Optimizing QUBO on a quantum computer by mimicking imaginary time evolution

TL;DR

This paper introduces a hybrid quantum-classical algorithm that mimics imaginary time evolution to efficiently solve QUBO problems, achieving high approximation ratios and demonstrating feasibility on real quantum hardware.

Contribution

The authors develop a novel ITEMC algorithm that reduces measurement overhead and improves convergence for QUBO optimization on quantum computers.

Findings

Achieved approximation ratios above 0.99 for up to 150 qubits.

Demonstrated successful hardware runs on IBM quantum devices for 40, 60, and 80 qubits.

Circuit entanglement scales linearly, indicating classical simulation difficulty.

Abstract

We propose a hybrid quantum-classical algorithm for solving QUBO problems using an Imaginary Time Evolution-Mimicking Circuit (ITEMC). The circuit parameters are optimized to closely mimic imaginary time evolution, using only single- and two-qubit expectation values. This significantly reduces the measurement overhead by avoiding full energy evaluation. By updating the initial state based on results from last step iteratively, the algorithm quickly converges to the low-energy solutions. With a pre-sorting step that optimizes quantum gate ordering based on QUBO coefficients, the convergence is further improved. Our classical simulations achieve approximation ratios above 0.99 up to 150 qubits. Furthermore, the linear scaling of entanglement entropy with system size suggests that the circuit is challenging to simulate classically using tensor networks. We also demonstrate hardware runs on IBM's device for 40, 60, and 80 qubits, and obtain solutions compatible with that from simulated annealing.