Method for generating quantum gate control signals for quantum computing using a variational quantum eigensolver

Abstract

The invention relates to methods for generating quantum gate control signals for quantum computing using a variational quantum eigensolver. The invention can be used for complex computing that cannot be done on classical computers. According to the invention, control signals are sent to quantum gates from a classical computer on which parameters for updating qubit spin rotation angles are recalculated using a Riemannian optimization which makes it possible to calculate the shortest path to a global minimum of the expectation value of the Hamiltonian of the qubit state, wherein control signal qubit vector rotation matrices considered as a manifold are optimized at each step rather than individual parameters of a control signal, and the rotation angles of the qubit vectors are back-calculated in order to generate the control signal.

Description

[0001] METHOD OF FORMING SIGNALS

[0002] CONTROL OF QUANTUM VALVES FOR PERFORMING QUANTUM COMPUTATIONS USING A VARIATIONAL ALGORITHM FOR FINDING EIGENVALUES OF OPERATORS

[0003] The field of technology to which the invention relates.

[0004] The invention relates to methods for generating quantum gate control signals for performing quantum computations using a variational algorithm for finding the eigenvalues ​​of operators, in which various states of a set of qubits on a quantum computer, expressing a vector, are used as the basis for computations, wherein a change in the orientation of the qubit state vector is implemented using quantum gates, and control signals are sent to the quantum gates from a classical computer. The invention can be used to perform complex computations that cannot be performed on classical computers.

[0005] The following terms are used in the description:

[0006] A qubit is a two-level quantum system that encodes the smallest unit of information in a quantum computer (analogous to a bit in a conventional computer), used for quantum computing. A qubit allows two eigenstates, denoted |0) and |1 ) (Dirac notation), but can also be in a superposition of them.

[0007] A quantum gate is a basic element of a quantum computer that transforms the input states of qubits into output states according to a certain law, depending on the physical implementation of the qubits of the quantum processor.

[0008] The qubit state vector is a vector of two complex numbers to describe the state of the qubit. The qubit state vector is also called the wave function, and this vector can point to any point on the Bloch sphere. The sphere itself has a unit radius, which ensures that for all states the sum of the squares of the amplitudes will be equal to one. The qubit state vector is a vector of dimension n 2 containing the superposition coefficients of the base states of an n-qubit system, which describes its current quantum state.

[0009] State of the art

[0010] A quantum computer is a computing device that uses the phenomena of quantum mechanics (quantum superposition, quantum entanglement) to store, transmit and process data. A quantum computer (unlike a classical one) operates not with bits (capable of taking the value of either 0 or 1), but with qubits, the values ​​of which represent a vector - a superposition of 0 and 1. Theoretically, this allows processing all possible states simultaneously, achieving a significant advantage (quantum superiority) over conventional computers in a number of algorithms.

[0011] There is an algorithm for finding the eigenvalues ​​of operators (VQE - variational quantum eigensolver) - which allows quantum computers to solve a narrow range of problems much more efficiently, reducing complexity from exponential to polynomial. This algorithm is a hybrid quantum algorithm, which implies the use of a classical computer along with a quantum one during calculations. This approach allows distributing parts of the problem between classical and quantum processors depending on their specifics, achieving optimal use of computing resources.

[0012] That is, to perform calculations, a classical computer is required that calculates the necessary operations for their further implementation by a quantum processor. To perform an iteration of calculations on a quantum one, it is necessary to create a quantum state each time anew in a quantum environment that is unstable to noise, which is technically difficult. A new state is created by quantum gates, which are mathematically represented by rotation matrices (for spin, for example) - we act on the qubit system according to the rules of quantum control, and then measure the result. In reality, rotation matrices are physical quantum gates, part of the installation, which reduce the accuracy of implementation due to the noise they introduce. The prior art knows methods for generating control signals for quantum gates to perform quantum calculations using a variational algorithm for finding the eigenvalues ​​of operators, for example, the method described in Russian Federation Patent for Invention No. 2806840, published in 2023.

[0013] It describes a method in which:

[0014] • use as the basis for calculations various states of a set of qubits on a quantum computer, expressing a vector, while

[0015] • changing the orientation of the state vector of qubits is implemented using quantum gates,

[0016] • control signals to quantum gates are sent from a classical computer, which also implements an optimization step to recalculate the parameters of control signals to quantum gates, at which the final value of the mathematical expectation of the Hamiltonian of the state of qubits will be minimal for the problem being solved.

