Feedback-Based Quantum Algorithm for Constrained Optimization Problems

Abstract

The feedback-based algorithm for quantum optimization (FALQON) has recently been proposed to solve quadratic unconstrained binary optimization problems. This paper efficiently generalizes FALQON to tackle quadratic constrained binary optimization (QCBO) problems. For this purpose, we introduce a new operator that encodes the problem's solution as its ground state. Using Lyapunov control theory, we design a quantum control system such that the state converges to the ground state of this operator. When applied to the QCBO problem, we show that our proposed algorithm saves computational resources by reducing the depth of the quantum circuit and can perform better than FALQON. The effectiveness of our proposed algorithm is further illustrated through numerical simulations.

This paper is accepted for publication in the 15th International Conference on Parallel Processing and Applied Mathematics (PPAM 2024)

References in corpus (9)

• Variational Quantum Algorithms
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Rapid Lyapunov control of finite-dimensional quantum systems
• On the representation of Boolean and real functions as Hamiltonians for quantum computing
• Feedback-based quantum optimization
• Constrained Optimization via Quantum Zeno Dynamics
• Digital quantum simulation of molecular dynamics and control
• Lyapunov control-inspired strategies for quantum combinatorial optimization
• Measurement-Based Control for Minimizing Energy Functions in Quantum Systems