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Вестник Российского университета дружбы народов. Серия: Математика, информатика, физика

Simulating QAOA operation using Cirq and qsim quantum frameworks

Yuri Palii, Alla A. Bogolubskaya, Denis A. Yanovich

Published Dec 7, 2025• 0 citations
Publisher

Abstract

The problem of finding the lowest-energy state in the Ising model with a longitudinal magnetic field is studied for two- and three-dimensional lattices of various sizes using the Quantum Approximate Optimization Algorithm (QAOA). The basis states of the quantum computer register correspond to spin configurations on a spatial lattice, and the Hamiltonian of the model is implemented using a sequence of quantum gates. The average energy value is efficiently measured using the Hadamard test. We simulate the QAOA operation on increasingly complex lattice configurations using the software libraries Cirq and qsim. The results of optimization, obtained using gradient-based and gradient-free methods, demonstrate the superiority of the latter in both modeling performance and quantum computer usage. Key arguments in favor of the advantages of quantum computation for this problem are presented.

DOI
10.22363/2658-4670-2025-33-4-440-460

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The problem of finding the lowest-energy state in the Ising model with a longitudinal magnetic field is studied for two- and three-dimensional lattices of various sizes using the Quantum Approximate Optimization Algorithm (QAOA). The basis states of the quantum computer register correspond to spin configurations on a spatial lattice, and the Hamiltonian of the model is implemented using a sequence of quantum gates. The average energy value is efficiently measured using the Hadamard test. We simulate the QAOA operation on increasingly complex lattice configurations using the software libraries Cirq and qsim. The results of optimization, obtained using gradient-based and gradient-free methods, demonstrate the superiority of the latter in both modeling performance and quantum computer usage. Key arguments in favor of the advantages of quantum computation for this problem are presented.
Abstract Simulation of the Quantum Approximate Optimization Algorithm (QAOA) was performed using the Cirq software library installed on the HybriLIT quantum computing testbed at JINR. The problem of finding the lowest energy state for the Ising model with a longitudinal magnetic field was solved for two- and three-dimensional lattices of various sizes. Quantum circuits with registers up to 27 qubits were investigated during the study. Optimization of the variational ansatz parameters was carried out using both gradient-based and gradient-free methods. The processes and results of optimization carried out by various methods were compared by a number of parameters.The influence of the configuration of the computing resources used on the efficiency of calculations has been demonstrated.
Simulation of the Quantum Approximate Optimization Algorithm (QAOA) was performed using the Cirq software library installed on the HybriLIT quantum computing testbed at JINR. The problem of finding the lowest energy state for the Ising model with a longitudinal magnetic field was solved for two- and threedimensional lattices of various sizes. Quantum circuits with registers of up to 27 qubits were investigated during the study. Optimization of the variational ansatz parameters was carried out using both gradient-based and gradient-free methods. The processes and results of optimization performed by different methods were compared based on a number of parameters. The dependence of the efficiency of calculations on the configuration of the computing resources used was demonstrated.
Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly improving performance for solving exponentially hard problems, such as optimization and satisfiability. Here, we report the implementation of a low-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator. We estimate the ground-state energy of the Transverse Field Ising Model with long-range interactions with tunable range, and we optimize the corresponding combinatorial classical problem by sampling the QAOA output with high-fidelity, single-shot, individual qubit measurements. We execute the algorithm with both an exhaustive search and closed-loop optimization of the variational parameters, approximating the ground-state energy with up to 40 trapped-ion qubits. We benchmark the experiment with bootstrapping heuristic methods scaling polynomially with the system size. We observe, in agreement with numerics, that the QAOA performance does not degrade significantly as we scale up the system size and that the runtime is approximately independent from the number of qubits. We finally give a comprehensive analysis of the errors occurring in our system, a crucial step in the path forward toward the application of the QAOA to more general problem instances.
Novel magnetic materials are important for future technological advances. Theoretical and numerical calculations of ground-state properties are essential in understanding these materials, however, computational complexity limits conventional methods for studying these states. Here we investigate an alternative approach to preparing materials ground states using the quantum approximate optimization algorithm (QAOA) on near-term quantum computers. We study classical Ising spin models on unit cells of square, Shastry-Sutherland and triangular lattices, with varying field amplitudes and couplings in the material Hamiltonian. We find relationships between the theoretical QAOA success probability and the structure of the ground state, indicating that only a modest number of measurements ([Formula: see text]) are needed to find the ground state of our nine-spin Hamiltonians, even for parameters leading to frustrated magnetism. We further demonstrate the approach in calculations on a trapped-ion quantum computer and succeed in recovering each ground state of the Shastry-Sutherland unit cell with probabilities close to ideal theoretical values. The results demonstrate the viability of QAOA for materials ground state preparation in the frustrated Ising limit, giving important first steps towards larger sizes and more complex Hamiltonians where quantum computational advantage may prove essential in developing a systematic understanding of novel materials. This article is part of the theme issue 'Quantum annealing and computation: challenges and perspectives'.
Quantum computers and simulators may offer significant advantages over their classical counterparts, providing insights into quantum many-body systems and possibly solving exponentially hard problems, such as optimization and satisfiability. Here we report the first implementation of a shallow-depth Quantum Approximate Optimization Algorithm (QAOA) using an analog quantum simulator to estimate the ground state energy of the transverse field Ising model with tunable long-range interactions. First, we exhaustively search the variational control parameters to approximate the ground state energy with up to 40 trapped-ion qubits. We then interface the quantum simulator with a classical algorithm to more efficiently find the optimal set of parameters that minimizes the resulting energy of the system. We finally sample from the full probability distribution of the QAOA output with single-shot and efficient measurements of every qubit.
Quantum computation appears to offer significant advantages over classical computation and this has generated a tremendous interest in the field. In this thesis we consider the application of quantum computers to scientific computing and combinatorial optimization. We study five problems. The first three deal with quantum algorithms for computational problems in science and engineering, including quantum simulation of physical systems. In particular, we study quantum algorithms for numerical computation, for the approximation of ground and excited state energies of the Schrödinger equation, and for Hamiltonian simulation with applications to physics and chemistry. The remaining two deal with quantum algorithms for approximate optimization. We study the performance of the quantum approximate optimization algorithm (QAOA), and show a generalization of QAOA, the quantum\textit{quantum}quantum alternating\textit{alternating}alternating operator\textit{operator}operator ansatz\textit{ansatz}ansatz, particularly suitable for constrained optimization problems and low-resource implementations on near-term quantum devices.