NISQ-compatible approximate quantum algorithm for unconstrained and constrained discrete optimization
Author:
Perelshtein M. R.123, Pakhomchik A. I.1, Melnikov Ar. A.1, Podobrii M.1, Termanova A.1, Kreidich I.1, Nuriev B.1, Iudin S.1, Mansell C. W.1, Vinokur V. M.14
Affiliation:
1. Terra Quantum AG, Kornhausstrasse 25, 9000 St. Gallen, Switzerland 2. QTF Centre of Excellence, Department of Applied Physics, Aalto University, P.O. Box 15100, FI-00076 AALTO, Finland 3. InstituteQ – the Finnish Quantum Institute, Aalto University, Finland 4. Physics Department, City College of the City University of New York, 160 Convent Ave, New York, NY 10031, USA
Abstract
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum algorithms training, the shape of their cost landscape, the accuracy of their output, and their ability to scale to large-size problems. Here, we present an approximate gradient-based quantum algorithm for hardware-efficient circuits with amplitude encoding. We show how simple linear constraints can be directly incorporated into the circuit without additional modification of the objective function with penalty terms. We employ numerical simulations to test it on MaxCut problems with complete weighted graphs with thousands of nodes and run the algorithm on a superconducting quantum processor. We find that for unconstrained MaxCut problems with more than 1000 nodes, the hybrid approach combining our algorithm with a classical solver called CPLEX can find a better solution than CPLEX alone. This demonstrates that hybrid optimization is one of the leading use cases for modern quantum devices.
Publisher
Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
Subject
Physics and Astronomy (miscellaneous),Atomic and Molecular Physics, and Optics
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