CN118014094A - Quantum computing method, quantum circuit, device and medium for determining function classification - Google Patents

Quantum computing method, quantum circuit, device and medium for determining function classification Download PDF

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CN118014094A
CN118014094A CN202410420939.7A CN202410420939A CN118014094A CN 118014094 A CN118014094 A CN 118014094A CN 202410420939 A CN202410420939 A CN 202410420939A CN 118014094 A CN118014094 A CN 118014094A
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quantum
bit
bits
gate
function
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周旭
周卓俊
罗乐
陈柳平
李杨
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Qike Quantum Technology Zhuhai Co ltd
Guokaike Quantum Technology Anhui Co ltd
Guokaike Quantum Technology Beijing Co Ltd
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Qike Quantum Technology Zhuhai Co ltd
Guokaike Quantum Technology Anhui Co ltd
Guokaike Quantum Technology Beijing Co Ltd
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Abstract

The application discloses a quantum computing method, a quantum circuit, equipment and a medium for determining function classification, which relate to the technical field of quantum computing, wherein the quantum computing method for determining function classification comprises the following steps: preparing n quantum bits in the state of |0 >; respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states; sequentially executing corresponding quantum operations on the n quantum bits based on the numerical value of the function to be classified and the serial number of the data bit; performing RY gate operation on n qubits or performing RY gate operation on one qubit of n qubits, respectively, and performing H gate operation on n-1 qubits; measuring all quantum bits, and counting the probability P 0 of all 0 states; determining a classification label of the function to be classified according to the probability P 0; the rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit. The method can efficiently solve the function classification problem by adopting a phase encoding mode.

Description

Quantum computing method, quantum circuit, device and medium for determining function classification
Technical Field
The present application relates to the field of quantum computing technology, and in particular, to a quantum computing method, a quantum circuit, an electronic device, and a computer-readable storage medium for determining function classification.
Background
The quantum algorithm is a novel calculation method based on the quantum mechanics principle, and is different from the classical algorithm, the quantum algorithm uses quantum bits (qubits) as basic units of information, and performs operation by using key characteristics such as quantum superposition, quantum entanglement and quantum interference. For example, the Shor algorithm can solve the problem of large prime factorization in polynomial time, the Grover algorithm can solve the problem of unordered database searching, and the like. Another class of quantum algorithms is quantum-classical hybrid algorithms, also known as variable component quantum algorithms (VQA), that use classical optimizers to optimize parameters in parameterized quantum circuits. VQA is well suited for noisy mid-scale quantum (NISQ) line applications and enables approximation and resolution of the problems associated with the absence of complete error correction. VQA include variable component sub-feature Solvers (VQEs), quantum Approximation Optimization Algorithms (QAOA), quantum Neural Networks (QNNs), and the like.
For a Boolean function f {0,1} - {0,1}, it is defined that it is one of three classes of functions: constant function (output 0 or 1 for all inputs), balanced function (output 0 for half of inputs, output 1 for the other half), or very value unbalanced function (all other possible functions). By designing parameterized quantum circuits, the three classification problem of the function can be solved. However, when the three-classification problem of the parameterized quantum circuit solving function is utilized, the accuracy is not high due to the circuit depth and noise in the quantum circuit, and the accurate classification cannot be realized; in addition, the quantum gates in the quantum circuit are too many, and the quantum gates are redundant due to design, so that the training time is too long.
Disclosure of Invention
Aiming at the technical problems existing in the prior art, the application provides a quantum computing method for determining function classification, the function to be classified is multi-bit binary data, the bit number N of the multi-bit binary data satisfies N=2 n, N is a natural number, and the method is executed on a quantum circuit and comprises the following steps: preparing n quantum bits in the state of |0 >; respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states; sequentially executing corresponding quantum operations on n quantum bits based on the numerical value of the function to be classified and the serial number of the multi-bit binary data bit; performing RY gate operation on n qubits or performing RY gate operation on one qubit of n qubits, respectively, and performing H gate operation on n-1 qubits; measuring all quantum bits, and counting the probability P 0 of all 0 states; determining a classification label of the function to be classified according to the probability P 0; the rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
A method as described above, the method performed on a quantum wire comprising: preparing n quantum bits in the state of |0 >; respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states; sequentially executing corresponding quantum operations on the n quantum bits based on the numerical value of the function to be classified and the serial number of the data bit; performing RY gate operations on the n qubits respectively; measuring all quantum bits, and counting the probability P 0 of all 0 states; determining a classification label of the function to be classified according to the probability P 0; the rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
A method as described above, the method performed on a quantum wire comprising: preparing n quantum bits in the state of |0 >; respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states; sequentially executing corresponding quantum operations on the n quantum bits based on the numerical value of the function to be classified and the serial number of the data bit; performing RY gate operation on one of n qubits, and performing H gate operation on n-1 qubits; measuring all quantum bits, and counting the probability P 0 of all 0 states; determining a classification label of the function to be classified according to the probability P 0; the rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
The method as described above, wherein the sequentially performing the corresponding quantum operations on the n quantum bits based on the numerical value of the function to be classified and the sequence number of the multi-bit binary data bit includes: sequentially performing the following operations on N quantum bits based on each data bit from the 0 th data bit of the data sample, wherein multi-bit binary data are represented as [ theta_0, theta_1, & gt, theta_m, & gt, theta_ (N-1) ], and converting a current data bit sequence number m of the multi-bit binary data into an N-bit binary character string [ j_0, j_1, & gt, j_k, & gt, j_ (N-1) ], wherein characters in the binary character string are in one-to-one correspondence with sequence numbers of the N quantum bits Q_k in order from low order to high order, wherein k is the sequence number of the quantum bits, k=0, 1, …, N-1; respectively executing first quantum operations on n quantum bits Q_k, wherein when a character j_k in a binary character string is 0, the first quantum operations on the k quantum bits Q_k are X gate operations, and when the character j_k in the binary character string is 1, the first quantum operations on the k quantum bits Q_k are I gate operations; calculating alpha_m=theta_m·pi, wherein pi is the circumference ratio; after performing a first quantum operation on n qubits q_k, performing a C { n-1} PS (alpha_m) gate operation on n qubits, wherein PS (alpha_m) =diag [1, e { i·alpha_m } ], i being an imaginary unit, n-1 th qubit being a target bit, and qubits from 0 th to n-2 th bits being control bits; and performing a third quantum operation on the n quantum bits, respectively, wherein the third quantum operation performed on the kth quantum bit q_k is an X-gate operation when the character j_k in the binary string is 0, and the third quantum operation performed on the kth quantum bit q_k is an I-gate operation when the character j_k in the binary string is 1.
