Evaluating the capabilities of classical computers in implementing quantum algorithm simulators

Modern quantum devices have severe limitations in the number of qubits, which limit the width and depth of the quantum circuit and have strong noise processes that make it difficult to obtain correct results. It is also necessary to design quantum circuits for a particular quantum device taking into account the coupling be-tween qubits and to apply quantum error mitigation. It is possible to avoid these problems using classical computers to simulate quantum computation. Classical computers are used both for quick testing of hypotheses before running on quantum devices and for solving real-world problems. The paper describes the process of designing and efficient modeling of quantum algorithms, approaches to developing quantum search algorithms, Grover's algorithm. Qiskit and QuEST quantum simulators were used to study the efficiency of using a supercomputer to simulate quantum circuits on CPUs and GPUs using the example of the quantum test circuit and Grover's algorithm. This paper describes a quantum phase estimation algorithm, which is a basic unit in some quantum algorithms of quantum computational physics and chemistry. The algorithm is simulated using NVIDIA's newest cuQuantum quantum simulator. It allows efficient simulation of quantum circuits on GPUs using multiple GPUs, which significantly increases speed and allows the quantum phase estimation algorithm to be executed with sufficient computational accuracy. The paper also notes the difficulties when simulating different algorithms using a large number of qubits or circuit depth.