Quantum block coding discrete adiabatic evolution solving method of direct current power flow equation

Abstract

The invention provides a quantum block coding discrete adiabatic evolution solving method for a direct current power flow equation, and the method mainly comprises the steps: designing Hamiltonian according to an admittance matrix of the direct current power flow equation and known node injection active power, and carrying out the post-processing of the Hamiltonian through an intrinsic separator, the improved block coding technology is embedded into a quantum discrete adiabatic linear solver, approximate Hamiltonian simulation is achieved through first-order approximation, and preparation of a quantum state solution bypassing complex Hamiltonian simulation and a power flow equation is achieved. According to the method, an improved block coding technology is introduced, and equivalent non-unitary operation on a quantum system in the discrete adiabatic evolution process is achieved; according to the method, the Hamiltonian containing information of a direct-current power flow equation solution is designed, the Hamiltonian is post-processed by introducing an intrinsic separation technology, the gap between a target eigenvalue and an adjacent eigenvalue is increased, the success rate of quantum discrete adiabatic evolution is increased, and the solving efficiency and precision are optimized.

Description

Technical Field

[0001] The invention belongs to the field of power system and quantum computing, relates to quantum discrete adiabatic evolution and quantum block coding technology, and is suitable for solving direct current power flow equations. Background Art

[0002] With the rapid development of quantum computing in recent decades, its huge potential has attracted widespread attention from researchers. DC power flow is an important method in power system analysis, mainly used to calculate the power distribution and voltage changes in the power grid. Due to its simplicity and efficiency, the DC power flow method still plays a key role in the preliminary analysis of power systems. Therefore, it is crucial to combine quantum computing with the solution of the DC power flow equation and develop effective DC power flow equation solution techniques and methods under the quantum computing paradigm.

[0003] Adiabatic quantum computing is a quantum computing principle based on quantum adiabatic evolution. In 2019, Subaşı et al. used quantum discrete adiabatic evolution technology and Hamiltonian simulation technology to propose a quantum discrete adiabatic linear solution method that can run on a universal quantum computer, and pointed out that the quantum discrete adiabatic linear solution method achieves exponential acceleration compared to the linear equation solution method under the classical computing paradigm. Since the problem of solving the DC power flow equation is essentially a problem of solving a linear equation system, the quantum discrete adiabatic linear solution method can be used to solve the DC power flow equation. However, the quantum discrete adiabatic linear solution method relies on complex Hamiltonian simulation, which hinders the practical application of the quantum discrete adiabatic linear solution method to solve the DC power flow equation.

[0004] In addition, the Hamiltonian proposed in the existing quantum discrete adiabatic linear solution method takes the lowest energy level as the target energy level and is greatly affected by the neighboring energy levels. When the gap between the eigenvalue of the neighboring energy level and the target energy level is small, a more precise adiabatic evolution is required, resulting in more discrete adiabatic evolution steps. Insufficient steps will lead to the failure of the adiabatic evolution.

[0005] Therefore, a quantum block coded discrete adiabatic evolution solution method for the DC power flow equation is proposed to solve the problem that the existing quantum discrete adiabatic linear solution method relies on complex Hamiltonian simulation, as well as the problem that the Hamiltonian proposed in the existing quantum discrete adiabatic linear solution method has low solution efficiency and limited solution result accuracy when the gap between the eigenvalue of the adjacent energy level and the lunar standard energy level is small. Summary of the invention

[0006] The present invention proposes a quantum block coded discrete adiabatic evolution solution method for the DC power flow equation, which combines the Hamiltonian containing the DC power flow equation information, the intrinsic separator, the block coding technology and the quantum discrete adiabatic linear solver to achieve the solution of the DC power flow equation under the quantum discrete adiabatic framework; the steps in the use process are:

[0007] Step (1): For the DC power flow equation , It's network dimensional node susceptance matrix, is the voltage phase angle vector of each node in the network to be solved, is the solution vector of the DC power flow equation, is the node injected active power vector; the node susceptance matrix and node injected active power vector Input this method and design the Hamiltonian of the adiabatic evolution process; inject active power vector according to the known nodes , design the following projection operator:

[0008] (1)

[0009] In the formula, yes dimensional identity matrix, is the right vector in Dirac notation, is the node injected active power vector The normalized form of the quantum state is is the left vector in Dirac notation, yes The conjugate transpose of and node susceptance matrix , design the following initial Hamiltonian and the final Hamiltonian :

[0010] (2)

[0011] (3)

[0012] In the formula, is the F-norm;