The method as described above, wherein determining the classification label of the function to be classified according to the probability P 0 comprises: judging the size relation between the probability P 0、1-P0 and 1- (2/N) 2 +epsilon, wherein epsilon is a real number, and the value range is (0, (2/N) 2); if P 0 is maximum, determining the function label to be classified as a constant function; if 1-P 0 is the largest, determining the function label to be classified as a balance function; if 1- (2/N) 2 +epsilon is maximum, determining the function label to be classified as a very valued function unbalanced function.
In the method, the optimization process of the rotation angle of the RY door comprises the following steps: initializing a rotation angle parameter of the RY door; executing the quantum computing method for determining function classification and determining measurement classification results; calculating a loss function value according to the measurement classification result and the actual classification result; calculating the loss function value through a classical optimizer to obtain an optimized RY door rotation angle parameter value; substituting the optimized rotation angle parameter value of the RY gate into the quantum circuit to calculate the loss function value again until the optimized rotation angle parameter value is converged to a set threshold value.
According to another aspect of the present application, a quantum circuit for determining a function classification is presented, the function to be classified is a multi-bit binary data, and the bit number N of the binary data satisfies n=2 n, N is a natural number, including: a column of H gates, which is used for executing H gate operation to the n quantum bits in the state of |0> to obtain a uniform superposition state; n columns of operation units, which are respectively in one-to-one correspondence with the data bits of the multi-bit binary data, wherein the operation units are used for sequentially executing corresponding quantum operations on N quantum bits based on the numerical value of the function to be classified and the serial number of the multi-bit binary data bits; one or more RY gates for performing RY gate operations on the qubits.
As described above, the quantum wire, each column of operation units sequentially includes, in order from front to back: a first operation column including n first quantum gates, performing first quantum operations on n quantum bits, respectively, wherein a current data bit sequence number m is converted into an n-bit binary string [ j_0, j_1, ], j_k, ] (n-1) ], the first quantum operation performed on a kth quantum bit q_k is an X-gate operation when a character j_k in the binary string is 0, and the first quantum operation performed on a kth quantum bit q_k is an I-gate operation when a character j_k in the binary string is 1; a second operation column for performing a C { n-1} PS (alpha_m) gate operation on n qubits, wherein PS (alpha_m) =diag [1, e { i.alpha_m }, i being an imaginary unit, n-1 th qubit being a target bit, and the qubits from 0 th bit to n-2 nd bit being control bits; and a third operation column including n third quantum gates for performing a third quantum operation on the n quantum bits, respectively, wherein the third quantum operation performed on the kth quantum bit q_k is an X-gate operation when the character j_k in the binary string is 0, and the third quantum operation performed on the kth quantum bit q_k is an I-gate operation when the character j_k in the binary string is 1.
According to another aspect of the application, an electronic device is presented, the electronic device comprising a processor and a memory storing computer program instructions; the electronic device, when executing the computer program instructions, implements a quantum computing method for determining a function classification as described above.
According to another aspect of the application, a computer-readable storage medium having stored thereon computer program instructions which, when executed by a processor, implement a quantum computing method for determining a function classification as described above is presented.
The method solves the function classification problem by using a phase coding mode, namely, classical information is coded in the phase of the corresponding quantum bit, so that any classical information cannot be lost. The quantum state after phase encoding is the maximum entangled state, and the advantage of quantum entanglement is utilized to the maximum extent. The function classification problem can be efficiently solved by adopting a phase encoding mode.
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Preferred embodiments of the present application will be described in further detail below with reference to the attached drawing figures, wherein:
FIG. 1 is a flow chart of a quantum computing method for determining a class of functions according to one embodiment of the application.
Fig. 2 is a flowchart of performing a corresponding quantum operation on n quantum bits based on the value theta_m of the mth data bit and the sequence number m of the current data bit in step S15 in fig. 1.
Fig. 3 is a flow chart of a process of performing a first quantum operation on n qubits by traversing characters in the binary string S at step S152 in fig. 2.
Fig. 4 is a flowchart of a method for determining a function classification label to be classified in step S20 in fig. 1.
FIG. 5 is a flow chart of a method of rotation angle parameter optimization in accordance with one embodiment of the present application.
Fig. 6 is a schematic diagram of a quantum circuit for determining a class of functions implemented in accordance with the method shown in fig. 1.
Fig. 7 is a flow chart of a quantum computing method for determining a classification of a function according to another embodiment of the invention.
Fig. 8 is a quantum circuit diagram obtained by performing the method shown in fig. 7.
Fig. 9 is a quantum circuit diagram after optimization of RY quantum gates, according to one embodiment of the application.
Fig. 10 is a schematic diagram of a quantum circuit obtained by encoding 16-bit classical data using 4 qubits based on the methods shown in fig. 1 to 3.
Fig. 11 is a schematic diagram of a quantum circuit obtained by optimizing fig. 10 based on the optimization method in fig. 7.
