distribution function p (R) of all coordinate points in the first set in an I-Q coordinate system |0> ) According to the secondStatistical center point coordinates (I) |1> ，Q |1> ) And the second standard deviation sigma 2 Determining a second probability density distribution function p (R) of all coordinate points in the second set in the I-Q coordinate system |1> ) Also included before is:
according to the first statistical center point coordinates (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Determining a first included angle between the connecting line of the first and the second coordinate axes of the I-Q coordinate system;
rotating and updating the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> )；
And rotating and updating all coordinate points in the first set and all coordinate points in the second set according to the first included angle.
Further, the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) The method specifically comprises the following steps:
determining the first included angle as the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) The connecting lines form an I-axis included angle with an I-Q coordinate system;
clockwise rotating the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> )；
Updating the first statistical center point coordinates (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Respectively (I' |0> ，Q′ |0> )、(I′ |1> ，Q′ |1> ) Wherein: q'. |0> ＝Q′ |1> 。
Further, whenUpdated first statistical center point coordinates (I' |0> ，Q′ |0> ) And updated said second statistical center point coordinates (I' |1> ，Q′ |1> ) When the longitudinal axes of (2) are equal, the threshold line is a vertical threshold line perpendicular to the I-axis;
the method for determining the threshold line corresponding to the fidelity function when taking the maximum value is an optimal threshold line comprises the following steps:
when the first space is the updated first statistical center point coordinate (I' |0> ，Q′ |0> ) The first space is located on the right side of the vertical threshold line, and the second space is the updated second statistical center point coordinate (I' |1> ，Q′ |1> ) The space is located, the second space is located on the left side of the vertical threshold line, 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.
Further, the sine value of the first included angle θ is:
further, the evaluation formula of the optimal threshold line can be converted into the following formula by simplification:
and (3) making:
wherein: g l′ The functional image of (I') is monotonically decreasing and intersects the I-axis, then solving equation (3) can be converted into solving the following equation:
obtaining the solution of formula (4) as a real solution I '=a, and obtaining the expression of the optimal threshold line l' is: i' =a.
Further, when the solution obtained in the formula (4) is a real solution I '=a, the expression for obtaining the optimal threshold line l' is: after I' =a, further comprising:
repeatedly acquiring a plurality of coordinate point data of a corresponding quantum bit reading signal on an orthogonal plane coordinate system when the quantum bit is in a certain quantum state, and marking the coordinate point data as a third set;
rotating and updating all coordinate point data in the third set according to the first included angle;
setting a termination condition by taking the optimal threshold line l' as an initial threshold line;
dividing the third set into two clusters, namely a first cluster and a second cluster, by using the initial threshold line, and counting n=1;
and respectively carrying out weight-free average on all coordinate point data in the first cluster and the second cluster to obtain corresponding expected coordinates, namely a first coordinate and a second coordinate, determining a second included angle of any coordinate axis of an I-Q coordinate system between a connecting line of the first coordinate and the second coordinate, rotating the second included angle and updating all coordinate point data in the first cluster and the second cluster, the first coordinate and the second coordinate, wherein: the updated connecting line of the first coordinate and the second coordinate is parallel to an I axis;
determining an update threshold line with the initial threshold line and the second coordinates before and after the update, wherein: the expression of the updated threshold line is the sum of the updated I-axis coordinate of the second coordinate and the expression of the initial threshold line minus the I-axis coordinate of the second coordinate before updating;
returning to the executing step by taking the updated threshold line as an initial threshold line: dividing the third set into two clusters, namely a first cluster and a second cluster, by using the initial threshold line, and counting n=n+1;
stopping execution until the termination condition is reached, and determining the updated threshold line as the optimal threshold line to be obtained.
Further, the setting termination condition specifically includes:
setting a maximum execution number N, and stopping execution when n=n, wherein: the maximum execution number N is manually selected.
Further, the setting termination condition specifically includes:
setting a first threshold, wherein: the first threshold is selected according to the actually required processing precision;
and stopping execution when the maximum value of the distance between the first coordinates before and after updating and the distance between the second coordinates before and after updating is smaller than the first threshold value.
