CN113222151B - Quantum state transformation method and device - Google Patents
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Abstract
The invention discloses a quantum state transformation method and a device, wherein the method comprises the following steps: obtaining element information of a group of quantum bits and a matrix; wherein a first quantum state of a set of quantum bits encodes a target value for a first type of subscript of an element; searching the value and the element value of a second type of subscript of a specific type element with the value of a first type of subscript as a target value from the element information of the matrix, and encoding the value and the element value information of the second type of subscript onto the quantum states of a first bit and a second bit of a group of quantum bits; and encoding element numerical information of the specific class element onto quantum state amplitude of a third bit of the group of quantum bits to transform the first quantum state into a second quantum state in a first preset form. By utilizing the embodiment of the invention, the quantum state can be converted into the relevant quantum state applied to quantum random walk, and the method is used for classical simulation of quantum calculation so as to fill the blank of the relevant technology.
Description
Technical Field
The invention belongs to the technical field of quantum computing, and particularly relates to a method and a device for transforming a quantum state.
Background
Quantum computers use the superposition of quanta and in theory have the ability to accelerate exponentially in some cases. For example, cracking RSA keys takes hundreds of years on classical computers, while executing quantum algorithms on quantum computers takes only a few hours. However, the current quantum computer is limited by the limited number of controllable bits caused by the development of quantum chip hardware, so that the computing power is limited, and the quantum algorithm cannot be universally run. Generally, quantum algorithms are operated by quantum computing simulation methods.
In the analog implementation of quantum algorithms, it is often necessary to construct the quantum algorithm with the aid of various quantum logic gates. For example, quantum random walk technology is widely used in quantum algorithms that solve hamiltonian simulation and solve a linear system of equations, but in order to obtain relevant quantum states for use in quantum random walk, corresponding quantum circuits are lacking. If various quantum logic gates are utilized to construct an equivalent quantum logic gate for realizing the requirement, the number of the required quantum logic gates is huge, and a quantum circuit corresponding to the constructed quantum algorithm is too complex, so that the research of quantum computing is seriously hampered.
Therefore, it is highly desirable to provide a technique capable of transforming a quantum state into a related quantum state applied in quantum random walk, for classical simulation of quantum computation, so as to fill the gap of the related art.
Disclosure of Invention
The invention aims to provide a quantum state conversion method and device, which are used for solving the defects in the prior art, can convert a quantum state into a relevant quantum state applied to quantum random walk, and is used for classical simulation of quantum computation so as to fill the blank of the relevant technology.
The technical scheme adopted by the invention is as follows:
a method of transforming a quantum state, comprising:
obtaining element information of a group of quantum bits and a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element;
searching the value and the element value of a second type of subscript of a specific type of element with the value of the first type of subscript being the target value from the element information of the matrix, and encoding the value and the element value information of the second type of subscript onto the quantum states of a first bit and a second bit of the group of quantum bits;
and encoding the element numerical information of the specific class element onto the quantum state amplitude of the third bit of the group of quantum bits so as to transform the first quantum state into a second quantum state in a first preset form.
Optionally, the first type subscripts are: row subscripts, the second category subscripts are: the subscripts are listed.
Optionally, the specific class elements are: non-0 element.
Optionally, the searching the value and the element value of the second class index of the specific class element with the same value as the target value from the element information of the matrix, and encoding the value and the element value information of the second class index to the quantum states of the first bit and the second bit of the group of quantum bits includes:
encoding the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row into a first bit in the group of quantum bits so as to transform the first quantum state into a third quantum state; the third quantum state comprises the target value and sequence number information, and each eigenstate forming the third quantum state corresponds to each sequence number one by one;
determining a column index of the non-0 element according to the target value and the sequence number, and encoding the column index into the first bit to transform the third quantum state into a fourth quantum state; wherein the fourth quantum state contains the target value information and the column index information of non-0 element;
And determining the element value of the non-0 element according to the target value information and the column index information, and encoding the element value into a third bit in the group of quantum bits to transform the fourth quantum state into a fifth quantum state containing the target value information, the column index information and the element value information.
Optionally, the determining the column index of the non-0 element according to the row index of the target row and the sequence number includes:
obtaining index relation between serial numbers and column subscripts of elements in all non-0 elements in a pre-constructed matrix row, wherein the elements are non-0 elements in the row;
and determining the column subscript of the non-0 element of the target row according to the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row and the index relation.
Optionally, the encoding the element value information of the specific class element onto the quantum state amplitude of the third bit of the set of quantum bits includes:
transforming an initial sub-quantum state of a third bit in the current set of sub-bits into a sub-quantum state of a second preset form; the second preset form is determined by the first preset form, and the amplitude of the sub-quantum state of the second preset form is determined by the element value of the specific class element.
Optionally, the set of quantum bits further includes: a fourth bit;
the method further comprises the steps of:
and judging whether to execute the step of converting the first quantum state into a second quantum state in a first preset form according to the fourth bit.
Optionally, the step of determining whether to execute the second quantum state of transforming the first quantum state into the first preset form according to the fourth bit includes:
obtaining a sub-quantum state corresponding to the fourth bit in the first quantum state;
and when all bits of the sub-quantum state are 1, executing the step of converting the first quantum state into a second quantum state in a first preset form.