[0013] Step (2): Use the intrinsic separator to process the final Hamiltonian. The final Hamiltonian after processing is:

[0014] (4)

[0015] Where D is the eigenseparation order;

[0016] Step (3): Construct the first-order approximation of the time-varying Hamiltonian and its Hamiltonian simulation operator. The time-varying Hamiltonian is:

[0017] (5)

[0018] In the formula, is the time parameter of the time-varying Hamiltonian; the first-order approximation of the Hamiltonian simulation operator is:

[0019] (6)

[0020] Where i is the imaginary unit, is a natural constant, is the time-varying Hamiltonian Hamiltonian simulation operator;

[0021] Step (4): Introduce block coding technology in the quantum discrete adiabatic evolution process, using auxiliary qubits, Encoded into a valid block of a block encoding operator, the block encoding operator is:

[0022] (7)

[0023] In the formula, * is an arbitrary Elements that satisfy unitary property;

[0024] Step (5): Apply the block coding operator to the quantum circuit to perform Step discrete adiabatic evolution, through post-selection operation, the system state evolves to:

[0025] (8)

[0026] In the formula, is the solution vector of the DC power flow equation The normalized form of the quantum state, M is the number of adiabatic evolution steps, is the step size, m is the index of the current evolution number in the discrete adiabatic evolution, is the current evolution time parameter, It means that after each execution of the block coding operator, the redundant quantum state is cleared and the probability amplitude corresponding to the non-zero auxiliary quantum bit in the quantum state vector is set to zero; after the quantum system completes the evolution, the auxiliary quantum bits in the quantum system are ignored, and the quantum state normalized form of the solution vector of the DC power flow equation is obtained ;

[0027] Step (6): Denormalize the quantum state normalized form of the solution vector of the DC power flow equation to obtain the solution vector of the DC power flow equation; the solution vector of the DC power flow equation Its quantum state normalized form The normalization coefficient between is:

[0028] (9)

[0029] In the formula, is the node injected active power vector Take the inverse of each element and transpose it; denormalize the quantum state normalized form of the solution vector of the DC power flow equation, and the solution vector of the DC power flow equation is:

[0030] (10)

[0031] Finally, the solution vector of the DC power flow equation problem is output .

[0032] Compared with the prior art, the present invention has the following advantages and effects:

[0033] (1) Existing quantum discrete adiabatic linear solvers rely on complex Hamiltonian simulation. However, the present invention embeds block coding technology into the quantum discrete adiabatic linear solver, applies the first-order approximation of the Hamiltonian simulation operator to the target quantum system through block coding technology, and avoids complex Hamiltonian simulation when solving the DC power flow equation.

[0034] (2) In the existing Hamiltonian design scheme, it is difficult for the quantum discrete adiabatic linear solver to achieve efficient solution of the DC power flow equation when the gap between the target energy level of the final Hamiltonian and the adjacent energy levels is small. The present invention improves the success rate of quantum discrete adiabatic evolution and optimizes the solution efficiency and accuracy by designing improved initial Hamiltonian and final Hamiltonian based on the principle of adiabatic evolution and using an intrinsic separator to expand the gap between the target energy level of the final Hamiltonian and the adjacent energy levels. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is the overall framework diagram of the method of the present invention.

[0036] Figure 2 1 is a flow chart of an intrinsic separator of the method of the present invention.

[0037] Figure 3 It is the block coding operator quantum circuit diagram of the method of the present invention. DETAILED DESCRIPTION

[0038] A quantum block coded discrete adiabatic evolution solution method for a DC power flow equation proposed in the present invention is described in detail as follows in conjunction with the accompanying drawings:

[0039] Figure 1 This is the overall framework diagram of the method of the present invention. Input quantum block coded discrete adiabatic solution method, according to the node injection active power vector Constructing the projection operator , and then design the initial Hamiltonian , and then according to the node susceptance matrix and projection operator Design the final Hamiltonian , and then use the intrinsic separator to process the final Hamiltonian to obtain the processed final Hamiltonian , and then according to the initial Hamiltonian and the final Hamiltonian after processing Construction of a time-varying Hamiltonian and its first-order approximation of the Hamiltonian simulation operator ,The next step is to construct a block coding operator using block coding technology. Encoding to a unitary matrix Then, the quantum state of the solution vector of the DC power flow equation is obtained by quantum block coding discrete adiabatic evolution Finally, the solution vector of the DC power flow equation is obtained and output through anti-normalization .