Compared with the prior art, the method has the advantages that two different quantum bit quantum states, namely a first quantum state and a second quantum state, are respectively prepared, a large number of repeated reading operations are carried out to obtain two sets, gaussian fitting is respectively carried out to obtain a first statistical center point coordinate and a second statistical center point coordinate, corresponding first standard deviation and second standard deviation are respectively obtained, corresponding first probability density distribution functions and second probability density distribution functions are respectively determined, a calculated threshold line divides the coordinate system into a first space and a second space, a fidelity function is determined according to the sum of the integral of the first probability density distribution functions in the first space and the integral of the second probability density distribution functions in the second space, and when the fidelity function takes the maximum value, the corresponding threshold line is the optimal threshold line; the invention firstly obtains a large number of data of quantum bits in a determined quantum state repeatedly, carries out Gaussian fitting on the data through a computer, determines each probability density distribution function according to the Gaussian fitting result, takes the integral of each probability density distribution function distributed on a corresponding space as a fidelity function, and when the fidelity function takes the maximum value, indicates that the threshold line used for dividing the space at the moment leads the best fidelity effect when the quantum bits on two sides of the threshold line read signals are read.
Drawings
Fig. 1 is a flow chart of a method of acquiring a threshold line for validating a qubit quantum state in accordance with an embodiment of the present invention.
Detailed Description
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
With reference to fig. 1, the invention provides a method for acquiring a threshold line for confirming a quantum state of a qubit, which comprises the following steps:
preparing the quantum bits into a first quantum state, repeatedly measuring the first quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a first set R |0> The method comprises the steps of carrying out a first treatment on the surface of the Preparing the quantum bits into a second quantum state, repeatedly measuring the second quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a second set R |1> Wherein: the first quantum state and the second quantum state are known quantum states and are different from each other, wherein: the orthogonal plane coordinate system is set as an I-Q coordinate system; specifically, any quantum state is expressed as phi=alpha|0 in the hilbert space>+β|1>Wherein |0>And |1>Is two orthogonal basis vectors of the Hilbert space, and corresponds to the first quantum state and the second quantum state in the embodiment. Specifically, when the first quantum state is quantum state |0>In the state, the second quantum state is |1>The method comprises the steps of carrying out a first treatment on the surface of the Or vice versa.
Respectively performing Gaussian fitting on all coordinate points in the first set and all coordinate points in the second set to obtain a first statistical center point seat of Gaussian fitting graphs respectively corresponding to the first set and the second setLabel (I) |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) First standard deviation sigma respectively corresponding to 1 And a second standard deviation sigma 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein: for use in the I-Q coordinate system for locating the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) A straight line divided in two spaces is denoted as a threshold line, and the threshold line is perpendicular to the first statistical center point coordinate (I |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) Is connected with the connecting line of the (a); the two spaces are respectively marked as a first space and a second space;
according to the first statistical center point coordinates (I |0> ，Q |0> ) And the first standard deviation sigma 1 Determining a first probability density distribution function p (R) of all coordinate points in the first set in an I-Q coordinate system |0> ) According to the second statistical center point coordinates (I |1> ，Q |1> ) And the second standard deviation sigma 2 Determining a second probability density distribution function p (R) of all coordinate points in the second set in the I-Q coordinate system |1> )；
Determining a fidelity function as said first probability density distribution function p (R |0> ) An integral function in the first space and the second probability density distribution function p (R |1 ) A sum of integral functions in the second space;
and determining the corresponding threshold line as the optimal threshold line when the fidelity function takes the maximum value.
