Multi-round QAOA and advanced mixers on a trapped-ion quantum computer

Abstract

Combinatorial optimization problems on graphs have broad applications in science and engineering. The Quantum Approximate Optimization Algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of variational circuits. However, there exist several challenges limiting the real-world applications of QAOA. In this paper, we demonstrate on a trapped-ion quantum computer that QAOA results improve with the number of rounds for multiple problems on several arbitrary graphs. We also demonstrate an advanced mixing Hamiltonian that allows sampling of all optimal solutions with predetermined weights. Our results are a step towards applying quantum algorithms to real-world problems.

arXiv comment8 pages, 5 figures

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• Encoding-Independent Optimization Problem Formulation for Quantum Computing
• High-Round QAOA for MAX $k$-SAT on Trapped Ion NISQ Devices
• Grover-QAOA for 3-SAT: Quadratic Speedup, Fair-Sampling, and Parameter Clustering
• Realization of programmable Ising models in a trapped-ion quantum simulator
• Exponential Qubit Reduction in Optimization for Financial Transaction Settlement
• Efficient Frequency Allocation for Superconducting Quantum Processors Using Improved Optimization Techniques
• Biased Degenerate Ground-State Sampling of Small Ising Models with Converged QAOA
• Applying Grover-mixer quantum alternating operator ansatz algorithm to higher-order unconstrained binary optimization problems