Fig. 12 is a schematic diagram of the quantum circuit obtained by optimizing fig. 11 based on the method of optimizing the RY gate.
FIG. 13 is a schematic block diagram of an apparatus for solving a function three-classification problem based on a variable component sub-algorithm in accordance with an embodiment of the invention.
Fig. 14 is a block diagram of an electronic device according to an embodiment of the invention.
Detailed Description
The principles and spirit of the present invention will be described below with reference to several exemplary embodiments. It will be appreciated that such embodiments are provided to make the principles and spirit of the invention clear and thorough, and enabling those skilled in the art to better understand and practice the principles and spirit of the invention. The exemplary embodiments provided herein are merely some, but not all embodiments of the invention. All other embodiments, which can be made by one of ordinary skill in the art without undue burden from the embodiments herein, are within the scope of the present invention.
Those skilled in the art will appreciate that embodiments of the invention may be implemented as a quantum computing method, quantum wire, electronic device, and computer readable storage medium for determining a class of functions. Accordingly, the present disclosure may be embodied in at least one of the following forms: complete hardware, complete software (including firmware, resident software, micro-code, etc.), or a combination of hardware and software.
In this document, terms such as first and second are used solely to distinguish one entity (or action) from another entity (or action) without necessarily requiring or implying any order or relationship between such entities (or actions). In this document, an element (e.g., a component, a composition, a process, a step) defined by the phrase "comprising … …" does not exclude the presence of other elements other than those listed, i.e., may include other elements not explicitly listed. Any elements in the figures and their number are used herein for illustration and not limitation, and any naming in the figures is used for distinction only and does not have any limiting meaning.
The principles and spirit of the present invention are explained in detail below with reference to several exemplary or representative embodiments thereof.
In order to solve the problems, the application provides an accurate variable component sub-algorithm solving function three-classification problem based on phase encoding. In solving classical problems using quantum algorithms, quantum encoding is an indispensable step, which refers to the process of converting classical information into quantum states. The three-classification problem of the function can be efficiently solved through the accurate variable component sub-algorithm of the phase coding, and the physical experiment implementation is easier.
FIG. 1 is a flow chart of a quantum computing method for determining a class of functions according to one embodiment of the application. In this embodiment, the function to be classified is a multi-bit binary data, where the number of bits N of the binary data satisfies n=2 n, N is a natural number, the function to be classified may be an N-bit data D, d= [ theta_0, theta_1, ], theta_m, -, theta_ (N-1) ], m is a data bit sequence number of the multi-bit binary data, m=0, 1, -, N-1, and n=2 n, and the method is performed on a quantum wire, and includes the following steps:
in step S11, the |0> state of n qubits q_k is prepared, where k is the number of qubits, k=0, 1, …, n-1.
And S12, respectively performing H gate operation on the n quantum bits in the state of |0> to obtain a uniform superposition state.
Step S13, setting m=0.
Step S14, the value theta_m of the mth data bit is obtained from the function to be classified.
In step S15, corresponding quantum operations are performed on the n quantum bits based on the value theta_m of the mth data bit and the sequence number m of the current data bit of the multi-bit binary data, and the specific process is shown in fig. 2.
Step S16, determining whether the sequence number m of the current data bit of the multi-bit binary data is equal to N-1, if the sequence number m of the current data bit is smaller than N-1, indicating that there are more data bits not encoded, setting m=m+1 in step S17, and returning to step S14. If the sequence number m of the current data bit is equal to N-1,
If it is indicated that the encoding of the data bit has been completed, step S18 is performed, where n qubits are respectively subjected to RY gate operation or one qubit of the n qubits is subjected to RY gate operation, and n-1 qubits are subjected to H gate operation, where the parameter of the RY gate corresponding to the kth qubit is beta_k.
Step S19, all quantum bits are measured, and the probability P 0 of all 0 states is counted.
And S20, determining a classification label of the function to be classified according to the probability P 0, wherein the rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
Referring to fig. 2, fig. 2 is a flowchart of fig. 1 in which corresponding quantum operations are performed on n quantum bits based on the value theta_m of the mth data bit and the sequence number m of the current data bit, and the following operations are sequentially performed on n quantum bits based on each data bit from the 0 th data bit of the data sample, and specifically include the following steps:
Step S151, converting the current data bit sequence number m into an n-bit binary string S, s= [ j_0, j_1, ], j_k, ], j_ (n-1) ], where the characters in the binary string correspond to the sequence numbers of the qubits one by one in the order from low to high.
Step S152, traversing the characters in the binary string S, and performing a first quantum operation on the n quantum bits based on the n character pairs in the binary string S, where the specific performing step is referred to in fig. 3.
In step S153, alpha_m=theta_m·pi is calculated, where pi is the circumference ratio.
In step S154, a C { n-1} PS (alpha_m) gate operation is performed on n qubits, where PS (alpha_m) =diag [1, e { i.alpha_m }, i is an imaginary unit, n-1 qubits are target bits, and qubits from 0 th bit to n-2 nd bit are control bits.
Step S155, traversing the characters in the binary string S, and performing a third quantum operation on the n quantum bits based on the n pairs of characters in the binary string S, respectively.
After the steps are executed, the coding of the mth data bit is realized, and the quantum gate and the quantum circuit for realizing the mth data bit are obtained.
Referring to fig. 3, fig. 3 is a flowchart of a process for performing a first quantum operation on n qubits by traversing characters in the binary string S at step S152 in fig. 2, and specifically includes the steps of:
In step S1521, k=0 is set.
In step S1522, the kth character j_k is acquired from the low order bits of the binary string S.
In step S1523, it is determined whether the character j_k is equal to 0, and if j_k is equal to 0, the X gate operation is performed on the kth qubit q_k in step S1524, and then step S1526 is performed. If j_k is not equal to 0 but equal to 1, an I gate operation is performed on the kth qubit q_k in step S1525, and then step S1526 is performed.
