CN114567418B - Quantum error correction method of matrix-based quantum platform - Google Patents
Quantum error correction method of matrix-based quantum platform Download PDFInfo
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Abstract
The invention belongs to a quantum computer in the electronic core industryThe method comprises the following steps of (1) obtaining a quantum bit number required by a quantum true machine type and an experimental circuit; applying 2 on a quantum true machine according to the number of quantum bits n The method comprises the steps that calibration circuits used for measuring operation results of a quantum true machine are planted, and measurement results of each calibration circuit are obtained, wherein n is the number of quantum bits, each calibration circuit is composed of n quantum circuits, X gates are applied to the respective quantum circuits of the calibration circuits respectively, and initial states of the calibration circuits are set according to the applied X gates; will 2 n The measurement result of a kind of calibration circuit turns into correction matrix, utilizes this correction matrix to rectify the experimental data that the real machine of target quantum was surveyed to the real machine experimental data of target quantum after obtaining the correction does not need supplementary physics quantum bit to carry out the quantum error correction, need not remove from the physical aspect and solve the quantum error correction problem, reduce cost promotes maneuverability.
Description
Technical Field
The invention belongs to the technical field of quantum computers in the electronic core industry, and particularly relates to a quantum error correction method of a quantum platform based on a matrix.
Background
The quantum computer (quantum computer) is a physical device which performs high-speed mathematical and logical operation, storage and processing of quantum information according to the law of quantum mechanics, and has the advantages of high running speed, strong information handling capacity, wide application range and the like. Compared with a common computer, the quantum computer has more information processing amount and more favorable operation, and can ensure the operation accuracy. The quantum system is extremely unstable, most of quantum systems are extremely sensitive to external environment and are easily influenced by noise, the decoherence time is extremely short, the environment is easily coupled, and errors can be generated when the calculation result of a quantum computer is processed. In the field related to quantum error correction, the mainstream technology at present is a three qubit code, shor code, surface code and the like which need auxiliary physical quantum bits, and the defects are as follows: a large number of ancillary physical qubits are required, and a very high fault tolerance is required for these qubits, the error rate having to be below a certain threshold; the preparation of an auxiliary qubit at the physical level requires a complex process, the preparation cost is extremely high, and the mass production cannot be realized by the current technology.
Disclosure of Invention
Therefore, the matrix-based quantum platform quantum error correction method provided by the invention has the advantages that the quantum error correction is carried out without auxiliary physical quantum bits, the quantum error correction problem is not solved from the physical level, the cost is reduced, and the operability is improved.
According to the design scheme provided by the invention, the quantum error correction method of the quantum platform based on the matrix comprises the following contents:
obtaining the type of a quantum true machine and the number of quantum bits required by an experimental circuit;
applying 2 to Quantum machines according to the number of Quantum bits n The method comprises the steps that calibration circuits used for measuring operation results of a quantum true machine are planted, and measurement results of each calibration circuit are obtained, wherein n is the number of quantum bits, each calibration circuit is composed of n quantum circuits, X gates are applied to the respective quantum circuits of the calibration circuits respectively, and initial states of the calibration circuits are set according to the applied X gates;
will 2 n And converting the measurement result of the calibration circuit into a correction matrix, and correcting the experimental data measured by the target quantum true machine by using the correction matrix to obtain the corrected experimental data of the target quantum true machine.
As the quantum error correction method of the matrix-based quantum platform, 2 in the form of n-bit binary accumulation is obtained by applying X gates on respective quantum wires aiming at calibration wires for measuring the operation result of a quantum true machine n Calibration circuit, and the first calibration circuit is firstInitial state is |0 1 0 2 …0 n >2 nd (2) th n The initial state of the calibration circuit is |1 1 1 2 …1 n >。
As the quantum error correction method of the matrix-based quantum platform, 2 of each calibration line is further used n Normalizing the measurement results, and taking the probability of the measurement result of the corresponding calibration line as a column vector; according to 2 n The probabilities of the measurements of the lines are calibrated to obtain a correction matrix.
As the quantum error correction method of the matrix-based quantum platform, further, a calculation formula of a correction matrix R is expressed as follows: r = M -1 Wherein M is 2 composed of column vectors n *2 n And (4) matrix.
As the matrix-based quantum platform quantum error correction method of the present invention, further, the process of correcting the experimental data measured by the target quantum true machine by using the correction matrix R is represented as follows: c ideal ＝RC noisy Wherein, C ideal Results of measuring the line for the ideal state of the quantum true machine, C noisy And obtaining a result for actually measuring a noisy line by a real quantum computer.
