期刊
PHYSICAL REVIEW LETTERS
卷 109, 期 3, 页码 -出版社
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.109.030503
关键词
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资金
- NSF [CCF-1116590, CCF-1117241]
- Direct For Computer & Info Scie & Enginr
- Division of Computing and Communication Foundations [1117241] Funding Source: National Science Foundation
- Division of Computing and Communication Foundations
- Direct For Computer & Info Scie & Enginr [1116590] Funding Source: National Science Foundation
We propose a form of parallel computing on classical computers that is based on matrix product states. The virtual parallelization is accomplished by representing bits with matrices and by evolving these matrices from an initial product state that encodes multiple inputs. Matrix evolution follows from the sequential application of gates, as in a logical circuit. The action by classical probabilistic one-bit and deterministic two-bit gates such as NAND are implemented in terms of matrix operations and, as opposed to quantum computing, it is possible to copy bits. We present a way to explore this method of computation to solve search problems and count the number of solutions. We argue that if the classical computational cost of testing solutions (witnesses) requires less than O(n(2)) local two-bit gates acting on n bits, the search problem can be fully solved in subexponential time. Therefore, for this restricted type of search problem, the virtual parallelization scheme is faster than Grover's quantum algorithm.
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