CN117669757A - Hamiltonian volume construction method and device - Google Patents
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Abstract
The invention discloses a method and a device for constructing Hamiltonian volume, wherein the method comprises the following steps: firstly, a matrix A corresponding to a system to be simulated is obtained, a weight of Zhang Cheng in the form of a Brix operator of the system to be simulated is determined according to the matrix A corresponding to the system to be simulated, and a Hamiltonian amount H corresponding to the system to be simulated is determined according to the weight of Zhang Cheng in the form of the Brix operator.
Description
Technical Field
The invention belongs to the technical field of quantum computation, and particularly relates to a method and a device for constructing Hamiltonian.
Background
Hamiltonian is a physical quantity related to the total energy of a physical system and may represent the energy of the whole system. For some systems, the modeling of the system construction-related time evolution line may be performed, before which the hamiltonian in the system needs to be characterized.
The simulation of hamiltonian is a fundamental but very important task in quantum computing, and currently, in the prior art, hamiltonian can be created by defining a container form, where the elements should be the coefficients of each term in the hamiltonian and its Brix. The hamiltonian constructed in this way describes only one simple interaction between two qubits.
Therefore, how to design a reasonable way and an efficient data structure to characterize the hamiltonian of the system to be simulated is particularly important for the subsequent simulation evolution operation is a problem to be solved.
Disclosure of Invention
The invention aims to provide a method and a device for constructing Hamiltonian, which solve the defects in the prior art, and improve the accuracy of Hamiltonian representation by providing a novel method for constructing Hamiltonian, thereby being beneficial to system simulation and solving the subsequent application requirements.
One embodiment of the present application provides a method for constructing hamiltonian, the method comprising:
obtaining a matrix A corresponding to a system to be simulated;
determining a weight Zhang Cheng in the form of a Brix operator of the system to be simulated according to the matrix A corresponding to the system to be simulated;
and determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix arithmetic.
Optionally, the determining the weighted multiplication of the form of the bubble benefit operator of the system to be simulated according to the matrix a corresponding to the system to be simulated includes:
converting non-zero element subscripts in a matrix A corresponding to the system to be simulated into a binary form, wherein the matrix A is a square matrix and the element types in the square matrix are complex numbers;
a weight in the form of a bolter of the system to be simulated is determined Zhang Cheng based on the binary representation of the non-zero element subscript in the matrix a.
Optionally, the converting the non-zero element subscript in the matrix a corresponding to the system to be simulated into a binary form includes:
converting non-zero element indices in the matrix a into binary representations by the following expression:
wherein s is an iteration index of a non-0 element in the matrix A, and k and j respectively represent the non-zero element A in the matrix A kj And the corresponding row subscript and column subscript, m is more than or equal to 1 and less than or equal to n, and n is the number of bits converted into binary by decimal row subscript or decimal column subscript.
Optionally, the determining the weighted multiplication of the form of the bubble-benefit operator of the system to be simulated based on the binary representation form of the non-zero element subscript in the matrix a includes:
expanding and re-representing each term in matrix a as a new matrix a' according to the binary representation of the non-zero element subscript in matrix a;
determining the logic gate type corresponding to each sub-item in the new matrix A 'according to the value of the sub-item in each item in the new matrix A';
and determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the logic gate type corresponding to each sub-item in the new matrix A'.
Alternatively, the matrix a is expressed as:
the new matrix a' is expressed as:
wherein S' is a set of non-zero elements in matrix a.
Optionally, the values of the sub-items in each item of the new matrix a' include: one of 0 < 0> <1, < 1> <0, < 1> <1, < 1> or a combination thereof; the determining the logic gate type corresponding to each sub-item of the new matrix a' includes:
wherein X is a Brix gate, Y is a Brix Y gate, Z is a Brix Z gate, I is a two-dimensional identity matrix, and I is an imaginary number.
Optionally, the determining, according to the weighted sum Zhang Cheng in the form of the bubble identifier, the hamiltonian H corresponding to the system to be simulated includes:
and determining the Hamiltonian quantity H corresponding to the system to be simulated by the following formula:
wherein H is Hamiltonian quantity corresponding to a system to be simulated, K is the number of terms, and C is K As the weight coefficient, p is an iteration index, M represents the number of required qubits, and
yet another embodiment of the present application provides a hamiltonian construction apparatus, the apparatus comprising:
the acquisition module is used for acquiring a matrix A corresponding to the system to be simulated;
the first determining module is used for determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the matrix A corresponding to the system to be simulated;
and the second determining module is used for determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix.