The invention has the beneficial effects that:
aiming at the situations that a simple method which does not need auxiliary physical quantum bit error correction and can reduce observable expected errors from a mathematical level in a programmable manner is lacked, and the quantum error correction in the latest quantum field is not mature enough, and a plurality of high-efficiency methods are urgently needed to correct the error result of a quantum circuit, the error result of a quantum true machine with a noise circuit is corrected by utilizing the thought of a correction matrix, and the quantum error correction can be realized from a software level. The traditional error correction scheme is operated on a hardware bottom layer, a large number of auxiliary physical qubits are needed, the manufacturing cost of the auxiliary physical qubits is extremely high, the large number of qubits with low error threshold are difficult to realize by the current technology, the quantum error correction problem is not needed to be solved from a physical layer in the scheme, the cost is extremely reduced, the scheme can be suitable for a plurality of quantum computers, such as the measurement error correction of an IBM quantum true machine, or the measurement error correction of a local quantum true machine, and the like, and has a good application prospect.
Description of the drawings:
FIG. 1 is a flow chart of a quantum error correction method for a matrix-based quantum platform according to an embodiment;
fig. 2 is a schematic diagram of a calibration circuit for two qubits in an embodiment.
The specific implementation mode is as follows:
in order to make the objects, technical solutions and advantages of the present invention clearer and more obvious, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.
The traditional error correction scheme is operated at the bottom layer of hardware, a large number of auxiliary physical qubits are needed, the manufacturing cost of the auxiliary physical qubits is extremely high, and a large number of qubits with low error thresholds are difficult to realize by the current technology. The embodiment of the invention provides a quantum error correction method of a matrix-based quantum platform, which is shown in figure 1 and comprises the following contents:
s101, obtaining a quantum true machine type and a quantum bit number required by an experimental circuit;
s102, applying 2 to the quantum true machine according to the number of quantum bits n The method comprises the steps that calibration circuits used for measuring operation results of a quantum true machine are planted, and measurement results of each calibration circuit are obtained, wherein n is the number of quantum bits, each calibration circuit is composed of n quantum circuits, X gates are applied to the respective quantum circuits of the calibration circuits respectively, and initial states of the calibration circuits are set according to the applied X gates;
s103, 2 n And converting the measurement result of the calibration line into a correction matrix, and correcting the experimental data measured by the target quantum true machine by using the correction matrix to obtain the corrected experimental data of the target quantum true machine.
The error result of the quantum true machine with noise is corrected by using the idea of the correction matrix, quantum error correction can be realized from a software layer, the problem of quantum error correction does not need to be solved from a physical layer, the cost is extremely reduced, and the method is suitable for a plurality of quantum computers, such as the measurement error correction of the IBM quantum true machine, or the measurement error correction of the original quantum true machine, and the like.
As the matrix-based quantum platform quantum error correction method in the embodiment of the present invention, further, for the calibration lines used for measuring the operation result of the quantum true machine, 2 in the form of n-bit binary accumulation is obtained by applying X gates to the respective quantum lines n A calibration line with an initial state of |0 1 0 2 …0 n >2 nd (2) th n The initial state of the calibration circuit is |1 1 1 2 …1 n >。
The implementation modes of the bottom quantum systems in each quantum real machine are different, the topological structures of each quantum bit link are different, and the type and the state of the current quantum real machine must be acquired to respectively perform experiments and discussion. The number of qubits required for different experiments is different, the number of bits is related to the dimension of the correction matrix, n bits correspond to 2 n ×2 n The correction matrix of (2). In the embodiment of the present invention, the initial state of the first calibration line is |0 1 0 2 …0 n >(the lower subscript n represents the first line); the second calibration line has an initial state of |1 1 0 2 …0 n >An X-gate is applied to the first quantum wire of the first type of wire. By analogy, 2 nd n The seed correction line is |1 1 1 2 …1 n >. Assuming that two qubits are required for the experiment, as shown in FIG. 2, there are 4 calibration lines, each representing an initial state of |00>,|10>,|01>,|11>And (3) measuring the result.
As the quantum error correction method of the matrix-based quantum platform in the embodiment of the invention, 2 of each calibration line is further used n Normalizing the measurement results, and taking the probability of the measurement results of the corresponding calibration line as a column vector; according to 2 n The probabilities of the measurements of the lines are calibrated to obtain a correction matrix.