[0040] Figure 2 The eigenvalue separator flow chart of the method of the present invention is shown in FIG. The final Hamiltonian is input into the eigenvalue separator. The working process of the eigenvalue separator is as follows: (1) the eigenvalue separation order D is set and the temporary final Hamiltonian is initialized. and the current order ; (2) Determine the current order Is it equal to the set eigenseparation order? , if they are equal, the program ends and the final Hamiltonian after processing is output , otherwise go to the third step; (3) Assign to the temporary final Hamiltonian , Assign value to current order , and return to step 2.

[0041] Figure 3 It is the block coding operator quantum circuit diagram of the method of the present invention. Dimensional Matrix Time, remember , represents rounding up, the block coding operator quantum circuit route , and It consists of three quantum registers. Used to store the element value of the matrix to be encoded, containing 1 quantum bit, and They are used to represent the row index and column index of the matrix elements to be encoded, respectively. qubits, of which and Total The qubit is an auxiliary qubit; The initial quantum state is , The initial quantum state is , The initial quantum state is any state First, Execute on H gates to prepare equal-amplitude superposition states; then perform unitary transformation , It consists of a series of controlled RY gates and a series of controlled RZ gates. The complex element in row i and column j , when encoding, the rotation parameter of the RY gate is , the rotation parameter of the RZ gate is ; and then execute a series of actions on and of SWAP gates, and of H gates; through post-selection operation, when the auxiliary qubits are collapsed into hour, The state of the quantum bit in the equation evolves to , is the two-norm.

[0042] The above description is only a preferred embodiment of the present invention, and does not limit the patent scope of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A quantum block coded discrete adiabatic evolution solution method for DC power flow equation, characterized in that: The Hamiltonian containing the DC power flow equation information, the eigen separator, the block coding technology and the quantum discrete adiabatic linear solver are combined to realize the solution of the DC power flow equation under the quantum discrete adiabatic framework; the steps in the use process are: Step (1): For the DC power flow equation , It's network dimensional node susceptance matrix, is the voltage phase angle vector of each node in the network to be solved, is the solution vector of the DC power flow equation, is the node injected active power vector; the node susceptance matrix and node injected active power vector Input this method and design the Hamiltonian of the adiabatic evolution process; inject active power vector according to the known nodes , design the following projection operator: (1) In the formula, yes dimensional identity matrix, is the right vector in Dirac notation, is the node injected active power vector The normalized form of the quantum state is is the left vector in Dirac notation, yes The conjugate transpose of and node susceptance matrix , design the following initial Hamiltonian and the final Hamiltonian : (2) (3) In the formula, is the F-norm; Step (2): Use the intrinsic separator to process the final Hamiltonian. The final Hamiltonian after processing is: (4) Where D is the eigenseparation order; Step (3): Construct the first-order approximation of the time-varying Hamiltonian and its Hamiltonian simulation operator. The time-varying Hamiltonian is: (5) In the formula, is the time parameter of the time-varying Hamiltonian; the first-order approximation of the Hamiltonian simulation operator is: (6) Where i is the imaginary unit, is a natural constant, is the time-varying Hamiltonian Hamiltonian simulation operator; Step (4): Introduce block coding technology in the quantum discrete adiabatic evolution process, using auxiliary qubits, Encoded into a valid block of a block encoding operator, the block encoding operator is: (7) In the formula, * is an arbitrary Elements that satisfy unitary property; Step (5): Apply the block coding operator to the quantum circuit to solve the power flow equation; Step discrete adiabatic evolution, through post-selection operation, the system state evolves to: (8) In the formula, is the solution vector of the DC power flow equation The normalized form of the quantum state, M is the number of adiabatic evolution steps, is the step size, m is the index of the current evolution number in the discrete adiabatic evolution, is the current evolution time parameter, It means that after each execution of the block coding operator, the redundant quantum state is cleared and the probability amplitude corresponding to the non-zero auxiliary quantum bit in the quantum state vector is set to zero; After the quantum system completes its evolution, ignoring the auxiliary quantum bits in the quantum system, the quantum state normalized form of the solution vector of the DC power flow equation is obtained: ; Step (6): Denormalize the quantum state normalized form of the solution vector of the DC power flow equation to obtain the solution vector of the DC power flow equation; the solution vector of the DC power flow equation Its quantum state normalized form The normalization coefficient between is: (9) In the formula, is the node injected active power vector Take the inverse of each element and transpose it; denormalize the quantum state normalized form of the solution vector of the DC power flow equation, and the solution vector of the DC power flow equation is: (10) Finally, the solution vector of the DC power flow equation problem is output .

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