In this paper, we address the joint maximum-likelihood detection of power-domain non-orthogonal multiple access and transform the detection problem into a binary optimization problem. Then, we solve it by a quantum algorithm, Grover adaptive search (GAS), and further accelerate the algorithm. Assuming fault-tolerant quantum computing, GAS provides a quadratic speedup for binary optimization problems in terms of query complexity. The proposed method designs the number of Grover operators using a time-invariant distribution of the number of solutions, which can be obtained in advance. Simulation results demonstrate that the proposed method is capable of reducing the query complexity in the classical domain while achieving the optimal performance.

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.