论文标题
依靠量子近似优化算法的ML检测的一般表示
General Hamiltonian Representation of ML Detection Relying on the Quantum Approximate Optimization Algorithm
论文作者
论文摘要
量子近似优化算法（QAOA）构想用于解决组合优化问题的问题引起了重大兴趣，因为它可以在现有的嘈杂中间尺度量子（NISQ）设备上运行。使用QAOA的主要步骤是基于不同问题实例的有效的哈密顿构建。因此，我们通过适当调整QAOA来解决一般星座的最大可能性（ML）检测问题，这在通信系统中产生了新的范式。我们首先将ML检测问题转换为加权的最小$ n $ - s缩合性（Wmin- $ n $ -sat）问题，在那里我们将Wmin-$ n $ -sat的目标函数作为伪布尔函数。此外，我们将目标函数程度与灰色标记的调制星座之间的联系形式化。明确地，我们显示了一系列结果，探讨了单元的系数与相关星座点的模式之间的连接，这实质上简化了目标函数，相对于QAOA的问题。特别是，对于M-Ary灰色映射的正交振幅调制（MQAM）星座，我们表明编码编码相位内组件的特定量子和编码二次组件的量子组件在量子系统中独立于量子系统中，这允许分别使用QAOAA分别检测到相位和Quadrature组件。此外，我们在Wmin- $ n $ -SAT问题中表征了目标函数的程度，该问题对应于ML检测多输入和多输出（MIMO）通道。最后，我们评估了依靠不同深度的QAOA电路的正交相移键合（QPSK）的ML检测问题的QAOA的近似值。
The quantum approximate optimization algorithm (QAOA) conceived for solving combinatorial optimization problems has attracted significant interest since it can be run on the existing noisy intermediate-scale quantum (NISQ) devices. A primary step of using the QAOA is the efficient Hamiltonian construction based on different problem instances. Hence, we solve the maximum likelihood (ML) detection problem for general constellations by appropriately adapting the QAOA, which gives rise to a new paradigm in communication systems. We first transform the ML detection problem into a weighted minimum $N$-satisfiability (WMIN-$N$-SAT) problem, where we formulate the objective function of the WMIN-$N$-SAT as a pseudo Boolean function. Furthermore, we formalize the connection between the degree of the objective function and the Gray-labelled modulation constellations. Explicitly, we show a series of results exploring the connection between the coefficients of the monomials and the patterns of the associated constellation points, which substantially simplifies the objective function with respect to the problem Hamiltonian of the QAOA. In particular, for an M-ary Gray-mapped quadrature amplitude modulation (MQAM) constellation, we show that the specific qubits encoding the in-phase components and those encoding the quadrature components are independent in the quantum system of interest, which allows the in-phase and quadrature components to be detected separately using the QAOA. Furthermore, we characterize the degree of the objective function in the WMIN-$N$-SAT problem corresponding to the ML detection of multiple-input and multiple-output (MIMO) channels. Finally, we evaluate the approximation ratio of the QAOA for the ML detection problem of quadrature phase shift keying (QPSK) relying on QAOA circuits of different depths.