Optionally, the first determining module includes:
the conversion unit is used for converting the non-zero element subscript in the matrix A corresponding to the system to be simulated into a binary form, wherein the matrix A is a square matrix and the element types in the square matrix are complex numbers;
a first determining unit, configured to determine a weight Zhang Cheng in the form of a bolter of the system to be simulated based on the binary representation of the non-zero element index in the matrix a.
Optionally, the conversion unit includes:
a conversion subunit, configured to convert the non-zero element subscripts in the matrix a into a binary representation by the following expression:
wherein s is an iteration index of a non-0 element in the matrix A, and k and j respectively represent the non-zero element A in the matrix A kj And the corresponding row subscript and column subscript, m is more than or equal to 1 and less than or equal to n, and n is the number of bits converted into binary by decimal row subscript or decimal column subscript.
Optionally, the first determining unit includes:
an expansion subunit for expanding and re-representing each term in matrix a as a new matrix a' according to the binary representation of the non-zero element subscript in matrix a;
a first determining subunit, configured to determine, according to the value of the subitem in each item of the new matrix a ', a logic gate type corresponding to the subitem in each item of the new matrix a';
and the second determining subunit is used for determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the logic gate type corresponding to each sub-item in the new matrix A'.
Optionally, the second determining module includes:
the second determining unit is configured to determine a hamiltonian H corresponding to the system to be simulated according to the following formula:
wherein H is Hamiltonian quantity corresponding to a system to be simulated, K is the number of terms, and C is K As the weight coefficient, p is an iteration index, M represents the number of required qubits, and
a further embodiment of the present application provides a storage medium having a computer program stored therein, wherein the computer program is arranged to perform the method of any of the above when run.
Yet another embodiment of the present application provides an electronic device comprising a memory having a computer program stored therein and a processor configured to run the computer program to perform the method described in any of the above.
Compared with the prior art, the method has the advantages that firstly, the matrix A corresponding to the system to be simulated is obtained, the weight of the system to be simulated in the form of the Brix is determined Zhang Cheng according to the matrix A corresponding to the system to be simulated, the Hamiltonian H corresponding to the system to be simulated is determined according to the weight of the Brix of the system to be simulated Zhang Cheng, and the accuracy of Hamiltonian representation is improved by providing a novel Hamiltonian construction method, so that the system simulation and the subsequent application requirements are favorably solved.
Drawings
Fig. 1 is a hardware block diagram of a computer terminal according to a method for constructing hamiltonian according to an embodiment of the present invention;
fig. 2 is a flow chart of a method for constructing hamiltonian according to an embodiment of the invention;
fig. 3 is a schematic structural diagram of a hamiltonian configuration device according to an embodiment of the invention.
Detailed Description
The embodiments described below by referring to the drawings are illustrative only and are not to be construed as limiting the invention.
The embodiment of the invention firstly provides a construction method of Hamiltonian volume, which can be applied to electronic equipment such as computer terminals, in particular to common computers, quantum computers and the like.
The following describes the operation of the computer terminal in detail by taking it as an example. Fig. 1 is a hardware block diagram of a computer terminal according to a method for constructing hamiltonian according to an embodiment of the present invention. As shown in fig. 1, the computer terminal 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 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 method of constructing hamiltonian in the embodiments 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 above-mentioned methods. 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 remotely located relative to the processor 102, which may be connected to the computer terminal 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. Specific examples of the network described above may include a wireless network provided by a communication provider of a computer terminal. 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 quantum circuits, and include single-bit quantum logic gates, such as Hadamard gates (H gates, hadamard gates), brix gates (X gates), brix-Y gates (Y gates), brix-Z gates (Z gates), RX gates, RY gates, RZ gates, and the like; multi-bit quantum logic gates such as CNOT gates, CR gates, iSWAP gates, toffoli gates, and the like. 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.
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 asWherein a and b are represented by |0>The complex number of states, |1> state amplitude (probability amplitude), which is not possessed by classical bits. After measurement, the state of the qubit collapses to a definite state (eigenstate, here |0> state, |1> state), where the probability of collapsing to |0> is |a| 2 Collapse to |1>The probability of (2) is |b| 2 ，|a| 2 +|b| 2 ＝1，|>Is a dirac symbol.
