Norio Konno, Kenichi Mitsuda, Takahiro Soshi, Hyun Jae Yoo
We investigate a connection between a property of the distribution and a conserved quantity for the reversible cellular automaton derived from a discrete-time quantum walk in one dimension. As a corollary, we give a detailed information of the quantum walk.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We provide an introduction to Quantum Cellular Automata.
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 implementation of Wolfram's cellular automata Rule 110, which has previously been shown to be a universal Turing machine, as a QUBO suitable for use on quantum annealing systems. We demonstrate back-propagation of cellular automata rule sets to determine initial cell states for a desired later system state. We show 2-D 2-color cellular automata, such as Conway's Game…
We provide algebraic criteria for the unitarity of linear quantum cellular automata, i.e. one dimensional quantum cellular automata. We derive these both by direct combinatorial arguments, and by adding constraints into the model which do not change the quantum cellular automata's computational power. The configurations we consider have finite but unbounded size.
We define quantum cellular automata as infinite quantum lattice systems with discrete time dynamics, such that the time step commutes with lattice translations and has strictly finite propagation speed. In contrast to earlier definitions this allows us to give an explicit characterization of all local rules generating such automata. The same local rules also generate the global time step for automata with periodic boundary conditions. Our main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitar…
It is shown that irreversible classical cellular automata can be performed by quantum algorithm using additional ancilla registers. The algorithm for cellular automata states analysis has been proposed. This algorithm is based on the elements of Grover's algorithm - the inversion of amplitude of searched states and unitary transform of inversion about the average. The inversion of searched states amplitudes can be performed by quantum Toffoli gate.
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and effective list of rules. Here we investigate explicitly how coherence is built and lost in the evolution of one-dimensional automata subject to noise. Our analysis illustrates the interplay between unitary and noisy dynamics, and draws considerations on their behaviour in the pseudo-frequency domain.
We study reversible quantum cellular automata with the restriction that these are also Clifford operations. This means that tensor products of Pauli operators (or discrete Weyl operators) are mapped to tensor products of Pauli operators. Therefore Clifford quantum cellular automata are induced by symplectic cellular automata in phase space. We characterize these symplectic cellular automata and find that all possible local rules must be, up to some global shift, reflection invariant with respect to the origin. In the one dimensional case we also find that every uniquely determined and translat…
Studies of quantum computer implementations suggest cellular quantum computer architectures. These architectures can simulate the evolution of quantum cellular automata, which can possibly simulate both quantum and classical physical systems and processes. It is however known that except for the trivial case, unitary evolution of one-dimensional homogeneous quantum cellular automata with one qubit per cell is not possible. Quantum cellular automata that comprise two qubits per cell are defined and their evolution is studied using a quantum computer simulator. The evolution is unitary and its l…
Motivated by the recent work of Patel et al., this paper clarifies a connection between coined quantum walks and quantum cellular automata in a general setting. As a consequence, their result is naturally derived from the connection.
To study relationship between quantum finite automata and probabilistic finite automata, we introduce a notion of probabilistic reversible automata (PRA, or doubly stochastic automata). We find that there is a strong relationship between different possible models of PRA and corresponding models of quantum finite automata. We also propose a classification of reversible finite 1-way automata.
We study the recognition of R-trivial idempotent (R1) languages by various models of "decide-and-halt" quantum finite automata (QFA) and probabilistic reversible automata (DH-PRA). We introduce bistochastic QFA (MM-BQFA), a model which generalizes both Nayak's enhanced QFA and DH-PRA. We apply tools from algebraic automata theory and systems of linear inequalities to give a complete characterization of R1 languages recognized by all these models. We also find that "forbidden constructions" known so far do not include all of the languages that cannot be recognized by measure-many QFA.
Quantum Circuits for Elementary Cellular Automata
该研究确定了22条可通过量子电路模拟的初等元胞自动机规则，且为每条规则设计了门数为O(N)的量子实现电路。
We apply the methods of lattice field theories to the quantization of cellular automata. We discuss the quantization of five main categories of cellular automata: bosonic, fermionic, supersymmetric, spin and quantum dot using path integral and operator formalisms of lattice field theories. We show that the quantization of supersymmetric cellular automata is related to recently discussed string bit models of Thorn and Bergman and represents a link of cellular automata theory to fundamental physics. We discuss spin and quantum dot cellular automata for their importance in experimental realizatio…
Gauge-invariance is a fundamental concept in Physics -- known to provide mathematical justification for the fundamental forces. In this paper, we provide discrete counterparts to the main gauge theoretical concepts directly in terms of Cellular Automata. More precisely, the notions of gauge-invariance and gauge-equivalence in Cellular Automata are formalized. A step-by-step gauging procedure to enforce this symmetry upon a given Cellular Automaton is developed, and three examples of gauge-invariant Cellular Automata are examined.
We examine the characteristic features of reversible and quantum computations in the presence of supplementary external information, known as advice. In particular, we present a simple, algebraic characterization of languages recognized by one-way reversible finite automata augmented with deterministic advice. With a further elaborate argument, we prove a similar but slightly weaker result for bounded-error one-way quantum finite automata with advice. Immediate applications of those properties lead to containments and separations among various language families when they are assisted by approp…
Reversible Cellular Automata (RCA) are a physics-like model of computation consisting of an array of identical cells, evolving in discrete time steps by iterating a global evolution G. Further, G is required to be shift-invariant (it acts the same everywhere), causal (information cannot be transmitted faster than some fixed number of cells per time step), and reversible (it has an inverse which verifies the same requirements). An important, though only recently studied special case is that of Time-symmetric Cellular Automata (TSCA), for which G and its inverse are related via a local operation…
Very much as its classical counterpart, quantum cellular automata are expected to be a great tool for simulating complex quantum systems. Here we introduce a partitioned model of quantum cellular automata and show how it can simulate, with the same amount of resources (in terms of effective Hilbert space dimension), various models of quantum walks. All the algorithms developed within quantum walk models are thus directly inherited by the quantum cellular automata. The latter, however, has its structure based on local interactions between qubits, and as such it can be more suitable for present …
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。