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ФИЗИКА ЭЛЕМЕНТАРНЫХ ЧАСТИЦ И АТОМНОГО ЯДРА

Моделирование работы алгоритма QAOA на квантовом полигоне ОИЯИ

Yu. G. Palii, D. V. Belyakov, Alla A. Bogolubskaya, M. I. Zuev, Denis A. Yanovich, Ю. Г. Палий, А. А. Боголюбская

Published Sep 24, 2025• 0 citations
OpenAlex

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 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.

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Simulation of the QAOA Algorithm at the JINR Quantum Testbed

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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.

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Simulating QAOA operation using Cirq and qsim quantum frameworks

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

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.

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Quantum approximate optimization of the long-range Ising model with a trapped-ion quantum simulator

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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.

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Quantum Approximate Optimization with a Trapped-Ion Quantum Simulator

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Seongmin Kim, In‐Saeng Suh

The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.

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Analysis of Quantum Approximate Optimization Algorithm under Realistic Noise in Superconducting Qubits

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The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.

arXiv:1907.09631•Jul 13, 2019•33 citations
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.
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.
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.
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.
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.
The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising tool for accelerating optimization processes in the Noisy Intermediate-Scale Quantum (NISQ) era. Compared to classical methods, QAOA efficiently solves optimization problems, often formulated as Quadratic Unconstrained Binary Optimization (QUBO) problems. Classical quantum simulators are crucial for evaluating quantum algorithms due to limited quantum resources. However, QAOA's performance can vary with different simulation methods. This study analyzes QAOA's performance using various quantum simulators (e.g., density _matrix, statevector, and matrix_product_state) and demonstrates the benefits of HPC-QC integrated systems in solving QUBO problems on an active learning workflow. By simulating QAOA on dense, large-matrix QUBO problems, we evaluate accuracy and problem-solving time. We also assess QAOA's performance on local computers and HPC-QC inte-grated systems, using Oak Ridge Leadership Computing Facility (OLCF)'s Frontier supercomputer with local Qiskit Aer and remote IBM Quantum simulators.
The quantum approximate optimization algorithm (QAOA) is a promising quantum-classical hybrid technique to solve combinatorial optimization problems in near-term gate-based noisy quantum devices. In QAOA, the objective is a function of the quantum state, which itself is a function of the gate parameters of a multi-level parameterized quantum circuit (PQC). A classical optimizer varies the continuous gate parameters to generate distributions (quantum state) with significant support to the optimal solution. Even at the lowest circuit depth, QAOA offers non-trivial provable performance guarantee which is expected to increase with the circuit depth. However, the existing analysis fails to consider non-idealities in the qubit quality i.e., short lifetime and imperfect gate operations in realistic quantum hardware. In this article, we investigate the impact of various noise sources on the performance of QAOA both in simulation and on a real quantum computer from IBM. Our analyses indicate that the optimal number of stages (p-value) for any QAOA instance is limited by the noise characteristics (gate error, coherence time, etc.) of the target hardware as opposed to the current perception that higher-depth QAOA will provide monotonically better performance for a given problem compared to the low-depth implementations.