Quantum Approximate Optimization Algorithm Based Maximum Likelihood Detection

Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where quantum approximation optimization algorithms (QAOAs) constitute promising candidates for demonstrating tangible quantum advantages based on NISQ devices. In this paper, we consider the maximum likelihood (ML) detection problem of binary symbols transmitted over a multiple-input and multiple-output (MIMO) channel, where finding the optimal solution is exponentially hard using classical computers. Here, we apply the QAOA for the ML detection by encoding the problem of interest into a level-p QAOA circuit having 2p variational parameters, which can be optimized by classical optimizers. This level-p QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in p consecutive rounds. More explicitly, we first encode the optimal solution of the ML detection problem into the ground state of a problem Hamiltonian. Using the quantum adiabatic evolution technique, we provide both analytical and numerical results for characterizing the evolution of the eigenvalues of the quantum system used for ML detection. Then, for level-1 QAOA circuits, we derive the analytical expressions of the expectation values of the QAOA and discuss the complexity of the QAOA based ML detector. Explicitly, we evaluate the computational complexity of the classical optimizer used and the storage requirement of simulating the QAOA. Finally, we evaluate the bit error rate (BER) of the QAOA based ML detector and compare it both to the classical ML detector and to the classical MMSE detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector. This paves the way for a host of large-scale classical optimization problems to be solved by NISQ computers.

翻译：量子技术的最新进步为杂音中间级量子(NISQ)设备铺平了道路, 量子近似优化算法(QAOAs)是展示基于新Q设备的实际量子优势的有希望的候选人。在本文中, 我们考虑通过多输入和多输出(MIMO)频道传输的二进制符号的最大可能性( MML) 问题, 通过古典计算机找到最佳的解决方案。在这里, 我们应用 QAAA 用于ML 检测, 将感兴趣的问题输入具有 2p 变异参数的 QA 级电路段。这个水平- pA 电路路是用预制的汉密尔密尔顿(MMMMMIMO), 将ML 检测问题的最佳解决方案加到汉密尔密尔密尔顿的地面状态。使用量级的量级的量子A QA 变异变法, 我们提供分析和数字结果, 将用于MLA 的量值 QA 的量值系统变异性质量, 、以我们测测测测测算的MLA 的MLA 的液、的MLA 级 O 、级级级的 O 级测算的 O 、级测测算的 O 的的级的级的的级的级的的的级的级的级的的级的级的级的级的级的级算的级算结果级级的、、、、级的级的级的级的级的级的级的级的级的级级级的级的级的级的级的级的、级的级的级的、级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级的级