Synthesis of Quantum Logic Circuits

We discuss efficient quantum logic circuits which perform two tasks: (i) implementing generic quantum computations and (ii) initializing quantum registers. In contrast to conventional computing, the latter task is nontrivial because the state-space of an n-qubit register is not finite and contains exponential superpositions of classical bit strings. Our proposed circuits are asymptotically optimal for respective tasks and improve published results by at least a factor of two. The circuits for generic quantum computation constructed by our algorithms are the most efficient known today in terms of the number of expensive gates (quantum controlled-NOTs). They are based on an analogue of the Shannon decomposition of Boolean functions and a new circuit block, quantum multiplexor, that generalizes several known constructions. A theoretical lower bound implies that our circuits cannot be improved by more than a factor of two. We additionally show how to accommodate the severe architectural limitation of using only nearest-neighbor gates that is representative of current implementation technologies. This increases the number of gates by almost an order of magnitude, but preserves the asymptotic optimality of gate counts.Comment: 18 pages; v5 fixes minor bugs; v4 is a complete rewrite of v3, with 6x more content, a theory of quantum multiplexors and Quantum Shannon Decomposition. A key result on generic circuit synthesis has been improved to ~23/48*4^n CNOTs for n qubit

Quantum Circuits for General Multiqubit Gates

We consider a generic elementary gate sequence which is needed to implement a general quantum gate acting on n qubits -- a unitary transformation with 4^n degrees of freedom. For synthesizing the gate sequence, a method based on the so-called cosine-sine matrix decomposition is presented. The result is optimal in the number of elementary one-qubit gates, 4^n, and scales more favorably than the previously reported decompositions requiring 4^n-2^n+1 controlled NOT gates.Comment: 4 pages, 3 figure

QudCom: Towards Quantum Compilation for Qudit Systems

Qudit-based quantum computation offers unique advantages over qubit-based systems in terms of noise mitigation capabilities as well as algorithmic complexity improvements. However, the software ecosystem for multi-state quantum systems is severely limited. In this paper, we highlight a quantum workflow for describing and compiling qudit systems. We investigate the design and implementation of a quantum compiler for qudit systems. We also explore several key theoretical properties of qudit computing as well as efficient optimization techniques. Finally, we provide demonstrations using physical quantum computers as well as simulations of the proposed quantum toolchain

Quantum Multiplexers, Parrondo Games, and Proper Quantization

A quantum logic gate of particular interest to both electrical engineers and game theorists is the quantum multiplexer. This shared interest is due to the facts that an arbitrary quantum logic gate may be expressed, up to arbitrary accuracy, via a circuit consisting entirely of variations of the quantum multiplexer, and that certain one player games, the history dependent Parrondo games, can be quantized as games via a particular variation of the quantum multiplexer. However, to date all such quantizations have lacked a certain fundamental game theoretic property. The main result in this dissertation is the development of quantizations of history dependent quantum Parrondo games that satisfy this fundamental game theoretic property. Our approach also yields fresh insight as to what should be considered as the proper quantum analogue of a classical Markov process and gives the first game theoretic measures of multiplexer behavior.Comment: Doctoral dissertation, Portland State University, 138 pages, 22 figure