Quantum Algorithm for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection

TL;DR

This paper introduces a quantum algorithm for higher-order unconstrained binary optimization with real coefficients, applying it to MIMO detection, and demonstrates potential for quadratic speedup and reduced complexity in quantum computing.

Contribution

It extends the Grover adaptive search to real-valued HUBO problems and formulates MIMO detection as a HUBO, enabling efficient quantum circuit construction and analysis.

Findings

Supports real-valued coefficients in HUBO problems

Formulates MIMO detection as a HUBO problem

Potential for quadratic speedup in quantum domain

Abstract

In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer coefficients. Next, as an application example, we formulate multiple-input multiple-output maximum likelihood detection as a HUBO problem with real-valued coefficients, where we use the Gray-coded bit-to-symbol mapping specified in the 5G standard. The proposed approach allows us to construct an efficient quantum circuit for the detection problem and to analyze specific numbers of required qubits and quantum gates, whereas other conventional studies have assumed that such a circuit is feasible as a quantum oracle. To further accelerate the quantum algorithm, we also derive a probability distribution of the objective function value and determine a unique threshold to sample better states. Assuming a future fault-tolerant quantum computing, our proposed algorithm has the potential for significantly reducing query complexity in the classical domain and providing a quadratic speedup in the quantum domain.