论文标题
二进制恒定重量代码的量子搜索算法
Quantum Search Algorithm for Binary Constant Weight Codes
论文作者
论文摘要
二进制恒定重量代码是一种具有多种应用程序的错误校正代码。长期以来，研究二进制恒定重量代码的问题一直是编码理论中的组合优化问题。在本文中，我们为二进制恒定重量代码提出了一种量子搜索算法。具体而言，搜索问题是新提出的，作为二次无约束的二进制优化（QUBO）和Grover自适应搜索（GAS）用于提供二次加速。着眼于问题的固有结构，我们在目标函数值的最小值上得出了上限，并在确切的解决方案数量上得出了下限。在我们的代数分析中，发现该提出的算法能够减少所需量子位的数量，从而提高可行性。此外，我们的模拟表明，在经典域中，它在量子域中将查询复杂性降低了63％，在量子域中将查询复杂性降低了31％。所提出的方法可能对其他量子搜索算法和优化问题有用。
A binary constant weight code is a type of error-correcting code with a wide range of applications. The problem of finding a binary constant weight code has long been studied as a combinatorial optimization problem in coding theory. In this paper, we propose a quantum search algorithm for binary constant weight codes. Specifically, the search problem is newly formulated as a quadratic unconstrained binary optimization (QUBO) and Grover adaptive search (GAS) is used for providing the quadratic speedup. Focusing on the inherent structure of the problem, we derive an upper bound on the minimum of the objective function value and a lower bound on the exact number of solutions. In our algebraic analysis, it was found that this proposed algorithm is capable of reducing the number of required qubits, thus enhancing the feasibility. Additionally, our simulations demonstrated that it reduces the query complexities by 63% in the classical domain and 31% in the quantum domain. The proposed approach may be useful for other quantum search algorithms and optimization problems.