Optionally, the method further comprises:
and performing a transpose conjugation operation corresponding to the step of transforming the first quantum state into a second quantum state in a first preset form, so as to restore the second quantum state into the first quantum state.
A quantum state conversion device, comprising:
the acquisition module is used for acquiring a group of quantum bits and element information of a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element;
The first coding module is used for searching the value and the element value of the second type of subscript of the specific type of element with the value of the first type of subscript being the target value from the element information of the matrix, and coding the value and the element value information of the second type of subscript to the quantum states of the first bit and the second bit of the group of quantum bits;
and the second encoding module is used for encoding the element numerical value information of the specific class element onto the quantum state amplitude of the third bit of the group of quantum bits so as to transform the first quantum state into a second quantum state in a first preset form.
Optionally, the first type subscripts are: row subscripts, the second category subscripts are: the subscripts are listed.
Optionally, the specific class elements are: non-0 element.
Optionally, the first encoding module is specifically configured to:
encoding the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row into a first bit in the group of quantum bits so as to transform the first quantum state into a third quantum state; the third quantum state comprises the target value and sequence number information, and each eigenstate forming the third quantum state corresponds to each sequence number one by one;
Determining a column index of the non-0 element according to the target value and the sequence number, and encoding the column index into the first bit to transform the third quantum state into a fourth quantum state; wherein the fourth quantum state contains the target value information and the column index information of non-0 element;
and determining the element value of the non-0 element according to the target value information and the column index information, and encoding the element value into a third bit in the group of quantum bits to transform the fourth quantum state into a fifth quantum state containing the target value information, the column index information and the element value information.
Optionally, the first encoding module is specifically configured to:
obtaining index relation between serial numbers and column subscripts of elements in all non-0 elements in a pre-constructed matrix row, wherein the elements are non-0 elements in the row;
and determining the column subscript of the non-0 element of the target row according to the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row and the index relation.
Optionally, the second encoding module is specifically configured to:
transforming an initial sub-quantum state of a third bit in the current set of sub-bits into a sub-quantum state of a second preset form; the second preset form is determined by the first preset form, and the amplitude of the sub-quantum state of the second preset form is determined by the element value of the specific class element.
Optionally, the set of quantum bits further includes: a fourth bit;
the apparatus further comprises:
and the judging module is used for judging whether to execute the step of converting the first quantum state into the second quantum state in the first preset form according to the fourth bit.
Optionally, the judging module is specifically configured to:
obtaining a sub-quantum state corresponding to the fourth bit in the first quantum state;
and when all bits of the sub-quantum state are 1, executing the step of converting the first quantum state into a second quantum state in a first preset form.
Optionally, the apparatus further includes:
and the transpose conjugation operation module is used for executing transpose conjugation operation corresponding to the step of converting the first quantum state into a second quantum state in a first preset form so as to restore the second quantum state into the first quantum state.
A storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of the preceding claims when run.
An electronic device comprising a memory having a computer program stored therein and a processor arranged to run the computer program to perform the method of any of the preceding claims.
Compared with the prior art, the invention provides a quantum state transformation method, which comprises the steps of firstly, obtaining element information of a group of quantum bit and a matrix, wherein the first quantum state of the group of quantum bit codes a target value of a first type index of an element. The method comprises the steps of searching for the value and the element value of a second type subscript of a specific type element, wherein the value of the first type subscript is taken as a target value, encoding the value and the element value information of the second type subscript into a first bit of a group of quantum bits, encoding the element value information of the specific type element into a second bit of the group of quantum bits, so as to convert a first quantum state into a second quantum state in a first preset form, and presetting the form of the quantum state as quantum random walk correlation in practical application, thereby obtaining a specific quantum state (namely the second quantum state) required by quantum random walk, being used for classical simulation of quantum computation, filling up the blank of related technologies, and further expanding researches on quantum algorithms and quantum computers.
Drawings
FIG. 1 is a block diagram of a hardware architecture of a computer terminal of a method for transforming quantum states according to an embodiment of the present invention;
FIG. 2 is a schematic flow chart of a method for transforming a quantum state according to an embodiment of the present application;
fig. 3 is a schematic diagram of a quantum circuit corresponding to a method for transforming a quantum state according to an embodiment of the present application;
fig. 4 is a schematic flow chart of a quantum state conversion device according to an embodiment of the present application.
Detailed Description
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the application.
It should be noted that the terms "first," "second," and the like in the description and in the claims are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order.
The embodiment of the application provides a quantum state conversion method which is used for simulating quantum state conversion operation in a quantum circuit, and can be applied to electronic equipment such as mobile terminals, in particular mobile phones and tablet computers; such as computer terminals, in particular general computers, quantum computers, etc.