Step S1526, determine whether k is equal to n-1, if not, set k=k+1, and return to step S1522. If k is equal to n-1, this indicates that the first quantum operation for the mth bit data bit of the n quantum bits has been completed, at which point step S153 in FIG. 2 is performed.
The process of traversing the character in the binary string S in step S155 to perform the third quantum operation on the n quantum bits is substantially the same as the process of traversing the character in the binary string S in step S152 to perform the first quantum operation on the n quantum bits, except that when k is equal to n-1, it is explained that the third quantum operation on the m-th data bit of the n quantum bits has been completed, and at this time, the process goes to step S16 in fig. 1, and the remaining steps are the same, so that the description of the process of step S155 is not repeated.
Fig. 4 is a flowchart of a method for determining a function classification label to be classified in step S20 in fig. 1, which specifically includes the following steps:
Step S201, judging the size relation between the probability P 0、1-P0 and 1- (2/N) 2 +epsilon, wherein epsilon is a real number, and the value range is (0, (2/N) 2);
Step S202, if P 0 is the largest, determining the function label to be classified as a constant function;
Step S203, if 1-P 0 is the largest, determining the function label to be classified as a balance function;
Step S204, if 1- (2/N) 2 +epsilon is maximum, determining the function label to be classified as a very valued function unbalanced function.
FIG. 5 is a flow chart of a method of rotation angle parameter optimization in accordance with one embodiment of the present application. The method specifically comprises the following steps:
step S501, initializing a rotation angle parameter of the RY door;
Step S502, executing the quantum computing method for determining function classification and determining measurement classification results;
step S503, calculating a loss function value according to the measurement classification result and the actual classification result;
Step S504, calculating the loss function value through a classical optimizer to obtain an optimized rotation angle parameter value of the RY door;
in step S505, the optimized rotation angle parameter value of the RY gate is substituted into the quantum circuit to calculate the loss function value again until the optimized rotation angle parameter value converges to the set threshold.
In the rotation angle parameter optimization process, training is required by utilizing data samples in a training set. The data sample is the functions to be classified, and each function to be classified comprises an input-output relationship and a classification label. According to the application, the optimized parameter value is calculated according to the loss function value through the classical optimizer, so that some common limitations in quantum calculation, such as quantum noise and errors of gate operation, are avoided. By iteratively optimizing the parameter values, the accuracy of the classification can be gradually improved. By iteratively optimizing the rotation angle parameter of the RY gate until a set convergence threshold is met, it can be ensured that the resulting solution is sufficiently close to the optimal solution. The smaller the convergence threshold, the closer the optimized rotation angle parameter is to the optimal solution.
The process of rotation angle parameter optimization requires some training time. On the premise of ensuring the classification accuracy, the number of RY is reduced in the quantum circuit, so that the optimization time is reduced, and the aim of high-efficiency optimization is fulfilled.
Fig. 6 is a schematic diagram of a quantum circuit for determining a class of functions implemented in accordance with the method shown in fig. 1. In this embodiment, n qubits are total, and each qubit of the quantum system is in the |0> state after going through step S11 of fig. 1. After step S12 of fig. 1, a current column of H gates is obtained, and a uniform superposition state is obtained by performing an H gate operation on the qubit. The units of 0,1, …, N-2, N-1 are separated by dotted lines in the figure and respectively correspond to data bits of one classical data, for convenience of explanation, quantum circuits corresponding to one data bit of classical data are named as operation units m_m, m=0, 1, and N-1, which respectively correspond to data bits of the data sample one by one, and the operation unit m_m is used for executing corresponding quantum operations on N quantum bits based on a value theta_m of an mth data bit and a sequence number M of a current data bit, and N operation units connected according to the sequence of the sequence numbers of the data bits are shared in fig. 6. After N qubits are performed by N columns of operation units m_m, RY gate operations are performed on N qubits through one column of RY gates.
Each column of the operation units m_m sequentially includes a first operation column, a second operation column, and a third operation column in order from front to back. The terms "front" and "rear" refer to "front" and "rear" in a temporal sense, corresponding to fig. 6, i.e., left front, right rear, in order from front to rear, i.e., in order from left to right.
The first operation column includes n quantum gates, and performs a first quantum operation on the n quantum bits, respectively. To determine whether a quantum gate to which a first quantum operation should be performed for each of the qubits according to the current data bit sequence number is an X gate or an I gate, the present embodiment converts the current data bit sequence number m into an n-bit binary string s= [ j_0, j_1 ], j_k, j_ (n-1) ], and when a kth bit character j_k from a low bit is 0, the quantum gate to which the first quantum operation is performed for the kth quantum bit q_k is an X gate, and when j_k is 1, the quantum gate to which the first quantum operation is performed for the kth quantum bit q_k is an I gate. Referring to fig. 6, when m=0, the corresponding binary string S is composed of n 0S, i.e., s= [0, ], 0] thus the binary character j_k corresponding to each qubit is 0, and thus the first operation column in the 0 th bit data bit is n X gates. When m=1, the corresponding binary string s= [0, ], 0, 1], i.e., the 0 th bit character of the least significant bit is 1, and thus the I-gate operation is performed on the 0 th qubit, as in the position illustrated by the dashed line box in the figure. Since the meaning of performing the I-gate operation in the quantum wire is not to perform any operation on the qubit, the present embodiment does not add any quantum gate symbol in the quantum wire, and the dashed box in the figure is only used to illustrate the I-gate in the foregoing description, where virtually no quantum operation is performed.