Compared with the prior art, the method has the advantages that two different quantum states, namely a first quantum state and a second quantum state, are respectively prepared, a large number of repeated reading operations are carried out to obtain two sets, gaussian fitting is respectively carried out to obtain a statistical center coordinate point and a second statistical center point coordinate, a first standard deviation and a second standard deviation which correspond to the first standard deviation and the second standard deviation respectively are obtained, a corresponding first probability density distribution function and a corresponding second probability density distribution function are respectively determined, a calculated threshold line divides the coordinate system into a first space and a second space, a fidelity function is determined according to the sum of the integral of the first probability density distribution function in the first space and the integral of the second probability density distribution function in the second space, and when the fidelity function takes the maximum value, the corresponding threshold line is the optimal threshold line; the invention firstly obtains a large number of data of quantum bits in a determined quantum state repeatedly, carries out Gaussian fitting on the data through a computer, determines each probability density distribution function according to the Gaussian fitting result, takes the integral of each probability density distribution function distributed on a corresponding space as a fidelity function, and when the fidelity function takes the maximum value, indicates that the threshold line used for dividing the space at the moment leads the best fidelity effect when the quantum bits on two sides of the threshold line read signals are read.
Example 1
Specifically, referring to fig. 1, an embodiment 1 of a method for acquiring a threshold line for confirming a quantum state of a qubit according to the present invention includes the following steps:
step 10, preparing the qubit into a first quantum state, repeatedly measuring the first quantum state to obtain coordinate point data of a plurality of qubit reading signals on an orthogonal plane coordinate system, and recording the coordinate point data as a first set R |0> The method comprises the steps of carrying out a first treatment on the surface of the Preparing the quantum bits into a second quantum state, repeatedly measuring the second quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a second set R |1> Wherein: the first quantum state and the second quantum state are known quantum states and are different from each other, wherein: the orthogonal plane coordinate system is set as an I-Q coordinate system;
specifically, the first quantum state may be an |0> state quantum state, the second quantum state may be an |1> state quantum state, the orthogonal plane coordinate system is set as an I-Q coordinate system, I is a horizontal axis, and Q is a vertical axis.
Wherein, the quantum bit is prepared into a first quantum state and repeated measurement is carried out to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and the coordinate point data is recorded as a first set R |0> Is obtained and analyzed by a qubit signal reading device to obtain a first set R |0> The data in the second set R is stored in the computer |1> Is also stored in the computer;
step 20, performing gaussian fitting on all coordinate points in the first set and all coordinate points in the second set, to obtain first statistical center point coordinates (I |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) First standard deviation sigma respectively corresponding to 1 And a second standard deviation sigma 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein: for use in the I-Q coordinate system for locating the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) A straight line divided in two spaces is denoted as a threshold line, and the threshold line is perpendicular to the first statistical center point coordinate (I |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) Is connected with the connecting line of the (a); the two spaces are respectively marked as a first space and a second space;
wherein the Gaussian fitting of all coordinate points in the first set and all coordinate points in the second set is accomplished by a computer, and the first set R is obtained by a computer program |0> And a second set R |0> Performing two-dimensional Gaussian fitting to obtain a two-dimensional Gaussian distribution graph, and obtaining first statistical center point coordinates (I |0> ，Q |0> ) And a second statistical center point coordinate (I |1> ，Q |1> ) First standard deviation sigma respectively corresponding to 1 And a second standard deviation sigma 2 ；
Step 30, according to the first statistical center point coordinates (I |0> ，Q |0> ) And the first standard deviation sigma 1 Determining a first probability density distribution function p (R) of all coordinate points in the first set in an I-Q coordinate system |0> ) According to the second statistical center point coordinates (I |1> ，Q |1> ) And the second standard deviation sigma 2 Determining a second probability density distribution function p (R) of all coordinate points in the second set in the I-Q coordinate system |1> )；
Wherein: the first probability density distribution function p (R |0> ) And a second probability density distribution function p (R |1> ) The method comprises the following steps of:
The above formula is a probability density distribution function corresponding to gaussian distribution, and the formula may be directly obtained after the first set and the second set are fitted by a computer, but the first probability density distribution function p (R |0> ) And a second probability density distribution function p (R |1> ) The derivation of (a) is not limited to this method.
Step 40, determining a fidelity function as the first probability density distribution function p (R |0> ) An integral function in the first space and the second probability density distribution function p (R |1 ) A sum of integral functions in the second space;
and 50, determining the corresponding threshold line as the optimal threshold line when the fidelity function takes the maximum value.