The following describes the operation of the computer terminal in detail by taking it as an example. FIG. 1 is a block diagram of a quantum computing analog hardware architecture according to an embodiment of the application. As shown in fig. 1, the computer terminal 10 may include one or more (only one is shown in fig. 1) processors 102 (the processor 102 may include, but is not limited to, a microprocessor MCU or a processing device such as a programmable logic device FPGA) and a memory 104 for storing data, and optionally, a transmission device 106 for communication functions and an input-output device 108. It will be appreciated by those skilled in the art that the configuration shown in fig. 1 is merely illustrative and is not intended to limit the configuration of the computer terminal described above. For example, the computer terminal 10 may also include more or fewer components than shown in FIG. 1, or have a different configuration than shown in FIG. 1.
The memory 104 may be used to store software programs and modules of application software, such as program instructions/modules corresponding to the quantum computing simulation method in the embodiment of the present application, and the processor 102 executes the software programs and modules stored in the memory 104 to perform various functional applications and data processing, i.e., implement the method described above. Memory 104 may include high-speed random access memory, and may also include non-volatile memory, such as one or more magnetic storage devices, flash memory, or other non-volatile solid-state memory. In some examples, the memory 104 may further include memory located remotely from the processor 102, which may be connected to the computer terminal 10 via a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The transmission means 106 is arranged to receive or transmit data via a network. The specific examples of the network described above may include a wireless network provided by a communication provider of the computer terminal 10. In one example, the transmission device 106 includes a network adapter (Network Interface Controller, NIC) that can connect to other network devices through a base station to communicate with the internet. In one example, the transmission device 106 may be a Radio Frequency (RF) module for communicating with the internet wirelessly.
It should be noted that a real quantum computer is a hybrid structure, which includes two major parts: part of the computers are classical computers and are responsible for performing classical computation and control; the other part is quantum equipment, which is responsible for running quantum programs so as to realize quantum computation. The quantum program is a series of instruction sequences written by a quantum language such as the qlunes language and capable of running on a quantum computer, so that the support of quantum logic gate operation is realized, and finally, quantum computing is realized. Specifically, the quantum program is a series of instruction sequences for operating the quantum logic gate according to a certain time sequence.
In practical applications, quantum computing simulations are often required to verify quantum algorithms, quantum applications, etc., due to the development of quantum device hardware. Quantum computing simulation is a process of realizing simulated operation of a quantum program corresponding to a specific problem by means of a virtual architecture (namely a quantum virtual machine) built by resources of a common computer. In general, it is necessary to construct a quantum program corresponding to a specific problem. The quantum program, namely the program for representing the quantum bit and the evolution thereof written in the classical language, wherein the quantum bit, the quantum logic gate and the like related to quantum computation are all represented by corresponding classical codes.
Quantum circuits, which are one embodiment of quantum programs, also weigh sub-logic circuits, are the most commonly used general quantum computing models, representing circuits that operate on qubits under an abstract concept, the composition of which includes qubits, circuits (timelines), and various quantum logic gates, and finally the results often need to be read out by quantum measurement operations.
Unlike conventional circuits, which are connected by metal lines to carry voltage or current signals, in a quantum circuit, the circuit can be seen as being connected by time, i.e., the state of the qubit naturally evolves over time, as indicated by the hamiltonian operator, during which it is operated until a logic gate is encountered.
One quantum program is corresponding to one total quantum circuit, and the quantum program refers to the total quantum circuit, wherein the total number of quantum bits in the total quantum circuit is the same as the total number of quantum bits of the quantum program. It can be understood that: one quantum program may consist of a quantum circuit, a measurement operation for the quantum bits in the quantum circuit, a register to hold the measurement results, and a control flow node (jump instruction), and one quantum circuit may contain several tens to hundreds or even thousands of quantum logic gate operations. The execution process of the quantum program is a process of executing all quantum logic gates according to a certain time sequence. Note that the timing is the time sequence in which a single quantum logic gate is executed.
It should be noted that in classical computation, the most basic unit is a bit, and the most basic control mode is a logic gate, and the purpose of the control circuit can be achieved by a combination of logic gates. Similarly, the way in which the qubits are handled is a quantum logic gate. Quantum logic gates are used, which are the basis for forming a quantum circuit, and comprise single-bit quantum logic gates, such as Hadamard gates (H gates), pauli-X gates, pauli-Y gates, pauli-Z gates, RX gates, RY gates and RZ gates; multi-bit quantum logic gates such as CNOT gate, CR gate, iSWAP gate, toffoli gate. Quantum logic gates are typically represented using unitary matrices, which are not only in matrix form, but also an operation and transformation. The effect of a general quantum logic gate on a quantum state is calculated by multiplying the unitary matrix by the matrix corresponding to the right vector of the quantum state.
Referring to fig. 2, fig. 2 is a schematic flow chart of a quantum state transformation method according to an embodiment of the present invention, which may include the following steps:
s201, obtaining element information of a group of quantum bits and a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element;
Specifically, a set of qubits and element information of a matrix H may be obtained through user input, and the number of the set of qubits may be set by a user according to the size of the matrix structure. Under the condition of sufficient computing resources, a large number of qubits can be set, and the requirements of the qubits under most conditions are satisfied unconditionally.
