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

• URL: http://arxiv.org/abs/2205.15478v1
• Date: Tue, 31 May 2022 00:14:49 GMT
• Title: Quantum Speedup for Higher-Order Unconstrained Binary Optimization and MIMO Maximum Likelihood Detection
• Authors: Masaya Norimoto, Ryuhei Mori, and Naoki Ishikawa
• Abstract summary: We propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization problem. The proposed algorithm is capable of reducing the query complexity in the classical domain and providing a quadratic speedup in the quantum domain.
• Score: 2.5272389610447856
• License: http://creativecommons.org/licenses/by/4.0/
• 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 a specific 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 convergence, we also derive a probability distribution of the objective function value and determine a unique threshold to sample better states for the quantum algorithm. Assuming a future fault-tolerant quantum computer, we demonstrate that the proposed algorithm is capable of reducing the query complexity in the classical domain and providing a quadratic speedup in the quantum domain.

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