The second operation column performs a C { n-1} PS (alpha_m) gate operation on n qubits, where alpha_m=theta_m·pi, PS (alpha_m) =diag [1, e { i·alpha_m } ], and i is an imaginary unit, pi is a peripheral rate, n-1 qubits are target bits, and qubits from 0 th bit to n-2 nd bits are control bits.
The third operation column is the same as the first operation column, and includes n quantum gates, and performs a third quantum operation on n quantum bits, respectively, and when j_k is 0, the quantum gate performing the third quantum operation on the kth quantum bit q_k is an X gate, and when j_k is 1, the quantum gate performing the third quantum operation on the kth quantum bit q_k is an I gate.
As can be seen from the above-described flow charts shown in fig. 1 to 3 and the quantum circuits shown in fig. 6, the n=2 n -dimensional data samples can be encoded with only N qubits. Since the dimension of each data sample is n=2 n, the number N of the quantum bits is the minimum number of the quantum bits applied to the encoded classical data, and auxiliary quantum bits are not needed, so that the advantage of quantum computation, namely quantum superposition, is reflected.
In addition, the quantum state after quantum phase encoding is the maximum entangled state. Because the elements in each data sample are only 0 and 1, classical information is encoded in the phase of the corresponding quantum bit, no classical information is lost, and the quantum state after phase encoding is the maximum entangled state, the invention maximally utilizes the other advantage of quantum computing, namely quantum entanglement. The quantum circuit for quantum coding provided by the invention can be realized by a programming code, and has small programming difficulty and easy realization.
After the coding of the data bit is completed, respectively executing RY gate operation on n quantum bits, then outputting and measuring all the quantum bits, and counting the probability P 0 of all 0 states; and finally, determining the classification label of the function to be classified according to the probability P 0. As shown in fig. 6, the rotation angle parameters of the n RY gates are β 0、β1、β2、……βn-1, respectively, and the rotation angle parameters of the RY gates are optimized by a classical optimizer and fixed in the quantum circuit.
Fig. 7 is a flow chart of a quantum computing method for determining a classification of a function according to another embodiment of the invention. In this embodiment, including the method according to fig. 1 to 3, the present embodiment further includes the following optimization step (first-order optimization) after obtaining the quantum wire:
And S31, eliminating the first column X gate after the H gate in the quantum circuit. Since performing an X gate operation on a qubit of a uniformly stacked state does not change the state of the qustate, the first column of X gates after the H gates are eliminated does not affect the state of the current qubit.
Because ofActing on the homogeneous superposition state without changing the quantum state, i.e.:
；
And step S32, checking the quantum operation performed on each quantum bit in the quantum circuit from front to back.
In step S33, it is determined whether or not two X-gate operations are continuously performed on one qubit, and when two X-gate operations are continuously performed on one qubit, in step S34, two adjacent X-gates are eliminated from the quantum wire, because when two X-gate operations are continuously performed on one qubit, it is equivalent to not performing any operation on the qubit, that is, X 2 =i, and the state after two X-gate operations are the same as the state before the operation, the quantum form is not changed after two adjacent X-gates are eliminated, and the quantum operation is reduced, and the quantum gate is saved.
If two X gate operations are not continuously performed on one qubit, in step S35, it is determined whether the last quantum operation of the quantum wire is checked, if the last quantum operation of the quantum wire is checked, the optimization operation is ended, if the last quantum operation of the quantum wire is not checked, the process returns to step S32, and the check is continued until the last quantum operation of the quantum wire is checked.
According to one embodiment of the application, the optimizing step further comprises (secondary optimization): n-1 RY gates are replaced with n-1H gates, only one RY gate is retained. Wherein, the RY door that remains can be any one of n RY doors, and the location of the reservation is not required. The number of RY gates is reduced, the training time can be further reduced, and the efficiency of parameter optimization is improved.
Fig. 6 is a schematic diagram of a quantum circuit for determining a function class implemented according to the method of fig. 1, resulting in the quantum circuit of fig. 8, when the method of fig. 7 is performed again on the basis of the method steps of fig. 1. The quantum circuit shown in fig. 9 is obtained after the second-level optimization is performed on the basis of fig. 8. As can be seen from comparison of fig. 6, 8 and 9, after the optimization step, the quantum gates in the quantum circuit, especially the parametric sub-gates, can be reduced. Therefore, the training time of the quantum circuit can be greatly shortened, and the running efficiency of the system is improved.
Fig. 10 is a schematic diagram of a quantum circuit obtained by encoding 16-bit classical data using 4 qubits based on the methods shown in fig. 1 to 3. As shown in fig. 10, the initial quantum circuit is trained with 10000 data samples (i.e., 10000 functions, each function containing its input-output relationship and its class labels) generated randomly. For example, the first 8000 data samples may be the training set and the last 2000 data samples the test set. According to the method shown in fig. 1-3, corresponding quantum gate operation is built in quantum computing software, and after training, the obtained quantum circuit is shown in fig. 10. Here, the classification criteria are [ P 0,1-P0, 63.5/64], and epsilon is 0.5/64.
The classification judgment is carried out on 2000 test samples through the quantum circuit, and the classification accuracy of 100% can be found, wherein the training time is 69.59 seconds.
Fig. 11 is a schematic diagram of a quantum circuit obtained by optimizing fig. 10 based on the optimization method in fig. 7. Similar to the above method, the classification judgment is performed on 2000 test samples through the quantum circuits optimized in fig. 11, and it is found that the classification accuracy of 100% can be achieved, wherein the training time is 50.04 seconds.
Fig. 12 is a schematic diagram of the quantum circuit obtained by optimizing fig. 11 based on the method of optimizing the RY gate. Similar to the above method, 2000 test samples were classified and judged via the quantum circuit optimized in fig. 12, and it was found that 100% classification accuracy could be achieved, in which the training time period was 44.57 seconds. Therefore, under the premise of ensuring the classification accuracy, the primary and secondary optimization schemes gradually reduce training time along with the reduction of the quantum gates and the parameter gates, and the training efficiency is greatly improved.