Quantum states, i.e., states of qubits, generally require the use of a set of orthographically complete basis vector descriptions, the computational basis typically used for which is 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 state of the computing groups, 8 computing groups refer to: i000>、|001>、|010>、|011>、|100>、|101>、|110>、|111>Each computation basis corresponds to a qubit, e.g., 000 > states, 000 corresponds to q2q1q0 from high to low. In short, a quantum state is an overlapped state composed of basis vectors, when the probability amplitude of other basis is 0, that is, at one of the determined basis vectors.
In quantum mechanics, all measurable mechanical quantities can be described by a hermite matrix, which is defined as the transposed conjugate of the matrix, i.e. the matrix itself, i.e. there is: h + Such a matrix is commonly referred to as a measurement operator, and the non-zero operator has at least oneEigenvalue λ other than 0 and eigenvalue |ψ >, satisfying h|ψ>If the eigenvalue of the operator H corresponds to the energy level of a certain system, =λ|ψ >, such an operator may also be referred to as Hamiltonian (Hamiltonian).
According to the schrodinger equation, the evolution from one state |ψ (t=0) > to another state |ψ (t=t) > is completed by using a unitary operator, namely U (0, T) |ψ (t=0) > = |ψ (t=t) >, wherein the relation between the hamiltonian and the unitary operator is that if a quantum state naturally evolves under a certain system, the energy of the system, i.e. the hamiltonian, is described, the unitary operator can be written by the hamiltonian:
when the system starts at time 0 and the hamiltonian does not change over time, the unitary operator, i.e., u=exp (-iHt). In quantum computing in a closed system, all quantum operations, except for measurements, can be described by a unitary matrix, which is defined as the transposed conjugate of the matrix, i.e., the inverse of the matrix, i.e., there is: u (U) + U＝UU + ＝UU -1 ＝U -1 U=i. In general, unitary operators are also known as quantum logic gates in quantum computing.
Referring to fig. 2, fig. 2 is a flow chart of a method for constructing hamiltonian according to an embodiment of the present invention, which may include the following steps:
s201: and obtaining a matrix A corresponding to the system to be simulated.
Specifically, the system to be simulated can be a system which needs to be subjected to quantum computing simulation later, and the system to be simulated can be an equation, a molecule or other physical closed systems, wherein each system to be simulated can be described by utilizing a matrix.
S202: and determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the matrix A corresponding to the system to be simulated.
Specifically, determining the weighted multiplication of the form of the bubble benefit operator of the system to be simulated according to the matrix a corresponding to the system to be simulated may include:
1. and converting the non-zero element subscript in a matrix A corresponding to the system to be simulated into a binary form, wherein the matrix A is a square matrix and the element types in the square matrix are complex numbers.
Specifically, the matrix a may be defined as a matrix n×n matrix, and the element types in the matrix are complex numbers. That is, for any given square matrix (element type is complex, expression is a+bi), the scheme of the present application can decompose the square matrix into a linear combination of real numbers (floating point numbers in the corresponding calculation) and quantum wires.
The conversion of the non-zero element subscript in the matrix a corresponding to the system to be simulated into a binary form may include:
converting non-zero element indices in the matrix a into binary representations by the following expression:
wherein s is an iteration index of a non-0 element in the matrix A, and k and j respectively represent the non-zero element A in the matrix A kj And the corresponding row subscript and column subscript, m is more than or equal to 1 and less than or equal to n, and n is the number of bits converted into binary by decimal row subscript or decimal column subscript.
2. A weight in the form of a bolter of the system to be simulated is determined Zhang Cheng based on the binary representation of the non-zero element subscript in the matrix a.
Specifically, the determining the weighted multiplication of the form of the bubble-benefit operator of the system to be simulated based on the binary representation of the non-zero element subscript in the matrix a may include:
step 1: expanding and re-representing each term in matrix a as a new matrix a' according to the binary representation of the non-zero element subscript in matrix a;
step 2: determining the logic gate type corresponding to each sub-item in the new matrix A 'according to the value of the sub-item in each item in the new matrix A';
step 3: and determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the logic gate type corresponding to each sub-item in the new matrix A'.
Specifically, the matrix a is expressed as:
the new matrix a' is expressed as:
where S' is the set of non-zero elements in matrix a or the number of terms that can also be understood as the linear combination before the coefficients are not combined. According to the representation of matrix a', wherein,the value of (2) can only be 0 or 1, < >>The value of (2) may only be 0 or 1. That is, for the sub-items in each item in matrix A +.>Its value can only be |0><0|、|0><1|、|1><0|、|1><1|.