And, the first type of subscript may be a row subscript, and the second type of subscript may be a column subscript; alternatively, the first type of subscript is a column subscript, the second type of subscript is a row subscript, and the former is taken as an example for description, the target value of the first type of subscript is the target row, and the current quantum state (i.e., the first quantum state) of the set of quantum bits encodes the target row information.
It will be appreciated by those skilled in the art that in classical computers, the basic unit of information is a bit, one bit having two states, 0 and 1, the most common physical implementation being to represent both states by the level of high and low. In quantum computing, the basic unit of information is a qubit, and one qubit also has two states of 0 and 1, which is marked as |0>And |1>But it can be in an overlapped state of two states of 0 and 1, and can be expressed as Wherein a and b are ∈10>Status of->Complex numbers of state amplitudes (probability magnitudes), which are not possessed by classical bits. After measurement, the state of the qubit collapses to a defined state (eigenstate, here +.>Status of->State), where collapse to |0>The probability of (2) is +.>Collapse to |1>The probability of (2) is +.>，/>，|>Is a dirac symbol.
Quantum states, i.e., states of a qubit, whose eigenstates are represented in binary in a quantum algorithm (or weighing subroutine). For example, a group of qubits q0, q1, q2, representing the 0 th, 1 st, and 2 nd qubits, ordered from high order to low order as q2q1q0, the quantum state of the group of qubits being 2 3 The superposition of the individual eigenstates, 8 eigenstates (defined states) refer to: i000>、|001>、|010>、|011>、|100>、|101>、|110>、|111>Each eigenstate corresponds to a qubit, e.g., |000>In states, 000 corresponds to q2q1q0 from high to low. In short, a quantum state is an overlapped state composed of each eigenstate, and when the probability amplitude of the other states is 0, it is in one of the determined eigenstates.
For example, the target value is 2, a group of quantum bits has 5 bits, and the first quantum state thereof may beWherein the two least significant bits are binary 10, which is used to represent row 2 of the target behavior. The useful information is the least significant two-bit information, so the first quantum state can also be abbreviated as +. >。
S202, searching the value and the element value of a second type of subscript of a specific type element with the value of the first type subscript being the target value from the element information of the matrix, and encoding the value and the element value information of the second type subscript onto the quantum states of a first bit and a second bit of the group of quantum bits;
specifically, the specific class element may be a non-0 element. Encoded onto the quantum state of the qubit, in particular onto the right vector of the quantum state, as described aboveIn the form of (a) describes a quantum state by means of a combination of vertical lines and angle brackets, which means that the quantum state is a vector (called state vector, baseVector, etc.),>representing right vector->Representing the left vector.
Specifically, step S202 may include:
step S2021: encoding the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row into a first bit in the group of quantum bits so as to transform the first quantum state into a third quantum state; the third quantum state comprises the target value and sequence number information, and each eigenstate forming the third quantum state corresponds to each sequence number one by one;
In one implementation, the form of the third quantum state may be as follows:
the abbreviation is:. J is a target value and represents the j-th row of the matrix; />Representing tensor product or tensor; d is the total number of non-0 elements of the j-th row; />The sequence numbers of all elements other than 0 in the j-th row for the elements other than 0, indicating +.>Element other than 0, ">The corresponding qubit is the first bit.
Exemplary, a 3-dimensional matrix. From the standpoint of the combination of the computer programming language and the text semantics, the following numbers, labels, etc. are all counted starting at 0. The target value information in the currently obtained first quantum state is 0, namely the target behavior is 0 th row. And in this matrix H d=2, < > and->. Will->The values 0 and 1 of (1) are encoded on the quantum state right vector of the first bit, and the amplitudes are set to +.>. The third quantum state is available:
wherein the sub-quantum stateEigenstates->、/>Corresponding to the 0 th and 1 st non-0 elements. In practical applications, the first quantum state may be transformed to obtain the third quantum state by using the existing H-gate, which is not described herein.
S2022: determining a column index of the non-0 element according to the target value and the sequence number, and encoding the column index into the first bit to transform the third quantum state into a fourth quantum state; wherein the fourth quantum state contains the target value information and the column index information of non-0 element;
In one implementation, the fourth quantum state may be in the form of:
wherein, the liquid crystal display device comprises a liquid crystal display device,column subscript of non-0 element, +.>Representing the set of index positions of the j-th row non-0 element column in matrix H, ++>The corresponding qubit is the first bit.
Continuing with the above example, the column indices of the 0 th and 1 st non-0 th elements in matrix H are 1, 2,. Will->Both values 1 and 2 of (2) are encoded onto the right vector of the quantum state of the first bit, a fourth quantum state is obtained as:
in practical application, the index relation between the serial numbers and the column subscripts of elements in all non-0 elements in a pre-constructed matrix row and all non-0 elements in the row can be obtained; and determining the column subscript of the non-0 element of the target row according to the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row and the index relation.
For example, the number of the cells to be processed,the subscripts of the 0 th row, the 0 th column and the 1 st column of the non-0 elements are 1 and 2, the subscript of the 0 th row and the 1 st column of the non-0 elements are 1, and the subscript of the 0 th column of the non-0 elements of the 2 nd row is 0, a two-dimensional vector (i.e. a matrix) can be constructed in advance by a userAs an index relationship.
