Concurrent Quantum Computation

Abstract

A quantum computer is a multi-particle interferometer that comprises beam splitters at both ends and arms, where the n two-level particles undergo the interactions among them. The arms are designed so that relevant functions required to produce a computational result is stored in the phase shifts of the 2^n arms. They can be detected by interferometry that allows us to utilize quantum parallelism. Quantum algorithms are accountable for what interferometers to be constructed to compute particular problems. A standard formalism for constructing the arms has been developed by the extension of classical reversible gate arrays. By its nature of sequential applications of logic operations, the required number of gates increases exponentially as the problem size grows. This may cause a crucial obstacle to perform a quantum computation within a limited decoherence time. We propose a direct and concurrent construction of the interferometer arms by one-time evolution of a physical system with arbitrary multi-particle interactions. It is inherently quantum mechanical and has no classical analogue. Encoding the functions used in Shor's algorithm for prime factoring, Grover's algorithm and Deutsch-Jozsa algorithm requires only one-time evolution of such a system regardless of the problem size n as opposed to its standard sequential counterpart that takes O(n^3), O(n) and O(n2^n).