Quantum Approximate Optimization Algorithm with Adaptive Bias Fields

Abstract

The quantum approximate optimization algorithm (QAOA) transforms a simple many-qubit wavefunction into one which encodes a solution to a difficult classical optimization problem. It does this by optimizing the schedule according to which two unitary operators are alternately applied to the qubits. In this paper, the QAOA is modified by updating the operators themselves to include local fields, using information from the measured wavefunction at the end of one iteration step to improve the operators at later steps. It is shown by numerical simulation on MaxCut problems that, for a fixed accuracy, this procedure decreases the runtime of QAOA very substantially. This improvement appears to increase with the problem size. Our method requires essentially the same number of quantum gates per optimization step as the standard QAOA, and no additional measurements. This modified algorithm enhances the prospects for quantum advantage for certain optimization problems.

16 pages, 13 figures

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• Variational Quantum Algorithms
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• Noisy intermediate-scale quantum (NISQ) algorithms
• Unsupervised Machine Learning on a Hybrid Quantum Computer
• MAXCUT QAOA performance guarantees for p >1
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• Simulation of a feedback-based algorithm for quantum optimization for a realistic neutral atom system with an optimized small-angle controlled-phase gate
• Benchmarking hybrid digitized-counterdiabatic quantum optimization
• Quantum annealing sampling with a bias field
• Warm Start Adaptive-Bias Quantum Approximate Optimization Algorithm
• Atom Cavity Encoding for NP-Complete Problems
• Constraint-Aware Quantum Optimization via Hamming Weight Operators
• Exploiting many-body localization for scalable variational quantum simulation
• Digitized Counter-Diabatic Quantum Optimization for Bin Packing Problem
• Depth Optimized Ansatz Circuit in QAOA for Max-Cut
• Efficient Digital Quadratic Unconstrained Binary Optimization Solvers for SAT Problems
• Constrained Quantum Optimization via Iterative Warm-Start XY-Mixers