Wherein: the evaluation formula of the optimal threshold line is as follows:
by solving the above equation, an expression about the optimal threshold line can be obtained, and the sum of the fidelity of the two sides of the threshold line can be maximized by satisfying the expression, so that the optimal threshold line required by the invention can be obtained.
It should be noted that, the fidelity function takes the most value, which means that the fidelity function takes the maximum value or the minimum value only, where, when the first statistical center point coordinate (I |0> ，Q |0> ) Located at the second statistical center point coordinate (I |1> ，Q |1> ) On the right, the fidelity function needs to take a maximum value, when the first statistical center point coordinate (I |0> ，Q |0> ) Located at the second statistical center point coordinate (I |1> ，Q |1> ) On the left, the fidelity function needs to take a minimum.
Example 2
On the premise of meeting the two-dimensional double-Gaussian distribution statistical model, the obtained current threshold line can be proved to be in a mathematical state with the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Perpendicular.
The proving process is as follows:
it is known that:
it is not a matter of course to assume that the expression of the last acquired optimal threshold line in the IQ coordinate system is:
aI+bQ+c=0, where ab+.0, b+.0, a 2 +b 2 ＝1
Obtaining an included angle phi between an optimal threshold line and an I axis, rotating all coordinate point data in a first set and a second set clockwise by an angle phi with a coordinate origin as a center under an IQ coordinate system, wherein the updated first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Is denoted as (I) |0>，mew ，Q |0>，new )、(I |1>，nem ，Q |1>，new ) The expression of the rotated optimal threshold line becomes q= -c, and we assume that in space q+-c; wherein: phi can be obtained by solving the following formula:
at this time, the space divided by q= -c and the fidelity correspondence calculation formula are:
and since the optimal threshold line is a straight line that maximizes fidelity, namely:
namely:
wherein:
the maximum optimization method of the multiple functions g (a, b, c) is as follows: in the problem, the maximum value exists certainly, so that we only need to solve all the resident points, and then find the maximum value point in the resident points.
In the constraint condition ab not equal to 0, b not less than 0, a 2 +b 2 For =1, the stationarity point can be solved using the lagrangian multiplier method:
where λ is an auxiliary parameter, namely:
from the above equation set, it can be sorted that the dwell point satisfies: (Q) |0> -Q |1> )a＝(I |0> -I |1> )b。
Due to
Is the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Slope k of the connection line o1 ，/>
Is the optimal thresholdSlope k of value line l That is k o1 k l -1, whereby the optimal threshold line must be perpendicular to the line of the first statistical center point coordinates and the second statistical center point coordinates, proving to end.
Based on the above facts, the present invention provides another embodiment, and on the basis of embodiment 1, further, the step 30 further includes:
step 22, based on the first statistical center point coordinates (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Determining a first included angle between the connecting line of the first and the second coordinate axes of the I-Q coordinate system;
step 24, rotating and updating the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> )；
And step 26, rotating and updating all coordinate points in the first set and all coordinate points in the second set according to the first included angle.
By adopting the technical scheme of the steps, the embodiment obtains the first included angle, and then rotates and updates the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) All coordinate points in the first set and all coordinate points in the second set are used for reducing the freedom degree of the fidelity function through rotation operation, and the calculation of the fidelity function maximum value in the later period is facilitated.
Further, the first included angle θ is the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) The two connecting lines form an I-axis included angle with an I-Q coordinate system, and the first statistical center point coordinate (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) And all coordinate points in the first set and all coordinate points in the second set, wherein: updated first statistical center point coordinates (I |0> ，Q |0> ) And the second statistical center point coordinates (I |1> ，Q |1> ) Respectively (I' |0> ，Q′ |0> )、(I′ |1> ，Q′ |1> ) And Q' |0> ＝Q′ |1> By a rotation operation, the obtained updated first statistical center point coordinates (I' |0> ，Q′ |0> ) And a second statistical center point coordinate (I' |1> ，Q′ |1> ) Is equal so that the optimal threshold line sought will be parallel to the Q axis.