Wherein, the elements of the 0 th row and the 0 st column of the matrix F、/>Column subscript indicating row 0, row 1, non-0 element of matrix H is +. >1 and 2. Since row 0 of matrix H has only 2 non-0 elements, the column subscripts of the 2 non-0 elements can be placed preferentially in front of row 0 of matrix F, followed by the redundant element +.>The column subscript representing row 0, element 0 of matrix H is 0. The remaining rows of matrix F are represented in the same way.
Obtaining the two-dimensional vector F input by a user, and taking out according to the condition that the subscript of the element row in the F corresponding to the 0 th row of the target row is 0 and the subscript of the element column in the F corresponding to the serial number 0 is 0I.e. the column subscript of the 0 th non-0 element of row 0 in matrix H. The column subscripts for the remaining non-0 elements are determined as such.
Alternatively, to conserve computing resources, the index constructed may be. Wherein, "%" indicates filling of the space, and is not true.
S2023: and determining the element value of the non-0 element according to the target value information and the column index information, and encoding the element value into a second bit in the group of quantum bits so as to transform the fourth quantum state into a fifth quantum state containing the target value information, the column index information and the element value information.
In one implementation, the fifth quantum state may be in the form of:
wherein, the liquid crystal display device comprises a liquid crystal display device,for row j of matrix- >Non-0 element value of column, ">The corresponding qubit is the second bit. The second bit is not represented in the third and fourth quantum states, does not represent its absence, but is formally ignored due to the absence of the previous conversion of the quantum states, and is the same as the third bit described below.
If it isAs complex numbers, the real and imaginary parts can be encoded onto the second bit positions, i.eReal represents the real part and image represents the imaginary part; if->Written in Euler form->Then +.>And->Is encoded into the second bit, i.e. +.>。
Continuing with the above-described example,，/>. Encoding 1 and 2 onto the third bit, a fifth quantum state is obtained as:
the method comprises the following steps:
and S203, encoding the element numerical information of the specific class element onto the quantum state amplitude of the third bit of the group of quantum bits so as to transform the first quantum state into a second quantum state in a first preset form.
Specifically, the first quantum state of the set of qubits is used as an initial state before transformation, and comprises the sub-quantum state of the qubit for coding jAnd the initial sub-quantum state of the rest of the qubits, the useful information contained is the target value j, i.e. the information of the j-th row, the first quantum state can be simply expressed as +. >The initial sub-quantum state of the remaining qubits is not limited, and is set to +.>A state.
The transformed final state is the second quantum state, its formThe specific quantum state preset by the user, namely the specific quantum state which the user wants to obtain, is used in the technical field of quantum random walk so as to solve the problems of simulating Hamiltonian quantity, solving a linear equation system and the like. The second quantum state->May be a first form:
or in a second form:
wherein, the liquid crystal display device comprises a liquid crystal display device,for row j of matrix H +.>Conjugation of non-0 element values of column, +.>The value of the element with the largest absolute value in the matrix H.
Specifically, an initial sub-quantum state of a third bit in the current set of quantum bits may be converted into a sub-quantum state of a second preset form; the second preset form is determined by the first preset form, and the amplitude of the sub-quantum state of the second preset form is determined by the element value of the specific class element.
The second preset form may be:
in case the first preset form is the first form, continuing with the above example,,/>,,/>,/>the fifth quantum state is:
at this time, the third bit is not formally represented in the fifth quantum state, and the initial sub-quantum state of the third bit is assumed to be The fifth quantum state is actually: />. Wherein (1)>The third bit corresponding to the state is used as an auxiliary bit, the bit number is not limited, and 1 bit is usually required to save the quantum bit resource.
Based onA second bit corresponding to the sub bit, and a qubit state corresponding to the sub bit>(i.e., the initial sub-quantum state) is transformed into a superposition state (i.e., a sub-quantum state of a second preset form), resulting in:
the binary representation is:
it can be seen that the set of qubits is set to at least 6 bits, and can be set to q5q4q3q2q1q0, q5 code j, q4q3 codeOr (b)Q2q1 codes->Q0 is the third bit. To satisfy matrix->General case for all rows: j is 2 at maximum, requiring 2-bit encoding; />Or->Maximum value is 2, 2-bit encoding is required; />Maximum value is 4, 3-bit encoding is required; the third bit, the auxiliary bit, requires 1 bit at the lowest, and a total of 8 bits are available for a set of quantum bits. For any M x N matrix, the number of bits of a set of qubits can be summarized as: />. Wherein the method comprises the steps ofIf (3)、/>Representing an upward rounding; s represents the number of qubits required to encode the matrix element values and 1 represents the third number of bits.
In fact, the user no longer needs information on the matrix element values themselves at this time, as it will Conversion intoAfter that, the above-described inverse transform operation (transpose conjugation operation) for transforming the fourth quantum state into the fifth quantum state may be performed, and the state before transformation may be restored: />Thereby releasing the code->And reduces the resource occupation. It can be seen that the second form is a form further converted from the first form, and is also a preferred form of the first predetermined form.