FIG. 13 is a schematic block diagram of a quantum computing device for determining a class of functions according to one embodiment of the invention, the quantum computing device for determining a class of functions comprising: a data acquisition unit 10, a bit sequence number conversion unit 20, a PS gate parameter calculation unit 30, a ground state preparation unit 40, an H gate operation unit 50, a first quantum operation unit 60, a second quantum operation unit 70, a RY gate operation unit 80, a probability statistics unit 90, and a classification determination unit 100. The data acquisition unit 10 is configured to acquire a function to be classified (classical data sample) and corresponding sample parameters, where the classical data sample is an N-bit data D, d= [ theta_0, theta_1, ], theta_m, theta_ (N-1) ], and satisfies: theta_m is the value of the mth data bit, belonging to {0,1}, m is the data bit sequence number of the data sample, m=0, 1,... The sample parameters are, for example, the data bit sequence number m of the classical data sample, the value theta_m of each data bit and the total number of bits N.
The bit sequence number conversion unit 20 is configured to convert each data bit sequence number into an n-bit binary string S, s= [ j_0, j_1 ], j_k ], j_ (n-1) ], where the characters in the binary string correspond to the sequence numbers of the qubits one by one in the order from low to high. Thus, a set { Sm } of all corresponding binary strings from the 0 th data bit to the N-1 th data bit is obtained, sm=s 0,S1,…,Sm,…,SN-1. The PS gate parameter calculation unit 30 is configured to calculate a PS gate parameter alpha_m, where alpha_m=theta_m·pi, pi is a circumference ratio.
The data acquisition unit 10, the bit sequence number conversion unit 20, and the PS gate parameter calculation unit 30 are used as data preparation units for obtaining data or parameters applied in the encoding process, respectively.
The ground state preparation unit 40 is connected to the data acquisition unit 10, and prepares a state |0> for n qubits q_k according to the obtained parameter n, where the sequence number k of the n qubits is the sequence number of the qubits, k=0, 1, …, n-1.
After the base state preparing unit 40 completes |0> for n qubits, the H-gate operating unit 50 performs H-gate operations on n qubits of the |0> state, respectively, to obtain a uniform superposition state.
The first quantum operation unit 60 and the second quantum operation unit 70 cooperate to encode classical data of each data bit in ascending order of classical data bits. The H-gate operation unit 50 performs H-gate operation on the n quantum bits in the |0> state, respectively, to obtain a uniform superposition state, and then sends a notification to the first quantum operation unit 60.
The first quantum operation unit 60 is connected to the bit sequence number conversion unit 20, and obtains an n-bit binary string S 0,S0 = [ j_0, j_1, ], j_k, ], j_ (n-1) ] of the 0-th data bit sequence number from the bit sequence number conversion unit 20. The characters in the binary string S 0 are traversed in accordance with the flow shown in fig. 3, and the first quantum operation is performed on the n qubits based on the n characters in the binary string S 0, respectively. Wherein the first quantum operation performed on the kth quantum bit q_k is an X-gate operation when j_k is 0, and the first quantum operation performed on the kth quantum bit q_k is an I-gate operation when j_k is 1. The second quantum operation unit 70 is notified after the first quantum operation is performed on the n-bit quantum bit.
The second quantum operation unit 70 is connected to the PS gate parameter calculation unit 30, from which the PS gate parameter alpha_m is obtained, and for the 0 th data bit, the PS gate parameter alpha_0 is obtained. Then, a C { n-1} PS (alpha_m) gate operation is performed on n qubits, where PS (alpha_m) =diag [1, e { i.alpha_m }, i is an imaginary unit, n-1 qubits are target bits, qubits from 0 th bit to n-2 nd bit are control bits, i.e., the last qubit is the target bit, and other qubits are control bits. After this operation is completed, a notification is sent to the first quantum operation unit 60.
The first quantum operation unit 60 traverses the characters in the binary string S 0 after receiving the notification of the second quantum operation unit 70, performs a third quantum operation on n quantum bits based on n characters in the binary string S 0, respectively, wherein the third quantum operation performed on the kth quantum bit q_k is an X gate operation when j_k is 0, and the third quantum operation performed on the kth quantum bit q_k is an I gate operation when j_k is 1.
When the first quantum operation unit 60 performs the third quantum operation on n quantum bits, an n-bit binary string S 1,S1 of the 1 st data bit sequence number is obtained from the bit sequence number conversion unit 20= [ j_0, j_1, ], j_k, ], j_ (n-1) ]. The operation on the 0 th data bit is repeated until the third quantum operation of the N-1 th data bit is performed on the N quantum bits.
After the first quantum operation unit 60 performs the third quantum operation of the N-1 th data bit on the N quantum bits, the RY gate operation unit 80 performs the RY gate operation on the N quantum bits. The probability statistics unit 90 is connected to the RY gate operation unit 80, and the probability statistics unit 90 is configured to measure all qubits and count the probability P 0 of all 0 states. The classification determining unit 100 is connected to the probability statistics unit 90, and the classification determining unit 100 is configured to determine a classification label of the function to be classified according to the probability P 0.
Further, an optimizing unit 110 is further included, which is connected to the RY gate operating unit 80 in one embodiment, and after the RY gate operating unit 80 performs RY gate operations on n qubits, after a quantum wire is obtained, the first column X gate after the H gate in the quantum wire is eliminated, and the quantum operation performed on each qubit in the quantum wire is checked, and when it is checked that two X gate operations are consecutively performed on one qubit, two adjacent X gates are eliminated from the quantum wire, thereby obtaining an optimized quantum wire as shown in fig. 8. In another embodiment, as the first and second quantum operation units 60 and 70 alternately perform the corresponding quantum operations on all the quantum bits according to the respective data bits, it is checked whether or not two X gate operations are consecutively performed on one quantum bit, so that the optimization is performed while performing the corresponding quantum operations on all the quantum bits, thereby obtaining an optimized quantum wire while completing all the quantum operations. Further, n-1 RY gates are replaced with n-1H gates, and only one RY gate is left, thereby obtaining an optimized quantum wire as shown in FIG. 9.
