Quantum Approximate Optimization

Stefan Isermann

Chun-Han Wu, Tian-Xiang Wei, Jia Liu +1 more

This paper studies the application of quantum approximate optimization algorithm in portfolio optimization problem, and focuses on the real stock market, analyzes and quantifies the real data of ten stocks, compares the performance of quantum approximate optimization algorithm and classical algorithm in solving this problem, and also analyzes the effect of noise on the solution using quantum approximate optimization, showing the performance of quantum approximate optimization algorithm in the financial stock market and the The performance and application value of the quantum approximate optimization algorithm in the financial stock market are shown.

Ansh Bansal

Weitang Li, Yufei Ge, Shi‐Xin Zhang +2 more

The variational quantum eigensolver (VQE) framework has been instrumental in advancing near-term quantum algorithms. However, parameter optimization remains a significant bottleneck for VQE, requiring a large number of measurements for successful algorithm execution. In this paper, we propose sequential optimization with approximate parabola (SOAP) as an efficient and robust optimizer specifically designed for parameter optimization of the unitary coupled-cluster ansatz on quantum computers. SOAP leverages sequential optimization and approximates the energy landscape as quadratic functions, minimizing the number of energy evaluations required to optimize each parameter. To capture parameter correlations, SOAP incorporates the average direction from previous iterations into the optimization direction set. Numerical benchmark studies on molecular systems demonstrate that SOAP achieves significantly faster convergence and greater robustness to noise compared with traditional optimization methods. Furthermore, numerical simulations of up to 20 qubits reveal that SOAP scales well with the number of parameters in the ansatz. The exceptional performance of SOAP is further validated through experiments on a superconducting quantum computer using a 2-qubit model system.

Pablo Herrero Gómez, Marcos Alemany Manzanaro, David Gil +1 more

Jaeho Choi, Seunghyeok Oh, Joongheon Kim

This paper proposes an application algorithm based on a quantum approximate optimization algorithm (QAOA) for wireless scheduling problems. QAOA is one of the promising hybrid quantum-classical algorithms to solve combinatorial optimization problems and it provides great approximate solutions to non-deterministic polynomial-time (NP) hard problems. QAOA maps the given problem into Hilbert space, and then it generates the Hamiltonian for the given objective and constraint. Then, QAOA finds proper parameters from the classical optimization loop in order to optimize the expectation value of the generated Hamiltonian. Based on the parameters, the optimal solution to the given problem can be obtained from the optimum of the expectation value of the Hamiltonian. Inspired by QAOA, a quantum approximate optimization for scheduling (QAOS) algorithm is proposed. The proposed QAOS designs the Hamiltonian of the wireless scheduling problem which is formulated by the maximum weight independent set (MWIS). The designed Hamiltonian is converted into a unitary operator and implemented as a quantum gate operation. After that, the iterative QAOS sequence solves the wireless scheduling problem. The novelty of QAOS is verified with simulation results implemented via Cirq and TensorFlow-Quantum.