Preferably, the first included angle θ may be obtained by calculating the following formula:
it should be noted that, the obtaining of the first included angle θ includes, but is not limited to, the above method.
Further, the evaluation formula of the optimal threshold line is as follows:
the following transformations may be performed:
wherein: consider the actual physical meaning P 1 -P 3 >0, then formula (2 a) converts to:
and (3) making:
wherein: g l′ The functional image of (I') is monotonically decreasing and intersects the I axis, then solving equation (3) can be converted to solving the following equation according to the integral property:
obtaining the solution of the formula (4) as a real solution I ' =a, and obtaining a first threshold line l ' with the expression of I ' =a.
In particular, if sigma 1 ＝σ 2 The expression for the current threshold line is available as:
through the embodiment, the current threshold line which is originally calculated is converted into the first threshold line which is a straight line perpendicular to the Q axis through rotation operation, so that the difficulty of solving the original equation (1) is greatly simplified from the algorithm, and the threshold straight line acquisition efficiency is improved.
Example 3
It should be noted that the repeated acquisition of qubits is at |0>State or |1>The data after signal analysis is read by the quantum bit in the state, and the first statistical center point coordinate (I |0> ，Q |0> ) And second statistical center point coordinates (I |1> ，Q |1> ) Will float, but the distance between the two central coordinates, i.e
Maintaining unchanged; second, the noise level of the system is not greatly changed and can still be approximate to sigma 1 Sum sigma 2 . Finally, the distribution of the qubit reading result on the i-q coordinate system still obeysTwo-dimensional double gaussian statistical distribution. On the premise that the above three are true, we can still adopt the rotation transformation method as in the embodiment 2 to transform the theoretical threshold straight line into the solution of a single variable, namely:
in the form of (a). Meanwhile, on the premise that the three are established, the mathematical demonstration of I ' -I ' can be carried out ' |0> Is a constant, and the numerical value is only sum
σ 1 Sigma (sigma) 2 In relation, the horizontal coordinate difference between the optimal threshold line l and the expected coordinate is a constant c.
The proving process is as follows:
the threshold line is known to be perpendicular to the line connecting the center point coordinates. And after the rotation operation, satisfies:
then if the first statistical center point coordinate (I |0> ，Q |0> ) And second statistical center point coordinates (I |1> ，Q |1> ) Floating changes, equivalent to the need to solve for:
due to
Unchanged, therefore, after rotation transformation, there is still:
also because the purpose of the rotation transformation is to make the central point coordinate line parallel to the I-axis, i.e. Q' |0> -Q′ |1> ＝Q″ |0> -Q″ |1> =0, therefore:
i.e. |I' |0> -I′ |1> |＝|I″ |0> -I″ |1> |＝m。
Respectively comparing the first statistical center point coordinates (I |0> ，Q |0> ) And second statistical center point coordinates (I |1> ，Q |1> ) The calculation process of the equation (4) before and after the floating change:
as can be seen from formulas (a) and (b), both equations are other than I' |0> And I' |0> Except for the differences, the rest is identical (note: consider that the actual constraint is that the threshold line is between two center point coordinates, the sign does not affect the process and conclusion of the solution), so the solution should be of exactly the same form: i '-I' |0> ＝I″-I″ |0> 。
The proof ends.
Based on the facts, the invention further provides an acquisition method for acquiring a more reliable updated threshold straight line by combining a K-means clustering method in machine learning;
the basic idea of the k-means clustering method is: initializing k different center points { mu } (1) ，…，μ (k) And then iteratively exchanging the two different steps until convergence. Step one, each training sampleAssigned to the nearest centre point mu (i) The represented cluster i. Step two, each center point mu (i) Updated as all training samples x in cluster i (j) Is a mean value of (c).