In another aspect, the present invention further provides an electronic device, referring to fig. 14, and fig. 14 is a schematic block diagram of a structure of the electronic device according to an embodiment of the present invention. As shown in fig. 14, the electronic device includes a processor 601 and a memory 602 storing computer program instructions; the processor 601, when executing the computer program instructions, implements the quantum phase encoding method of the previous embodiments.
In particular, processor 601 may include a Central Processing Unit (CPU) or Graphics Processor (GPU), or an Application SPECIFIC INTEGRATED Circuit (ASIC), or may be configured as one or more integrated circuits that implement embodiments of the present invention. Memory 602 may include memory for data or instructions. For example, the memory 602 may be at least one of: a hard disk drive (HARD DISK DRIVE, HDD), read-only memory (ROM), random-access memory (RAM), floppy disk drive, flash memory, optical disk, magneto-optical disk, magnetic tape, universal serial bus (Universal Serial Bus, USB) drive, or other physical/tangible memory storage device. As another example, the memory 602 includes removable or non-removable (or fixed) media. For another example, memory 602 may be internal or external to the integrated gateway disaster recovery device. The memory 602 may be a non-volatile solid state memory. In other words, generally the memory 602 includes a tangible (non-transitory) computer-readable storage medium (e.g., a memory device) encoded with executable instructions that, when executed by the processor 601 (e.g., by one or more processors), implement the quantum phase encoding method in embodiments of the invention.
In one example, the electronic device shown in fig. 14 may also include a communication interface 603 and a bus 610. The processor 601, the memory 602, and the communication interface 603 are connected to each other through a bus 610 and perform communication with each other. The communication interface 603 is primarily used to enable communication between modules, devices, units and/or apparatuses in an electronic apparatus.
Bus 610 includes hardware, software, or both, and may couple components of the online data flow billing device to each other. For example, the bus may include at least one of: accelerated Graphics Port (AGP) or other graphics bus, enhanced Industry Standard Architecture (EISA) bus, front Side Bus (FSB), hyperTransport (HT) interconnect, industry Standard Architecture (ISA) bus, infiniBand interconnect, low Pin Count (LPC) bus, memory bus, micro channel architecture (MCa) bus, peripheral Component Interconnect (PCI) bus, PCI-Express (PCI-X) bus, serial Advanced Technology Attachment (SATA) bus, video electronics standards Association local (VLB) bus, or other suitable bus. Bus 610 may include one or more buses. Although embodiments of the invention describe or illustrate a particular bus, embodiments of the invention contemplate any suitable bus or interconnection.
In another aspect, embodiments of the present invention also provide a computer readable storage medium having stored thereon computer program instructions which, when executed by a processor, implement the foregoing quantum phase encoding method.
The foregoing exemplary flowcharts and/or block diagrams of methods and systems according to embodiments of the present invention are described above and related aspects are described. It will be understood that each block of the flowchart illustrations and/or block diagrams, or combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions, special purpose hardware which perform the specified functions or acts, and combinations of special purpose hardware and computer instructions. For example, these computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the present invention, enable the implementation of the functions/acts specified in the flowchart and/or block diagram block or blocks. Such a processor may be a general purpose processor, a special purpose processor, an application specific processor, or a field programmable logic circuit.
Functional blocks shown in the block diagrams of the embodiments of the present invention can be implemented in hardware, software, firmware, or a combination thereof. When implemented in hardware, it may be, for example, an electronic circuit, an Application Specific Integrated Circuit (ASIC), suitable firmware, a plug-in, a function card, or the like; when implemented in software, are the programs or code segments used to perform the required tasks. The program or code segments can be stored in a memory or transmitted over transmission media or communication links through data signals carried in carrier waves. The code segments may be downloaded via computer networks such as the internet, intranets, etc.
It should be noted that the present invention is not limited to the specific configurations and processes described above or shown in the drawings. The foregoing is merely specific embodiments of the present invention, and it will be clearly understood by those skilled in the art that, for convenience and brevity of description, specific working processes of the described system, apparatus, module or unit may refer to corresponding processes in the method embodiments, and need not be repeated. It should be understood that the scope of the present invention is not limited thereto, and any person skilled in the art may conceive various equivalent modifications or substitutions within the technical scope of the present invention, which are intended to be included in the scope of the present invention.

Claims (10)

1. A quantum computing method for determining a class of functions, the functions to be classified being a multi-bit binary data, and the number of bits N of the multi-bit binary data satisfying n=2 n, N being a natural number, characterized in that the method is performed on a quantum wire and comprises:
Preparing n quantum bits in the state of |0 >;
Respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states;
sequentially executing corresponding quantum operations on n quantum bits based on the numerical value of the function to be classified and the serial number of the current data bit of the multi-bit binary data;
Performing RY gate operation on n qubits or performing RY gate operation on one qubit of n qubits, respectively, and performing H gate operation on n-1 qubits;
measuring all quantum bits, and counting the probability P 0 of all 0 states;
Determining a classification label of the function to be classified according to the probability P 0;
The rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
2. The method of claim 1, wherein performing the method on a quantum wire comprises:
Preparing n quantum bits in the state of |0 >;
Respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states;
sequentially executing corresponding quantum operations on n quantum bits based on the numerical value of the function to be classified and the serial number of the multi-bit binary data bit;
Performing RY gate operations on the n qubits respectively;
measuring all quantum bits, and counting the probability P 0 of all 0 states;
Determining a classification label of the function to be classified according to the probability P 0;
The rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
3. The method of claim 1, wherein performing the method on a quantum wire comprises:
Preparing n quantum bits in the state of |0 >;
Respectively executing H gate operation on n quantum bits in the state of |0> to obtain uniform superposition states;
sequentially executing corresponding quantum operations on the n quantum bits based on the numerical value of the function to be classified and the serial number of the data bit;
Performing RY gate operation on one of n qubits, and performing H gate operation on n-1 qubits;
measuring all quantum bits, and counting the probability P 0 of all 0 states;
Determining a classification label of the function to be classified according to the probability P 0;
The rotation angle parameter of the RY gate is optimized by a classical optimizer and is fixed in a quantum circuit.
