Studies on Methods for the Synthesis of Quantum Circuits
Y. Nakajima · Institutional Repositories DataBase (IRDB) · 2009
A quantum computer is expected to solve some problems far faster than today's computers and may be a promising device with low power consumption.This computer is based on the physical theory of quantum mechanics.In the theory of quantum mechanics, quantum states and evolutions of quantum states are represented by vectors in a Hilbert space and unitary operators, respectively.A unitary matrix can then be regarded as an algorithm in the conventional computer.Since it is generally difficult to develop an arbitrary unitary matrix in a quantum system, quantum computation is carried out by combining elementary operations such as one-or two-qubit operations, where a qubit is the smallest unit of information in quantum computation.A unitary matrix is said to be performed effectively if there exists a quantum circuit composed of a polynomial number of elementary gates.Therefore, translating a unitary matrix into an efficient sequence of elementary gates is a fundamental problem in designing quantum circuits.In this dissertation, the problem involved in synthesizing minimal quantum circuits for carrying out any (large) quantum operation is described.The author considers two quantum systems, namely, the two-level quantum system and the d-level quantum system, where d is any integer greater than two.Here, the two-level quantum system can be regarded as a quantum mechanical analogue of conventional computation, and the d-level quantum system can be regarded as a quantum mechanical analogue of conventional multilevel logic.