Then, on the basis of embodiment 2, after obtaining the expression of the optimal threshold line, the following steps are further included:
step 60, repeatedly obtaining a plurality of coordinate point data of a corresponding quantum bit reading signal on an orthogonal plane coordinate system when the quantum bit is in a certain quantum state, and marking the coordinate point data as a third set;
wherein: the repeatedly obtaining the data of the plurality of coordinate points of the corresponding qubit reading signal on the orthogonal plane coordinate system when the qubit is in a certain quantum state, and marking the data as a third set means that the certain qubit is prepared to a certain determined quantum state, whether the certain quantum state is unknown or not, repeatedly obtaining the data of the plurality of coordinate points of the corresponding qubit reading signal of the certain qubit on the orthogonal plane coordinate system for a plurality of times, and marking the data as the third set
Step 70, rotating and updating all coordinate point data in the third set according to the first included angle;
wherein all coordinate point data in the third set are rotated and updated according to the first included angle theta in order to make the third set
Is consistent with the first set and the second set.
Step 80, setting a termination condition by taking the optimal threshold line l' as an initial threshold line;
step 90, dividing the third set into two clusters, namely a first cluster and a second cluster, by using the initial threshold line, and counting n=1;
specifically, the use of the initial threshold line l' will
Segmentation into two clusters->
And->
Counting n=1;
step 100, respectively carrying out weight-free averaging on all coordinate point data in the first cluster and the second cluster to obtain corresponding expected coordinates, namely a first coordinate and a second coordinate, determining a second included angle of any coordinate axis of an I-Q coordinate system and a connecting line of the first coordinate and the second coordinate, rotating the second included angle and updating all coordinate point data in the first cluster and the second cluster, the first coordinate and the second coordinate, wherein: the updated connecting line of the first coordinate and the second coordinate is parallel to an I axis;
specifically, cluster
And->
All sample coordinates in (1) are respectively weighted-free averaged to obtain corresponding expected coordinates +.>
And +.>
Obtaining a second angle theta ', wherein the sine value of the second angle theta' is as follows:
will cluster
And->
The first coordinate and the second coordinate rotate clockwise by an angle theta' in an I-Q coordinate system by taking a coordinate origin as a center, so that the aim of carrying out subsequent calculation by utilizing the important property that the difference value of the horizontal coordinate of the optimal threshold line and the expected coordinate is constant is achieved;
step 110, determining an updating threshold line according to the initial threshold line and the second coordinates before and after updating, wherein: the expression of the updated threshold line is the sum of the updated I-axis coordinate of the second coordinate and the expression of the initial threshold line minus the I-axis coordinate of the second coordinate before updating;
specific: at this time, an update threshold line l is acquired 1 I.e.
The following formula will be satisfied:
Step 110, step l 1 I.e.
Returning to the executing step as a new initial threshold line: will be at the initial threshold line
Segmentation into two clusters->
And->
Counting n=n+1;
and 120, stopping execution until the termination condition is reached, and determining the updated threshold line as the threshold line to be obtained.
Through the steps, the core idea of the K-means clustering algorithm is used, the large clusters are divided into two small clusters by using the threshold line, the rotation angle is determined according to the expected coordinates of the two small clusters, the large clusters are rotated clockwise, then the threshold line is redetermined, the redetermined threshold line is used for dividing the large clusters into the two small clusters, the two small clusters are executed in sequence, and after the termination condition is met, the execution is stopped, and it is expected that the distance between the expected center coordinates of the small clusters which are re-divided by the new threshold line and the expected center coordinates of the small clusters which are divided by the previous threshold line is smaller and smaller, namely, the distance between the expected center coordinates of the small clusters which are divided by the new threshold line and the expected center coordinates of the small clusters which are divided by the previous threshold line is more and more converged, and the updated threshold line is closer to the theoretical threshold dividing line, namely, the distance is more and more accurate.
Further, the step 80 of setting a termination condition specifically includes:
setting a maximum execution number N, and stopping execution when n=n, wherein: the maximum execution times N are manually selected, and the numerical value of the maximum execution times N can be determined according to the actual required running time; thus, the execution time can be effectively controlled.