[0017] This method is the closest in technical essence and achieved technical result and is chosen as a prototype of the proposed invention. The disadvantage of this method is that to solve the problem of finding the minimum mathematical expectation of the qubit state Hamiltonian for the problem being solved, it is necessary to perform many optimization iterations on both classical and quantum processors to find the optimal configuration of the quantum gate angles. For this, first-order optimization methods such as stochastic gradient descent or Adam optimization, or second-order optimization such as BFGS and others have historically been used, but all these methods work poorly with the function, the mathematical expectation of the qubit state Hamiltonian, which is the optimization goal, and often find a local, rather than a global minimum.By means of a long enumeration of the optimization starting points, it is possible to identify which sequence of rotation matrices allows using the VQE algorithm relatively effectively. In the event that the desired accuracy of the algorithm has not been achieved, then additional quantum gates are added in order to be able to add optimization degrees of freedom according to the “new layer” principle.

[0018] All this makes the method complex, time-consuming, and requires many quantum gates to control the state of the qubits.

[0019] Disclosure of invention.

[0020] Based on this original observation, the present invention is primarily intended to propose a method for generating quantum gate control signals for performing quantum computations using a variational algorithm for finding the eigenvalues ​​of operators, in which various states of a set of qubits on a quantum computer, expressing a vector, are used as the basis for computations, while changing the orientation of the qubit state vector is implemented using quantum gates, control signals are sent to the quantum gates from a classical computer, which makes it possible to stably reduce the number of steps and increase the accuracy of the result, as well as reduce the number of necessary quantum gates, which is the technical problem being solved.

[0021] To achieve this goal:

[0022] • control signals to quantum gates are sent from a classical computer, on which the parameters are recalculated to update the rotation angles of the qubit spins using Riemann optimization, which allows calculating the shortest path to the global minimum of the mathematical expectation of the Hamiltonian of the qubit state, while

[0023] • at each step, not individual parameters of the control signal are optimized, but its matrices of rotations of the qubit vectors, which are considered as a manifold, and the inverse recalculation is performed on the rotation angles of the qubit vectors to form the control signal.

[0024] Thanks to these new characteristics of the method, it becomes possible to sort through the values ​​not blindly, but to immediately move along the shortest path to the global minimum, significantly reducing the number of optimization steps and, as a consequence, the number of required quantum gates. Indeed, Riemannian optimization allows us to consider the parameters of the rotation matrices as a space of manifolds, along which the gradient descent step occurs when searching for the global minimum. This approach requires transferring the classical description of multidimensional optimization from Euclidean space to the space of manifolds.

[0025] Thus, the parameters for updating the state of the quantum circuit are calculated taking into account the topological properties of the matrices, rather than using standard methods. This allows using fewer quantum gates than in the traditional approach.

[0026] There is a variant of the invention in which a rotational manifold and a spectral linear transformation are used to implement the optimization step and to calculate unitary matrices.

[0027] Thanks to these advantageous characteristics, it becomes possible to specify the stage of calculating unitary matrices.

[0028] There is another possible variant of the invention, in which a rotation manifold and a singular linear transformation are used to implement the optimization step, as well as to calculate unitary matrices.

[0029] Thanks to these advantageous characteristics, it becomes possible to specify the stage of calculating unitary matrices.

[0030] There is also a possible variant of the invention in which the Stiefel manifold and singular linear transformation are used to implement the optimization step and calculate the Hermitian matrices.

[0031] Thanks to these advantageous characteristics, it becomes possible to specify the stage of calculating Hermitian matrices.

[0032] Brief description of the drawings.

[0033] Other distinctive features and advantages of the present invention are clearly evident from the description given below for illustration and not as limiting, with reference to the accompanying drawings, in which:

[0034] - Figure 1 depicts a standard circuit for implementing a method for generating control signals for quantum gates for performing quantum computations using a variational algorithm for finding the eigenvalues ​​of operators, the state of the art, - Figure 2 depicts an improved circuit described in this document with a separate block for Riemann optimization, according to the invention.

[0035] The figures indicate:

[0036] 1 - quantum processor;

[0037] 2 - classical computer (EC);

[0038] 3 - a chain of quantum gates for preparing the state of qubits;

[0039] 4 - result measurement block;

[0040] 51 - block for recalculating the parametric optimization step on a classical computer;

[0041] 52 - block for performing Riemann optimization on a classical computer to find the manifold;

[0042] 61 - block for recalculating the update of quantum gate parameters;

[0043] 62 - block for recalculation into quantum gate angles;

[0044] 7 - quantum gate parameter update block.

[0045] Implementation of the invention.

