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.
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.
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.
Test case optimization (TCO) reduces the software testing cost while preserving its effectiveness. However, to solve TCO problems for large-scale and complex software systems, substantial computational resources are required. Quantum approximate optimization algorithms (QAOAs) are promising combinatorial optimization algorithms that rely on quantum computational resources, with the potential to offer increased efficiency compared to classical approaches. Several proof-of-concept applications of QAOAs for solving combinatorial problems, such as portfolio optimization, energy optimization in power systems, and job scheduling, have been proposed. Given the lack of investigation into QAOA's application for TCO problems, and motivated by the computational challenges of TCO problems and the potential of QAOAs, we present IGDec-QAOA to formulate a TCO problem as a QAOA problem and solve it on both ideal and noisy quantum computer simulators, as well as on a real quantum computer. To solve bigger TCO problems that require many qubits, which are unavailable these days, we integrate a problem decomposition strategy with the QAOA. We performed an empirical evaluation with five TCO problems and four publicly available industrial datasets from ABB, Google, and Orona to compare various configurations of IGDec-QAOA, assess its decomposition strategy of handling large datasets, and compare its performance with classical algorithms (i.e., Genetic Algorithm (GA) and Random Search). Based on the evaluation results achieved on an ideal simulator, we recommend the best configuration of our approach for TCO problems. Also, we demonstrate that our approach can reach the same effectiveness as GA and outperform GA in two out of five test case optimization problems we conducted. In addition, we observe that, on the noisy simulator, IGDec-QAOA achieved similar performance to that from the ideal simulator. Finally, we also demonstrate the feasibility of IGDec-QAOA on a real quantum computer in the presence of noise.