Recent advances in quantum technologies pave the way for noisy intermediate-scale quantum (NISQ) devices, where the quantum approximation optimization algorithm (QAOA) constitutes a promising candidate 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- [Math Processing Error]p QAOA circuit having [Math Processing Error]2p variational parameters, which can be optimized by classical optimizers. This level- [Math Processing Error]p QAOA circuit is constructed by applying the prepared Hamiltonian to our problem and the initial Hamiltonian alternately in [Math Processing Error]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 minimum mean squared error (MMSE) detector, demonstrating that the QAOA based ML detector is capable of approaching the performance of the classical ML detector.

中文翻译：

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用于集成传感和通信的具有不匹配负载阻抗的高隔离双工器


量子技术的最新进展为噪声中尺度量子 (NISQ) 设备铺平了道路，其中量子近似优化算法 (QAOA) 成为展示基于 NISQ 设备的切实量子优势的有希望的候选者。在本文中，我们考虑通过多输入多输出（MIMO）信道传输的二进制符号的最大似然（ML）检测问题，使用传统计算机找到最佳解决方案是指数级困难的。在这里，我们将 QAOA 应用于 ML 检测，将感兴趣的问题编码到具有 [数学处理误差]2p 变分参数的 [数学处理误差]p 级 QAOA 电路中，该电路可以通过经典优化器进行优化。这个级别-[数学处理误差]p QAOA电路是通过在[数学处理误差]p连续轮中交替地将准备好的哈密顿量应用于我们的问题和初始哈密顿量来构建的。更明确地说，我们首先将 ML 检测问题的最优解编码为问题哈密顿量的基态。使用量子绝热演化技术，我们提供了解析和数值结果来表征用于机器学习检测的量子系统特征值的演化。然后，对于 1 级 QAOA 电路，我们推导了 QAOA 期望值的解析表达式，并讨论了基于 QAOA 的 ML 检测器的复杂性。明确地，我们评估了所使用的经典优化器的计算复杂性以及模拟 QAOA 的存储要求。 最后，我们评估基于 QAOA 的 ML 检测器的误码率 (BER)，并将其与经典 ML 检测器和经典最小均方误差 (MMSE) 检测器进行比较，证明基于 QAOA 的 ML 检测器能够接近经典 ML 检测器的性能。