4. The method of claim 1, wherein sequentially performing respective quantum operations on n qubits based on the value of the function to be classified and the sequence number of the data bits comprises: the following operations are performed on N qubits in sequence, starting with the 0 th data bit of the data sample, on each data bit, the multi-bit binary data being denoted [ theta_0, theta_1, ], theta_m, ], theta_ (N-1) ]:
Converting the current data bit sequence number m of the multi-bit binary data into an n-bit binary character string [ j_0, j_1 ],. J_k ],. J_ (n-1) ], wherein characters in the binary character string correspond to sequence numbers of n quantum bits Q_k one by one in the sequence from low bit to high bit, k is the sequence number of the quantum bits, and k=0, 1, … and n-1;
Respectively executing first quantum operations on n quantum bits Q_k, wherein when a character j_k in a binary character string is 0, the first quantum operations on the k quantum bits Q_k are X gate operations, and when the character j_k in the binary character string is 1, the first quantum operations on the k quantum bits Q_k are I gate operations;
calculating alpha_m=theta_m·pi, wherein pi is the circumference ratio;
After performing a first quantum operation on n qubits q_k, performing a C { n-1} PS (alpha_m) gate operation on n qubits, wherein PS (alpha_m) =diag [1, e { i·alpha_m } ], i being an imaginary unit, n-1 th qubit being a target bit, and qubits from 0 th to n-2 th bits being control bits;
and performing a third quantum operation on the n quantum bits, respectively, wherein the third quantum operation performed on the kth quantum bit q_k is an X-gate operation when the character j_k in the binary string is 0, and the third quantum operation performed on the kth quantum bit q_k is an I-gate operation when the character j_k in the binary string is 1.
5. The method of claim 1, wherein determining the classification label of the function to be classified according to probability P 0 comprises:
Judging the size relation between the probability P 0、1-P0 and 1- (2/N) 2 +epsilon, wherein epsilon is a real number, and the value range is (0, (2/N) 2);
If P 0 is maximum, determining the function label to be classified as a constant function;
if 1-P 0 is the largest, determining the function label to be classified as a balance function;
If 1- (2/N) 2 +epsilon is maximum, determining the function label to be classified as a very valued function unbalanced function.
6. The method of claim 1, wherein the optimization of the rotation angle of the RY door comprises:
Initializing a rotation angle parameter of the RY door;
Executing the quantum computing method for determining function classification and determining measurement classification results;
calculating a loss function value according to the measurement classification result and the actual classification result;
Calculating the loss function value through a classical optimizer to obtain an optimized RY door rotation angle parameter value;
Substituting the optimized rotation angle parameter value of the RY gate into the quantum circuit to calculate the loss function value again until the optimized rotation angle parameter value is converged to a set threshold value.
7. A quantum circuit for determining a class of functions, wherein the function to be classified is a multi-bit binary data, and the number of bits N of the multi-bit binary data satisfies n=2 n, N being a natural number, comprising:
a column of H gates, which is used for executing H gate operation to the n quantum bits in the state of |0> to obtain a uniform superposition state;
The N columns of operation units are respectively in one-to-one correspondence with the data bits of the multi-bit binary data, and are used for sequentially executing corresponding quantum operations on N quantum bits based on the numerical value of the function to be classified and the serial number of the multi-bit binary data bits;
One or more RY gates for performing RY gate operations on the qubits.
8. The quantum wire of claim 7, wherein each column of operation units sequentially comprises, in order from front to back:
A first operation column including n first quantum gates, performing first quantum operations on n quantum bits, respectively, wherein a current data bit sequence number m is converted into an n-bit binary string [ j_0, j_1, ], j_k, ] (n-1) ], the first quantum operation performed on a kth quantum bit q_k is an X-gate operation when a character j_k in the binary string is 0, and the first quantum operation performed on a kth quantum bit q_k is an I-gate operation when a character j_k in the binary string is 1;
A second operation column for performing a C { n-1} PS (alpha_m) gate operation on n qubits, wherein PS (alpha_m) =diag [1, e { i.alpha_m }, i being an imaginary unit, n-1 th qubit being a target bit, and the qubits from 0 th bit to n-2 nd bit being control bits;
And a third operation column including n third quantum gates for performing a third quantum operation on the n quantum bits, respectively, wherein the third quantum operation performed on the kth quantum bit q_k is an X-gate operation when the character j_k in the binary string is 0, and the third quantum operation performed on the kth quantum bit q_k is an I-gate operation when the character j_k in the binary string is 1.
9. An electronic device comprising a processor and a memory storing computer program instructions; the electronic device, when executing the computer program instructions, implements a quantum computing method for determining a function classification as claimed in any one of claims 1-6.
10. A computer-readable storage medium, having stored thereon computer program instructions which, when executed by a processor, implement the quantum computing method for determining function classification of any of claims 1-6.
CN202410420939.7A 2024-04-09 2024-04-09 Quantum computing method, quantum circuit, device and medium for determining function classification Pending CN118014094A (en)

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