The Study On Multi-valued Quantum Reversible Logic Circuit Synthesis Method

With the rapid development of compute, it’s bound to run into a bottleneck asenergy dissipation in a near future. The past researches reveal that the origin of energydissipation lies in the nonreversible compute, from which a brand-new compute modecomes into the world: reversible compute. Hereinto quantum computing is a typicalreversible compute, and plenty of achievements have been brought forward. The mainstudy model of quantum compute research is the Quantum Circuit Model. Thereversible quantum logic circuit synthesis is the priority among the priorities in thestudy of quantum circuit model.Horizontally speaking, this is a comprehensive research which consists oftwo-valued quantum system and multi-valued quantum system primarily. Given that themany valued system absolutely prevails the two-valued quantum system in size,encoding, information security and so on, the many valued one presents a new focus.This paper keeps a watchful eye on the approaches of reversible logic circuitsynthesis within the many valued quantum system, and as a research prototype ofthree-valued quantum systems. Here are the procedures:1. Employ a special circuit (remain ground state when input and output), firstlypropose a three-valued quantum reversible logic synthesis compute based onpermutation group. Then analyse the complexity to bring up the basic quantum gatewhich takes TX system and TCX system as the three-valued quantum system, and proveits generality through some constructive approaches. In the last place extend theapplication of the arithmetic which comes from the three-valued system into thecommon multi-valued quantum system.2. According to the knowledge of Quantum Physics, all the quantum statecalculations correspond to the unitary operators. From the representation theory ofgroup, each unitary operator could be expressed as the unitary matrix in complex space,and each unitary matrix could be abstracted to be a quantum logic gate. Therefore thequantum reversible logic circuit synthesis equals the disintegration of the unitary matrix.The fourth chapter pays attention to the approaches of disintegration based on CSD primarily, which proves any3~n×3~nunitary matrix can be achieved by12controlunitary gates,12Dual-shift gates,3~n(n-1)-control swing gates and2(n1)3~n1TXgates together.