General Hamiltonian Representation of ML Detection Relying on the Quantum Approximate Optimization Algorithm
General Hamiltonian Representation of ML Detection Relying on the Quantum Approximate Optimization Algorithm
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DOI：
10.48550/arxiv.2204.05126
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发表时间：
2022-04
期刊：
影响因子：
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通讯作者：
Jingjing Cui;G. Long;L. Hanzo
中科院分区：
文献类型：
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作者：
Jingjing Cui;G. Long;L. Hanzo
量子近似优化算法（QAOA）是一种用于解决组合优化问题的算法，由于它可以在现有的噪声中尺度量子（NISQ）器件上运行，因此引起了人们极大的兴趣。使用QAOA的主要步骤是基于不同问题实例的有效哈密顿构造。因此，我们解决了一般星座的最大似然（ML）检测问题，通过适当地调整QAOA，这在通信系统中产生了一个新的范例。我们首先将ML检测问题转化为加权最小N -萨蒂斯度（WMIN-N-SAT）问题，其中我们将WMIN-N-SAT的目标函数表示为伪布尔函数。此外，我们形式化的目标函数的程度和灰度标记的调制星座之间的联系。明确地说，我们展示了一系列探索单项式的系数与相关星座点的模式之间的联系的结果，这大大简化了QAOA的问题哈密顿量的目标函数。特别是，对于M元格雷映射正交幅度调制（MQAM）星座，我们证明了编码同相分量的特定量子比特和编码正交分量的特定量子比特在感兴趣的量子系统中是独立的，这允许使用QAOA单独检测同相和正交分量。此外，我们描述的程度在WMIN-N-SAT问题对应的多输入多输出（MIMO）信道的ML检测。最后，我们评估的近似比QAOA的正交相移键控（QPSK）的ML检测问题依赖于不同深度的QAOA电路。各种通信系统的组成部分。最大似然（ML）检测能够发现
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. component of various communication systems. Maximum likelihood (ML) detection is capable of finding