Further, the set of qubits may further include: the fourth bit, used to simulate the controlled operation in quantum computing, specifically refers to: and judging whether to execute the step of converting the first quantum state into a second quantum state in a first preset form according to the fourth bit. The second bit is used as a controlled identification bit, has no other physical significance, is not limited, and is preferably one bit in order to reduce the occupation of computing resources.
Specifically, a sub-quantum state corresponding to the fourth bit in the first quantum state may be obtained; and when all bits of the sub-quantum state are 1, executing the step of converting the first quantum state into a second quantum state in a first preset form. Of course, this step is performed with all bits of the sub-quantum state set to 0, except that the former is more general.
In practical application, the transformation scheme is applied to the whole quantum circuit, and when the quantum state evolves to the first quantum state along with the circuit, the transformation scheme is assumed to be thatQ6 represents a fourth bit, and if the fourth bit corresponding to the current first quantum state is 1, the conversion operation from the current first quantum state to the second quantum state is performed.
Further, in order to facilitate subsequent reduction, the transformed second quantum state may be subjected to an inverse transformation operation, that is: and performing a transpose conjugation operation corresponding to the step of transforming the first quantum state into a second quantum state in a first preset form, so as to restore the second quantum state into the first quantum state. In practical quantum applications, the transform and transpose conjugate operations tend to occur in pairs.
In quantum applications, an Oracle or an Oracle combination can be constructed, and the internal principle of the Oracle or the Oracle combination is the flow of the method of the invention. In particular, oracle can be understood as a module (like a black box) that performs a specific function in a quantum algorithm, and there is a specific implementation in a specific problem.
Currently, existing quantum circuit construction can only utilize existing single quantum logic gates, double quantum logic gates and the like, and the following problems generally exist:
For a quantum circuit with complex functions, the number of quantum bits required is very large, huge memory space is consumed when a classical computer is used for simulation, the number of logic gates required is very large, and the simulation time is very long. And, some complex algorithms are difficult to implement using quantum wires.
Based on this, a specific complex function is realized by changing the way of Oracle simulation, and controlled and transposed conjugation operations are realized. Parameters of the user's incoming Oracle may include: oracle name (for identifying the functional purpose of Oracle), the aforementioned set of qubits, matrix elements (which may be stored in a one-dimensional vector V), index relationships (such as the aforementioned two-dimensional vector M), and so forth.
The advantage of this approach is that Oracle as a whole is a known module, without paying attention to the implementation details inside it, which is very straightforward in quantum application scenarios such as quantum wire representation. The classical simulated Oracle function module can be equivalent to a quantum logic gate, so that a constructed quantum circuit is simplified, the memory space required by running is saved, and the simulation verification of a quantum algorithm is quickened.
Referring to fig. 3, fig. 3 is a schematic diagram of a quantum circuit corresponding to a method for transforming a quantum state according to an embodiment of the present application. As will be appreciated by those skilled in the art, H represents an H gate,oracle, representing different functions +.>Representation ofT represents the whole functional module of the H gate and Oracle combination, and the function of the T module is +.>Conversion into. And the matrix input into the T module is an N-order matrix, which is above +.>Location->N in (2) represents the number of rows, belowN in (2) represents the number of columns, and the rest are the same as above. The constructed T module can be equivalent to a quantum logic gate in a quantum circuit, and the matrix form is as follows: />Wherein->Is a quantum state left vector.
Specifically, the H gate is utilized to construct the superposition state:；/>the transformation is realized:；/>the transformation is realized: />；/>The transformation is realized: />The method comprises the steps of carrying out a first treatment on the surface of the Finally, call again +.>Performing transpose conjugation to ∈>Is recovered and output +.>。
It should be noted that, the schematic diagram only shows a part of quantum circuits related to the present application, and the labels and connection relationships in the diagram are merely examples, and do not limit the present application.
It can be seen that the target value of the first type index of the element is encoded by the first quantum state of the group of quantum bits by obtaining the element information of the group of quantum bits and the matrix. The method comprises the steps of searching for the value and the element value of a second type subscript of a specific type element, wherein the value of the first type subscript is taken as a target value, encoding the value and the element value information of the second type subscript into a first bit of a group of quantum bits, encoding the element value information of the specific type element into a second bit of the group of quantum bits, so as to convert a first quantum state into a second quantum state in a first preset form, and presetting the form of the quantum state as quantum random walk correlation in practical application, thereby obtaining a specific quantum state (namely the second quantum state) required by quantum random walk, being used for classical simulation of quantum computation, filling up the blank of related technologies, and further expanding researches on quantum algorithms and quantum computers.
Referring to fig. 4, fig. 4 is a schematic structural diagram of a quantum state conversion device according to an embodiment of the present invention, which corresponds to the flow shown in fig. 2, and may include:
an obtaining module 401, configured to obtain a set of quantum bits and element information of a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element;
a first encoding module 402, configured to find, from the element information of the matrix, a value and an element value of a second type of subscript of a specific type of element whose value is the target value, and encode the value and the element value information of the second type of subscript onto a quantum state of a first bit and a second bit of the set of quantum bits;
a second encoding module 403, configured to encode element numerical information of the specific class element onto a quantum state amplitude of a third bit of the set of quantum bits, so as to transform the first quantum state into a second quantum state in a first preset form.