Because the quantum true machine has certain errors, each calibration line has 2 n Seed result, e.g. initial state of |0 1 0 2 …0 n >The calibration line of (1) may show |10 \82300; after measurement>，|01…0>Etc. to obtain a result of 2 n After normalizing the results of this probability occurrence, the measured 2 is n The probability of a possible outcome is recorded as a column vector C 1 . Then with the other 2 n 1 column vector C of the probabilities of the measured results of the calibration lines 2 ,C 2 …C n Etc. together form a 2 n *2 n This matrix is denoted as M. The following expression is given:
C noisy ＝MC ideal (1)
wherein C is ideal Is the result of measuring the line in the ideal state of the quantum true machine, C noisy The method is a result of a noisy line actually measured by a real quantum computer. From the above formula (1), it can be obtained
Where R is the correction matrix we require
Suppose an experiment requires two qubits, e.g., one initial state of |00>The calibration circuit of (1) measures 10000 times, and the results of { '00':9782, '01':114, '10':103, '11':1} may be obtained by normalization
The results of the other three calibration circuits are measured in the same way to obtain
M＝(C 1 ,C 2 ,C 3 ,C 4 ) Calibration matrix R = M -1 。
From the formula (2), the correction matrix R can measure the result C of the noisy line noisy Conversion into the result C of the line measured under the ideal condition ideal Therefore, the correction matrix R can be applied to the experimental data measured under the true machine to obtain correction data and an experimental resultThe accuracy of the result can be greatly improved, the error result of the quantum true machine with noise circuit can be corrected by using the thought of the correction matrix from the aspect of mathematical software, and the method is suitable for a plurality of quantum platforms, such as the measurement error correction of the IBM quantum true machine, or the measurement error correction of the original quantum true machine, and the like, and the cost is reduced.
Unless specifically stated otherwise, the relative steps, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the present invention.
Based on the foregoing method and/or system, an embodiment of the present invention further provides a server, including: one or more processors; a storage device for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement the method described above.
Based on the method and/or system, the embodiment of the invention further provides a computer readable medium, on which a computer program is stored, wherein the program, when executed by a processor, implements the method.
In all examples shown and described herein, any particular value should be construed as merely exemplary, and not as a limitation, and thus other examples of example embodiments may have different values.
It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, it need not be further defined and explained in subsequent figures.
Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (1)
1. A quantum error correction method of a quantum platform based on a matrix is characterized by comprising the following contents:
obtaining the type of a quantum real machine and the quantum bit number required by an experimental circuit;
applying 2 to Quantum machines according to the number of Quantum bits n The method comprises the steps that a calibration line used for measuring operation results of a quantum real machine is obtained, and measurement results of each calibration line are obtained, wherein n is the number of quantum bits, each calibration line is composed of n quantum lines, the calibration lines are respectively provided with an X gate on the respective quantum lines, and the calibration lines are set to be in initial states according to the X gates;
will 2 n Converting the measurement result of the seed calibration circuit into a correction matrix, and correcting the experimental data measured by the target quantum true machine by using the correction matrix to obtain the corrected experimental data of the target quantum true machine;
for a calibration line for measuring the result of a running quantum truth machine, a 2 in the form of an n-bit binary accumulation is obtained by applying an X-gate to the respective quantum line n A calibration line with an initial state of |0 1 0 2 …0 n >The initial state of the second calibration line is |1 1 0 2 …0 n >That is, an X-gate is applied to the first quantum wire of the first wire, under the form of n-bit binary accumulation, 2 nd n The initial state of the calibration circuit is |1 1 1 2 …1 n >Subscript n is the quantum wire serial number;
2 of each calibration line n Normalizing the measurement results, and taking the probability of the measurement results of the corresponding calibration line as a column vector; according to 2 n Measurement result of calibration circuitObtaining a correction matrix according to the probability of the error;
the correction matrix R is calculated as: r = M -1 Wherein M is 2 composed of column vectors n *2 n A matrix;
the process of correcting the experimental data measured by the target quantum true machine by using the correction matrix R is represented as follows: c ideal ＝RC noisy Wherein, C ideal Results of the line measured for the ideal state of the quantum true machine, C noisy Is the result of a noisy line actually measured by a quantum true machine.
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| CN113159324A (en) * | 2021-02-26 | 2021-07-23 | 山东英信计算机技术有限公司 | Quantum equipment calibration method, device, equipment and medium |
| CN113919501A (en) * | 2021-10-11 | 2022-01-11 | 北京量子信息科学研究院 | Calibration method, device, computer equipment and storage medium for CZ door operation |
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| EP3059864A1 (en) * | 2015-02-20 | 2016-08-24 | Nederlandse Organisatie voor toegepast- natuurwetenschappelijk onderzoek TNO | Qubit circuit state change control system |
| CN113159324A (en) * | 2021-02-26 | 2021-07-23 | 山东英信计算机技术有限公司 | Quantum equipment calibration method, device, equipment and medium |
| CN113919501A (en) * | 2021-10-11 | 2022-01-11 | 北京量子信息科学研究院 | Calibration method, device, computer equipment and storage medium for CZ door operation |
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