Suksmono Andriyan Bayu, Minato Yuichiro
The School of Electrical Engineering and Informatics, Institut Teknologi Bandung, Bandung, Indonesia.
Blueqat Inc., Tokyo, Japan.
Sci Rep. 2022 Jan 7;12(1):197. doi: 10.1038/s41598-021-03586-0.
Finding a Hadamard matrix (H-matrix) among all possible binary matrices of corresponding order is a hard problem that can be solved by a quantum computer. Due to the limitation on the number of qubits and connections in current quantum processors, only low order H-matrix search of orders 2 and 4 were implementable by previous method. In this paper, we show that by adopting classical searching techniques of the H-matrices, we can formulate new quantum computing methods for finding higher order ones. We present some results of finding H-matrices of order up to more than one hundred and a prototypical experiment of the classical-quantum resource balancing method that yields a 92-order H-matrix previously found by Jet Propulsion Laboratory researchers in 1961 using a mainframe computer. Since the exactness of the solutions can be verified by an orthogonality test performed in polynomial time; which is untypical for optimization of hard problems, the proposed method can potentially be used for demonstrating practical quantum supremacy in the near future.
在所有对应阶数的可能二进制矩阵中找到一个哈达玛矩阵（H 矩阵）是一个难题，可由量子计算机解决。由于当前量子处理器中量子比特数和连接数的限制，先前的方法仅能实现 2 阶和 4 阶的低阶 H 矩阵搜索。在本文中，我们表明通过采用 H 矩阵的经典搜索技术，可以制定新的量子计算方法来寻找高阶 H 矩阵。我们展示了一些找到高达一百阶以上 H 矩阵的结果，以及经典 - 量子资源平衡方法的一个典型实验，该实验得到了喷气推进实验室的研究人员在 1961 年使用大型计算机先前找到的一个 92 阶 H 矩阵。由于解的正确性可以通过在多项式时间内执行的正交性测试来验证；这对于难题优化来说并不常见，所提出的方法在不久的将来有可能用于展示实际的量子优越性。