Specifically, the first type subscripts are as follows: row subscripts, the second category subscripts are: the subscripts are listed.
Specifically, the specific class elements are: non-0 element.
Specifically, the first encoding module is specifically configured to:
encoding the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row into a first bit in the group of quantum bits so as to transform the first quantum state into a third quantum state; the third quantum state comprises the target value and sequence number information, and each eigenstate forming the third quantum state corresponds to each sequence number one by one;
determining a column index of the non-0 element according to the target value and the sequence number, and encoding the column index into the first bit to transform the third quantum state into a fourth quantum state; wherein the fourth quantum state contains the target value information and the column index information of non-0 element;
and determining the element value of the non-0 element according to the target value information and the column index information, and encoding the element value into a third bit in the group of quantum bits to transform the fourth quantum state into a fifth quantum state containing the target value information, the column index information and the element value information.
Specifically, the first encoding module is specifically configured to:
Obtaining index relation between serial numbers and column subscripts of elements in all non-0 elements in a pre-constructed matrix row, wherein the elements are non-0 elements in the row;
and determining the column subscript of the non-0 element of the target row according to the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row and the index relation.
Specifically, the second encoding module is specifically configured to:
transforming an initial sub-quantum state of a third bit in the current set of sub-bits into a sub-quantum state of a second preset form; the second preset form is determined by the first preset form, and the amplitude of the sub-quantum state of the second preset form is determined by the element value of the specific class element.
Specifically, the set of quantum bits further includes: a fourth bit;
the apparatus further comprises:
and the judging module is used for judging whether to execute the step of converting the first quantum state into the second quantum state in the first preset form according to the fourth bit.
Specifically, the judging module is specifically configured to:
obtaining a sub-quantum state corresponding to the fourth bit in the first quantum state;
and when all bits of the sub-quantum state are 1, executing the step of converting the first quantum state into a second quantum state in a first preset form.
Specifically, the device further comprises:
and the transpose conjugation operation module is used for executing transpose conjugation operation corresponding to the step of converting the first quantum state into a second quantum state in a first preset form so as to restore the second quantum state into the first quantum state.
It can be seen that the target value of the first type index of the element is encoded by the first quantum state of the group of quantum bits by obtaining the element information of the group of quantum bits and the matrix. The method comprises the steps of searching for the value and the element value of a second type subscript of a specific type element, wherein the value of the first type subscript is taken as a target value, encoding the value and the element value information of the second type subscript into a first bit of a group of quantum bits, encoding the element value information of the specific type element into a second bit of the group of quantum bits, so as to convert a first quantum state into a second quantum state in a first preset form, and presetting the form of the quantum state as quantum random walk correlation in practical application, thereby obtaining a specific quantum state (namely the second quantum state) required by quantum random walk, being used for classical simulation of quantum computation, filling up the blank of related technologies, and further expanding researches on quantum algorithms and quantum computers.
The embodiments of the present invention further comprise a storage medium having a computer program stored therein, wherein the computer program is arranged to perform the steps of any of the method embodiments described above when run.
Specifically, in the present embodiment, the above-described storage medium may be configured to store a computer program for executing the steps of:
s1, obtaining element information of a group of quantum bits and a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element;
s2, searching the value and the element value of a second type of subscript of a specific type element, wherein the value of the first type of subscript is the target value, from the element information of the matrix, and encoding the value and the element value information of the second type of subscript onto the quantum states of a first bit and a second bit of the group of quantum bits;
and S3, encoding the element numerical information of the specific class element onto the quantum state amplitude of the third bit of the group of quantum bits so as to convert the first quantum state into a second quantum state in a first preset form.
Specifically, in the present embodiment, the storage medium may include, but is not limited to: a usb disk, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), a removable hard disk, a magnetic disk, or an optical disk, or other various media capable of storing a computer program.
It can be seen that the target value of the first type index of the element is encoded by the first quantum state of the group of quantum bits by obtaining the element information of the group of quantum bits and the matrix. The method comprises the steps of searching for the value and the element value of a second type subscript of a specific type element, wherein the value of the first type subscript is taken as a target value, encoding the value and the element value information of the second type subscript into a first bit of a group of quantum bits, encoding the element value information of the specific type element into a second bit of the group of quantum bits, so as to convert a first quantum state into a second quantum state in a first preset form, and presetting the form of the quantum state as quantum random walk correlation in practical application, thereby obtaining a specific quantum state (namely the second quantum state) required by quantum random walk, being used for classical simulation of quantum computation, filling up the blank of related technologies, and further expanding researches on quantum algorithms and quantum computers.
The present invention also includes an electronic device comprising a memory having a computer program stored therein and a processor configured to run the computer program to perform the steps of any of the method embodiments described above.
Specifically, the electronic apparatus may further include a transmission device and an input/output device, where the transmission device is connected to the processor, and the input/output device is connected to the processor.
