Related papers: Quantum Circuits for Elementary Cellular Automata
In this paper we present a systematic view of Quantum Cellular Automata (QCA), a mathematical formalism of quantum computation. First we give a general mathematical framework with which to study QCA models. Then we present four different…
Quantum-dot fabrication and characterization is a well-established technology, which is used in photonics, quantum optics and nanoelectronics. Four quantum-dots placed at the corners of a square form a unit cell, which can hold a bit of…
Suppose that a quantum circuit with K elementary gates is known for a unitary matrix U, and assume that U^m is a scalar matrix for some positive integer m. We show that a function of U can be realized on a quantum computer with at most…
We propose an architecture based on Quantum cellular Automata which allows the use of only one type of quantum gates per computational step in order to perform nearest neighbor interactions. The model is built in partial steps, each one of…
We introduce the first complete equational theory for quantum circuits. More precisely, we introduce a set of circuit equations that we prove to be sound and complete: two circuits represent the same unitary map if and only if they can be…
Constructing general programmable circuits to be able to run any given unitary operator efficiently on a quantum processor is of fundamental importance. We present a new quantum circuit design technique resulting two general programmable…
Linear quantum cellular automata were introduced recently as one of the models of quantum computing. A basic postulate of quantum mechanics imposes a strong constraint on any quantum machine: it has to be unitary, that is its time evolution…
We present herein an introduction to implementing 2-color cellular automata on quantum annealing systems, such as the D-Wave quantum computer. We show that implementing nearest-neighbor cellular automata is possible. We present an…
We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one…
In this paper, we will introduce the quantum circuit simulator we developed in C++ environment. We devise a novel method for efficient memory handling using linked list structures that enables us to simulate a quantum circuit of up to 20…
Quantum algorithms and protocols are often presented as quantum circuits for a better understanding. We give a list of equivalence rules which can help in the analysis and design of quantum circuits. As example applications we study quantum…
In this work, we provide an overview of circuits for quantum computing. We introduce gates used in quantum computation and then present resource cost measurements used to evaluate circuits made from these gates. We then illustrate how the…
We study the implementation of quantum channels with quantum computers while minimizing the experimental cost, measured in terms of the number of Controlled-NOT (C-NOT) gates required (single-qubit gates are free). We consider three…
Number-conserving cellular automata are discrete dynamical systems that simulate interacting particles like e.g. grains of sand. In an earlier paper, I had already derived a uniform construction for all transition rules of one-dimensional…
We give a one-dimensional quantum cellular automaton (QCA) capable of simulating all others. By this we mean that the initial configuration and the local transition rule of any one-dimensional QCA can be encoded within the initial…
Construction of explicit quantum circuits follows the notion of the "standard circuit model" introduced in the solid and profound analysis of elementary gates providing quantum computation. Nevertheless the model is not always optimal (e.g.…
This paper describes a novel approach to emulate a universal quantum computer with a wholly classical system, one that uses a signal of bounded duration and amplitude to represent an arbitrary quantum state. The signal may be of any…
Efficient simulation of quantum computers is essential for the development and validation of near-term quantum devices and the research on quantum algorithms. Up to date, two main approaches to simulation were in use, based on either full…
In this work, we develop a method to use Quantum- Dot Cellular Automata (QCA) for universal quantum computing. This method is based conceptually on refocusing in NMR systems. We show how an array of QCA cells can be used for isolated single…
We identify a broad class of physical processes in an optical quantum circuit that can be efficiently simulated on a classical computer: this class includes unitary transformations, amplification, noise, and measurements. This…