Specifically, the values of the sub-items in each item of the new matrix a' include: one of 0 < 0> <1, < 1> <0, < 1> <1, < 1> or a combination thereof.
According to the subitem value status in each item in the matrix a ', each value can be defined to correspond to a logic gate type formed by combining a logic gate in a berlite form and a two-dimensional identity matrix I, and the determining the logic gate type corresponding to each subitem in the new matrix a' includes:
wherein X is a Brix gate, Y is a Brix Y gate, Z is a Brix Z gate, I is a two-dimensional identity matrix, and I is an imaginary number.
S203: and determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix arithmetic.
Specifically, hamiltonian is the sum of the kinetic energy of all the particles of the system to be simulated plus the potential energy of the particles associated with the system. The hamiltonian is different for different situations or numbers of particles, because it includes the sum of the kinetic energies of the particles and the potential energy function corresponding to this situation, generally denoted by H. In quantum mechanics, the physical quantity of classical mechanics becomes a corresponding operator, and the Hamiltonian quantity corresponds to the Hamiltonian operator.
In an alternative embodiment, based on the mechanical analysis of the target system, the hamiltonian of the target system can be obtained, and the obtaining of the fermi sub hamiltonian corresponding to the target system is realized by means of creating an operator and an annihilation operator, which satisfy the anti-reciprocal relationship.
In another alternative embodiment, the hamiltonian H corresponding to the system to be simulated is determined by the following equation:
wherein H is Hamiltonian quantity corresponding to a system to be simulated, K is the number of terms, and C is K As the weight coefficient, p is an iteration index, M represents the number of required qubits, and
it can be seen that the present invention firstly obtains the matrix a corresponding to the system to be simulated, determines the weighted sum Zhang Cheng of the form of the bubble-figure operator of the system to be simulated according to the matrix a corresponding to the system to be simulated, and determines the hamiltonian H corresponding to the system to be simulated according to the weighted sum Zhang Cheng of the form of the bubble-figure operator.
Referring to fig. 3, fig. 3 is a schematic structural diagram of a hamiltonian configuration device according to an embodiment of the invention, which corresponds to the flow shown in fig. 2, and may include:
an obtaining module 301, configured to obtain a matrix a corresponding to a system to be simulated;
a first determining module 302, configured to determine a weighted sum Zhang Cheng in the form of a bolter of the system to be simulated according to the matrix a corresponding to the system to be simulated;
and a second determining module 303, configured to determine a hamiltonian H corresponding to the system to be simulated according to the weighted sum Zhang Cheng in the form of the berkovich operator.
Specifically, the first determining module includes:
the conversion unit is used for converting the non-zero element subscript in the matrix A corresponding to the system to be simulated into a binary form, wherein the matrix A is a square matrix and the element types in the square matrix are complex numbers;
a first determining unit, configured to determine a weight Zhang Cheng in the form of a bolter of the system to be simulated based on the binary representation of the non-zero element index in the matrix a.
Specifically, the conversion unit includes:
a conversion subunit, configured to convert the non-zero element subscripts in the matrix a into a binary representation by the following expression:
wherein s is an iteration index of a non-0 element in the matrix A, and k and j respectively represent the non-zero element A in the matrix A kj And the corresponding row subscript and column subscript, m is more than or equal to 1 and less than or equal to n, and n is the number of bits converted into binary by decimal row subscript or decimal column subscript.
Specifically, the first determining unit includes:
an expansion subunit for expanding and re-representing each term in matrix a as a new matrix a' according to the binary representation of the non-zero element subscript in matrix a;
a first determining subunit, configured to determine, according to the value of the subitem in each item of the new matrix a ', a logic gate type corresponding to the subitem in each item of the new matrix a';
and the second determining subunit is used for determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the logic gate type corresponding to each sub-item in the new matrix A'.
Specifically, the second determining module includes:
the second determining unit is configured to determine a hamiltonian H corresponding to the system to be simulated according to the following formula:
wherein H is Hamiltonian quantity corresponding to a system to be simulated, K is the number of terms, and C is K As the weight coefficient, p is an iteration index, M represents the number of required qubits, and
compared with the prior art, the method has the advantages that firstly, the matrix A corresponding to the system to be simulated is obtained, the weight of the system to be simulated in the form of the Brix is determined Zhang Cheng according to the matrix A corresponding to the system to be simulated, the Hamiltonian H corresponding to the system to be simulated is determined according to the weight of the Brix of the system to be simulated Zhang Cheng, and the accuracy of Hamiltonian representation is improved by providing a novel Hamiltonian construction method, so that the system simulation and the subsequent application requirements are favorably solved.