Further, the step 80 of setting a termination condition specifically includes:
setting a first threshold, wherein: the first threshold is selected according to the actually required processing precision;
and stopping execution when the maximum value of the distance between the first coordinates before and after updating and the distance between the second coordinates before and after updating is smaller than the first threshold value.
Specifically, a first threshold e is set, where: the first threshold epsilon is selected according to the actually required processing precision; when (when)
And stopping execution.
The first threshold value epsilon is determined by human, and the physical meaning of the first threshold value epsilon 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 smaller than the first threshold value epsilon, the execution is stopped, and the finally obtained threshold line meets the precision requirement.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (10)
1. An acquisition method for confirming a threshold line of a qubit quantum state, applied to a quantum chip, is characterized by comprising the following steps:
preparing the quantum bits into a first quantum state, repeatedly measuring the first quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a first set R |0> The method comprises the steps of carrying out a first treatment on the surface of the Preparing the quantum bits into a second quantum state, repeatedly measuring the second quantum state to obtain coordinate point data of a plurality of quantum bit reading signals on an orthogonal plane coordinate system, and marking the coordinate point data as a second set R |1> Wherein: the first quantum state and the second quantum state are known quantum states and are different from each other, wherein: the orthogonal plane coordinate system is set as an I-Q coordinate system;
respectively performing Gaussian fitting on all coordinate points in the first set and all coordinate points in the second set to obtain first statistical center point coordinates (I |0> ,Q |0> ) And a first standard deviation sigma 1 Second statistical center point coordinates (I |1> ,Q |1> ) And a second standard deviation sigma 2 The method comprises the steps of carrying out a first treatment on the surface of the Wherein the method comprises the steps of: for use in the I-Q coordinate system for locating the first statistical center point coordinate (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> ) A straight line divided in two spaces is denoted as a threshold line, and the threshold line is perpendicular to the first statistical center point coordinate (I |0> ,Q |0> ) And a second statistical center point coordinate (I |1> ,Q |1> ) Is connected with the connecting line of the (a); the two spaces are respectively marked as a first space and a second space;
according to the first statistical center point coordinates (I |0> ,Q |0> ) And the first standard deviation sigma 1 Determining a first probability density distribution function p (R) of all coordinate points in the first set in an I-Q coordinate system |0> ) According to the second statistical center point coordinates (I |1> ,Q |1> ) And the second standard deviation sigma 2 Determining a second probability density distribution function p (R) of all coordinate points in the second set in the I-Q coordinate system |1＞ )；
Determining a fidelity function as said first probability density distribution function p (R |0＞ ) An integral function in the first space and the second probability density distribution function p (R |1＞ ) A sum of integral functions in the second space;
and determining the corresponding threshold line as the optimal threshold line when the fidelity function takes the maximum value.
2. The method for obtaining a threshold line for validating qubits quantum states of claim 1, wherein said first probability density distribution function p (R |0＞ ) And a second probability density distribution function p (R |1＞ ) The method comprises the following steps of:
The evaluation formula of the optimal threshold line is as follows:
3. the method for obtaining a threshold line for validating qubits quantum states as claimed in claim 1, wherein said determining the first statistical center point coordinates (I |0> ,Q |0> ) And the first standard deviation sigma 1 Determining a first probability density distribution function p (R) of all coordinate points in the first set in an I-Q coordinate system |0> ) According to the second statistical center point coordinates (I |1> ,Q |1> ) And the second standard deviation sigma 2 Determining a second probability density distribution function p (R) of all coordinate points in the second set in the I-Q coordinate system |1> ) Also included before is:
according to the first statistical center point coordinates (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> ) Determining a first included angle between the connecting line of the first and the second coordinate axes of the I-Q coordinate system;
rotating and updating the first statistical center point coordinate (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> )；
And rotating and updating all coordinate points in the first set and all coordinate points in the second set according to the first included angle.