Specifically, in the present embodiment, the above-described processor may be configured to execute the following steps by a computer program:
s1, obtaining element information of a group of quantum bits and a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element;
s2, searching the value and the element value of a second type of subscript of a specific type element, wherein the value of the first type of subscript is the target value, from the element information of the matrix, and encoding the value and the element value information of the second type of subscript onto the quantum states of a first bit and a second bit of the group of quantum bits;
and S3, encoding the element numerical information of the specific class element onto the quantum state amplitude of the third bit of the group of quantum bits so as to convert the first quantum state into a second quantum state in a first preset form.
It can be seen that the target value of the first type index of the element is encoded by the first quantum state of the group of quantum bits by obtaining the element information of the group of quantum bits and the matrix. The method comprises the steps of searching for the value and the element value of a second type subscript of a specific type element, wherein the value of the first type subscript is taken as a target value, encoding the value and the element value information of the second type subscript into a first bit of a group of quantum bits, encoding the element value information of the specific type element into a second bit of the group of quantum bits, so as to convert a first quantum state into a second quantum state in a first preset form, and presetting the form of the quantum state as quantum random walk correlation in practical application, thereby obtaining a specific quantum state (namely the second quantum state) required by quantum random walk, being used for classical simulation of quantum computation, filling up the blank of related technologies, and further expanding researches on quantum algorithms and quantum computers.
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 (7)
1. A method of quantum state transformation comprising:
obtaining element information of a group of quantum bits and a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element; the first category of subscripts is a row subscript, and the second category of subscripts is a column subscript;
encoding the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row into a first bit in the group of quantum bits so as to transform the first quantum state into a third quantum state; the third quantum state comprises the target value and sequence number information, and each eigenstate forming the third quantum state corresponds to each sequence number one by one;
obtaining a pre-constructed two-dimensional vector, wherein the two-dimensional vector only comprises index relations between sequence numbers of elements of non-0 elements of a matrix row in all non-0 elements of the row and column subscripts;
Determining a column index of the non-0 element of the target row according to the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row and the index relation;
encoding the column index to the first bit to transform the third quantum state to a fourth quantum state; wherein the fourth quantum state contains the target value information and the column index information of non-0 element;
determining an element value of the non-0 element according to the target value information and the column index information, and encoding the element value into a second bit of the group of quantum bits to transform the fourth quantum state into a fifth quantum state containing the target value information, the column index information and the element value information;
transforming an initial sub-quantum state of a third bit in the current set of sub-bits into a sub-quantum state of a second preset form; the second preset form is determined by the first preset form, and the amplitude of the sub-quantum state of the second preset form is determined by the element value of the specific class element.
2. The method of claim 1, wherein the set of quantum bits further comprises: a fourth bit;
The method further comprises the steps of:
and judging whether to execute the step of converting the first quantum state into a second quantum state in a first preset form according to the fourth bit.
3. The method of claim 2, wherein the step of determining whether to perform the conversion of the first quantum state to the second quantum state of the first preset form based on the fourth bit comprises:
obtaining a sub-quantum state corresponding to the fourth bit in the first quantum state;
and when all bits of the sub-quantum state are 1, executing the step of converting the first quantum state into a second quantum state in a first preset form.
4. The method according to claim 1, wherein the method further comprises:
and performing a transpose conjugation operation corresponding to the step of transforming the first quantum state into a second quantum state in a first preset form, so as to restore the second quantum state into the first quantum state.
5. A quantum state conversion device, comprising:
the acquisition module is used for acquiring a group of quantum bits and element information of a matrix; wherein a first quantum state of the set of quantum bits encodes a target value for a first type of subscript of an element; the first category of subscripts is a row subscript, and the second category of subscripts is a column subscript;
The first coding module is used for coding the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row to the first bit in the group of quantum bits so as to transform the first quantum state into a third quantum state; the third quantum state comprises the target value and sequence number information, and each eigenstate forming the third quantum state corresponds to each sequence number one by one;
the first coding module is further used for obtaining a pre-constructed two-dimensional vector, and the two-dimensional vector only comprises index relations between sequence numbers and column subscripts of elements of non-0 elements of a matrix row in all non-0 elements of the row;
the first coding module is further used for determining a column index of the non-0 element of the target row according to the sequence numbers of the non-0 elements of the target row corresponding to the target value in all non-0 elements of the row and the index relation;
a first encoding module further for encoding the column index to the first bit to transform the third quantum state to a fourth quantum state; wherein the fourth quantum state contains the target value information and the column index information of non-0 element;
the first coding module is further configured to determine an element value of the non-0 element according to the target value information and the column index information, and code the element value to a second bit in the set of quantum bits to transform the fourth quantum state into a fifth quantum state that includes the target value information, the column index information, and the element value information;
The second coding module is used for converting the initial sub-quantum state of the third bit in the current group of the quantum bits into a sub-quantum state of a second preset form; the second preset form is determined by the first preset form, and the amplitude of the sub-quantum state of the second preset form is determined by the element value of the specific class element.
6. A storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of claims 1 to 4 when run.
7. An electronic device comprising a memory and a processor, characterized in that the memory has stored therein a computer program, the processor being arranged to run the computer program to perform the method of any of the claims 1 to 4.
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