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

Masaya Norimoto

doi:10.1109/TCOMM.2023.3244924

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

2023-04-01

Masaya Norimoto

Ryuhei Mori

Naoki Ishikawa *

DOI：10.1109/TCOMM.2023.3244924

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Abstract

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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.

Keywords:

Qubit

Symbols

Quantum computing

Linear programming

Complexity theory

Optimization

MIMO communication

Grover adaptive search (GAS)

quadratic unconstrained binary optimization (QUBO)

higher-order unconstrained binary optimization (HUBO)

multiple-input multiple-output (MIMO)