[0046] The method for generating control signals for quantum gates to perform quantum computations using a variational algorithm for finding the eigenvalues ​​of operators is carried out as follows.

[0047] Stage 1. Prepare the starting state of qubits, initialize.

[0048] Step 2. Assemble a quantum circuit consisting of quantum gates according to the planned scheme. Quantum gates include RX, RY, RZ, CNOT, CZ. Random initialization of parameters for quantum gates to start optimization.

[0049] Step 3. Launch the quantum circuit, realizing a new quantum state of qubits and components of the Hamiltonian, and measure the mathematical expectation.

[0050] Stage 4. Recalculation of the parameters of quantum gates is carried out by implementing the Riemann optimization step. Stage 5. The Riemann optimization step is carried out by retraction - linear decomposition of matrices, shift of parameters and subsequent normalization of matrices, preserving their topological properties of the manifold.

[0051] Step 6. Recalculate the values ​​of the updated matrices into rotation angles for the valves. Prepare the valves for the next step.

[0052] Step 7. Repeat the steps starting from the first step until the optimization stop conditions are met, for example, until the function gradient stops changing significantly in absolute value.

[0053] Step 8. The final measurement is performed to obtain the final value of the mathematical expectation of the Hamiltonian of the qubit state.

[0054] Example of the method implementation

[0055] An example of calculating a problem for the Hamiltonian of a 6-qubit system.

[0056] Table 1. Stiefel manifold results

[0057] Adam is a first-order Adam optimization based on gradient descent. geoAdam is an implementation of Riemann optimization for the first-order method, according to the invention.

[0058] BSGS - Broyden-Fletcher-Goldfarb-Shanno algorithm for second-order optimization.

[0059] Industrial applicability.

[0060] The proposed method of generating control signals for quantum gates to perform quantum computations using a variational algorithm for finding the eigenvalues ​​of operators can be implemented by a specialist in practice and, when implemented, ensures the implementation of the declared purpose, which allows us to conclude that the invention meets the "industrial applicability" criterion. Tests of the proposed method of quantum computations using a variational algorithm for finding the eigenvalues ​​of operators have shown that it allows us to increase the accuracy of the final value of the mathematical expectation and reduce the number of steps required for this, while significantly fewer quantum gates are needed.

[0061] During the tests, it was found that the number of iterations is reduced by hundreds of times, the accuracy increases by 4 orders of magnitude, and the number of quantum gates is reduced by 3-10 times depending on the size of the circuit and the number of qubits.

[0062] In this way, the stated technical result is achieved: the ability to reduce the number of required quantum gates, which simplifies the creation of a physical quantum installation, and in addition, when using the proposed method based on Riemann optimization, the measurement accuracy increases, the number of iterations for the convergence of the algorithm decreases, which are also important indicators for the practical application of this technology.

[0063] It is also possible to make a primary assessment of the reduction of quantum noise when implementing this algorithm. Since the maximum accuracy (quantum fidelity) of preserving the signal after the action of the quantum gate on the qubit is preserved at a maximum of 99.5%, and the number of necessary gates is reduced by an average of 5 times, this will increase the accuracy of the result by 2.5%, which is significant for this technological area.

Claims

CLAUSE OF THE INVENTION 1 . A method for generating control signals for quantum gates to perform quantum computations using a variational algorithm for finding the eigenvalues ​​of operators, in which • use as the basis for calculations various states of a set of qubits on a quantum computer, expressing a vector, while • changing the state of qubits is implemented using quantum gates, • control signals to quantum gates are sent from a classical computer, which • also implements an optimization step for recalculating the parameters of control signals to quantum gates, at which the final value of the mathematical expectation of the Hamiltonian of the qubit state will be minimal for the problem being solved, characterized in that • control signals to quantum gates are sent from a classical computer, on which the parameters are recalculated to update the rotation angles of the qubit spins using Riemann optimization, which allows calculating the shortest path to the global minimum of the mathematical expectation of the Hamiltonian of the qubit state, while • at each step, not individual parameters of the control signal are optimized, but its matrices of rotations of the qubit vectors, which are considered as a manifold, and the inverse recalculation is performed on the rotation angles of the qubit vectors to form the control signal.

2. The method according to paragraph 1, characterized in that a rotational manifold and a spectral linear transformation are used to implement the optimization step, as well as to calculate unitary matrices.

3. The method according to paragraph 1, characterized in that a rotational manifold and a singular linear transformation are used to implement the optimization step and also to calculate unitary matrices.

4. The method according to item 1, characterized in that the Stiefel manifold and singular linear transformation are used to implement the optimization step and also to calculate the Hermitian matrices.

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