The embodiment of the invention also provides a storage medium in which a computer program is stored, wherein the computer program is arranged to perform the steps of the method embodiment of any of the 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:
s201: obtaining a matrix A corresponding to a system to be simulated;
s202: determining a weight Zhang Cheng in the form of a Brix operator of the system to be simulated according to the matrix A corresponding to the system to be simulated;
s203: and determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix arithmetic.
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.
An embodiment of the invention also provides an electronic device comprising a memory having stored therein a computer program and a processor arranged to run the computer program to perform the steps of the method embodiment of any of the 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:
s201: obtaining a matrix A corresponding to a system to be simulated;
s202: determining a weight Zhang Cheng in the form of a Brix operator of the system to be simulated according to the matrix A corresponding to the system to be simulated;
s203: and determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix arithmetic.
While the foregoing is directed to embodiments of the present invention, other and further embodiments of the invention may be devised without departing from the basic scope thereof, and the scope thereof is determined by the claims that follow.
Claims (10)
1. A method of constructing a hamiltonian, the method comprising:
obtaining a matrix A corresponding to a system to be simulated;
determining a weight Zhang Cheng in the form of a Brix operator of the system to be simulated according to the matrix A corresponding to the system to be simulated;
and determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix arithmetic.
2. The method according to claim 1, wherein the determining the weighted tensor in the form of the berlites of the system to be simulated according to the matrix a corresponding to the system to be simulated comprises:
converting non-zero element subscripts in a matrix A corresponding to the system to be simulated into a binary form, wherein the matrix A is a square matrix and the element types in the square matrix are complex numbers;
a weight in the form of a bolter of the system to be simulated is determined Zhang Cheng based on the binary representation of the non-zero element subscript in the matrix a.
3. The method according to claim 2, wherein converting the non-zero element index in the matrix a corresponding to the system to be simulated into a binary form comprises:
converting non-zero element indices in the matrix a into binary representations by the following expression:
wherein s is an iteration index of a non-0 element in the matrix A, and k and j respectively represent the non-zero element A in the matrix A kj And the corresponding row subscript and column subscript, m is more than or equal to 1 and less than or equal to n, and n is the number of bits converted into binary by decimal row subscript or decimal column subscript.
4. The method of claim 2, wherein the determining a weight-plus-multiplication of the system-to-be-simulated in the form of a bubble-plus-li operator based on the binary representation of the non-zero element subscript in the matrix a comprises:
expanding and re-representing each term in matrix a as a new matrix a' according to the binary representation of the non-zero element subscript in matrix a;
determining the logic gate type corresponding to each sub-item in the new matrix A 'according to the value of the sub-item in each item in the new matrix A';
and determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the logic gate type corresponding to each sub-item in the new matrix A'.
5. The method of claim 4, wherein the matrix a is represented as:
the new matrix a' is expressed as:
wherein S' is a set of non-zero elements in matrix a.
6. The method of claim 4, wherein the values of the sub-entries in each entry of the new matrix a' comprise: one of 0 < 0> <1, < 1> <0, < 1> <1, < 1> or a combination thereof; the determining the logic gate type corresponding to each sub-item of the new matrix a' includes:
wherein X is a Brix gate, Y is a Brix Y gate, Z is a Brix Z gate, I is a two-dimensional identity matrix, and I is an imaginary number.
7. The method according to claim 1, wherein the determining the hamiltonian H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the berkovich operator includes:
and determining the Hamiltonian quantity H corresponding to the system to be simulated by the following formula:
wherein H is Hamiltonian quantity corresponding to a system to be simulated, K is the number of terms, and C is K As the weight coefficient, p is an iteration index, M represents the number of required qubits, and
8. a hamiltonian construction device, the device comprising:
the acquisition module is used for acquiring a matrix A corresponding to the system to be simulated;
the first determining module is used for determining the weight Zhang Cheng in the form of the Brix arithmetic of the system to be simulated according to the matrix A corresponding to the system to be simulated;
and the second determining module is used for determining the Hamiltonian quantity H corresponding to the system to be simulated according to the weighted addition Zhang Cheng in the form of the Brix.
9. 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 7 when run.
10. 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 7.
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