4. A method for obtaining a threshold line for validating qubit quantum states as claimed in claim 3 wherein said rotating and updating said first statistical center point coordinates (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> ) The method specifically comprises the following steps:
determining the first included angle as the first statistical center point coordinate (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> ) The connecting lines form an I-axis included angle with an I-Q coordinate system;
clockwise rotating the first statistical center point coordinate (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> )；
Updating the first statistical center point coordinates (I |0> ,Q |0> ) And the second statistical center point coordinates (I |1> ,Q |1> ) Respectively (I' |0> ,Q′ |0> )、(I′ |1> ,Q′ |1> ) Wherein: q'. |0> ＝Q′ |1> 。
5. The method for obtaining a threshold line for validating qubit quantum states of claim 4 wherein,
when the updated first statistical center point coordinates (I' |0> ,Q′ |0> ) And updated said second statistical center point coordinates (I' |1> ,Q′ |1＞ ) When the longitudinal axes of (2) are equal, the threshold line is a vertical threshold line perpendicular to the I-axis;
the method for determining the threshold line corresponding to the fidelity function when taking the maximum value is an optimal threshold line comprises the following steps:
when the first space is the updated first statistical center point coordinate (I' |0> ,Q′ |0> ) The first space is located on the right side of the vertical threshold line, and the second space is the updated second statistical center point coordinate (I' |1＞ ,Q′ |1＞ ) The space is located, the second space is located on the left side of the vertical threshold line, 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.
6. The method for obtaining a threshold line for validating qubit quantum states of claim 4, wherein the sine value of the first included angle θ is:
7. the method of claim 6, wherein the evaluation formula of the optimal threshold line is converted by simplification into the following formula:
and (3) making:
wherein: g l′ The functional image of (I') is monotonically decreasing and intersects the I-axis, then solving equation (3) can be converted into solving the following equation:
obtaining the solution of formula (4) as a real solution I '=a, and obtaining the expression of the optimal threshold line l' is: i' =a.
8. The method for obtaining a threshold line for confirming a qubit quantum state according to claim 7, wherein when the solution obtained by the formula (4) is a real solution I '=a, an expression for obtaining an optimal threshold line l' is: after I' =a, further comprising:
repeatedly acquiring a plurality of coordinate point data of a corresponding quantum bit reading signal on an orthogonal plane coordinate system when the quantum bit is in a certain quantum state, and marking the coordinate point data as a third set;
rotating and updating all coordinate point data in the third set according to the first included angle;
setting a termination condition by taking the optimal threshold line l' as an initial threshold line;
dividing the third set into two clusters, namely a first cluster and a second cluster, by using the initial threshold line, and counting n=1;
and respectively carrying out weight-free average on all coordinate point data in the first cluster and the second cluster to obtain corresponding expected coordinates, namely a first coordinate and a second coordinate, determining a second included angle of any coordinate axis of an I-Q coordinate system between a connecting line of the first coordinate and the second coordinate, rotating the second included angle and updating all coordinate point data in the first cluster and the second cluster, the first coordinate and the second coordinate, wherein: the updated connecting line of the first coordinate and the second coordinate is parallel to an I axis;
determining an update threshold line with the initial threshold line and the second coordinates before and after the update, wherein: the expression of the updated threshold line is the sum of the updated I-axis coordinate of the second coordinate and the expression of the initial threshold line minus the I-axis coordinate of the second coordinate before updating;
returning to the executing step by taking the updated threshold line as an initial threshold line: dividing the third set into two clusters, namely a first cluster and a second cluster, by using the initial threshold line, and counting n=n+1;
stopping execution until the termination condition is reached, and determining the updated threshold line as the optimal threshold line to be obtained.
9. The method for obtaining a threshold line for confirming a qubit quantum state according to claim 8, wherein the setting of the termination condition specifically comprises:
setting a maximum execution number N, and stopping execution when n=n, wherein: the maximum execution number N is manually selected.
10. The method for obtaining a threshold line for confirming a qubit quantum state according to claim 8, wherein the setting of the termination condition specifically comprises:
setting a first threshold, wherein: the first threshold is selected according to the actually required processing precision;
and stopping execution when the maximum value of the distance between the first coordinates before and after updating and the distance between the second coordinates before and after updating is smaller than the first threshold value.
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