On one-dimensional quantum cellular automata
@article{Watrous1995OnOQ,
title={On one-dimensional quantum cellular automata},
author={John Watrous},
journal={Proceedings of IEEE 36th Annual Foundations of Computer Science},
year={1995},
pages={528-537}
}Since Richard Feynman introduced the notion of quantum computation in 1982, various models of "quantum computers" have been proposed (R. Feynman, 1992). These models include quantum Turing machines and quantum circuits. We define another quantum computational model, one dimensional quantum cellular automata, and demonstrate that any quantum Turing machine can be efficiently simulated by a one dimensional quantum cellular automaton with constant slowdown. This can be accomplished by…
170 Citations
An Introduction to Quantum Cellular Automata
- Physics, Computer Science
- 2008
The quantum cellular automaton (QCA) is discussed, a model which is exciting not only for its simple and elegant structure, but also for its “physical” flavor.
A universal quantum cellular automaton
- Computer Science
- 2004
It is shown that every proper qca obeys a local constraint which is comparable with the ‘inverse neighborhood’ of classical reversible cellular automata, which allows us to describe every qca as a periodic quantum gate array, which can be simulated (with a bounded error) by a universal automaton U.
An overview of quantum computation models: quantum automata
- Computer ScienceFrontiers of Computer Science in China
- 2008
A basic progress in the research on quantum automata is outlined, focusing on QFA, QSM, QPDA, QTM, and orthomodular lattice-valued automata, and a number of problems to be studied in future are addressed.
Reversible quantum cellular automata
- Computer Science
- 2004
The main structure theorem asserts that any quantum cellular automaton is structurally reversible, i.e., that it can be obtained by applying two blockwise unitary operations in a generalized Margolus partitioning scheme.
WHEN IS A QUANTUM CELLULAR AUTOMATON A QUANTUM LATTICE GAS AUTOMATON
- Computer Science
- 2012
It is established necessary and sufficient conditions for unbounded, finite Quantum Cellular Automata (QCA) (finitely many active cells in a quiescent background) to be Quantum Lattice Gas Automata.
An overview of quantum cellular automata
- Computer ScienceNatural Computing
- 2019
An overview of quantum cellular automata theory is given, with particular focus on structure results; computability and universality results; and quantum simulation results.
A Decision Procedure for Unitary Linear Quantum Cellular Automata
- Computer ScienceSIAM J. Comput.
- 2002
An efficient algorithm to decide if a linear quantum cellular automaton is unitary is given and the complexity of the algorithm is O(n(4r-3)/(r+1))=O(n/sup 4/) if the automaton has a continuous neighborhood of size r.
Reversibility and quantum coherence in one-dimensional quantum cellular automata
- PhysicsPhysical Review A
- 2018
Quantum cellular automata are important tools in understanding quantum dynamics, thanks to their simple and
effective list of rules. Here we consider a class of noisy, one-dimensional quantum…
Discrete Time Quantum Lattice Systems
- Physics
- 2009
Discrete time quantum lattice systems recently have come into the focus of quantum computation because they provide a versatile tool for many different applications and they are potentially…
Quantum walks via quantum cellular automata
- Physics, Computer ScienceQuantum Inf. Process.
- 2018
A partitioned model of quantum cellular automata is introduced and it is shown how it can simulate, with the same amount of resources, various models of quantum walks.
References
SHOWING 1-10 OF 12 REFERENCES
Quantum complexity theory
- Computer ScienceSTOC '93
- 1993
This paper gives the first formal evidence that quantum Turing machines violate the modern (complexity theoretic) formulation of the Church--Turing thesis, and proves that bits of precision suffice to support a step computation.
Computation universality of one-dimensional reversible (injective) cellular automata
- Computer Science
- 1989
This paper gives a construction method of a reversible CA which simulates a given 1-tape reversible Turing machine and introduces a "one-dimensional partitioned cellular automaton" (1-PCA), which has the property that the local reversibility is equivalent to the global reversibility.
Quantum theory, the Church–Turing principle and the universal quantum computer
- Physics, PhilosophyProceedings of the Royal Society of London. A. Mathematical and Physical Sciences
- 1985
It is argued that underlying the Church–Turing hypothesis there is an implicit physical assertion. Here, this assertion is presented explicitly as a physical principle: ‘every finitely realizible…
Quantum Circuit Complexity
- Computer ScienceFOCS
- 1993
It is shown that any function computable in polynomial time by a quantum Turing machine has aPolynomial-size quantum circuit, and this result enables us to construct a universal quantum computer which can simulate a broader class of quantum machines than that considered by E. Bernstein and U. Vazirani (1993), thus answering an open question raised by them.
Algorithms for quantum computation: discrete logarithms and factoring
- Computer ScienceProceedings 35th Annual Symposium on Foundations of Computer Science
- 1994
Las Vegas algorithms for finding discrete logarithms and factoring integers on a quantum computer that take a number of steps which is polynomial in the input size, e.g., the number of digits of the integer to be factored are given.
The Quantum Theory
- PhysicsNature
- 1928
IN a lecture on the quantum theory it might be thought fitting to commence with a clear explanation of the purpose, nature, and scope of the subject; but an attempt to answer briefly the question,…
Simulating physics with computers
- Education, Physics
- 1982
On the program it says this is a keynote speech--and I don't know what a keynote speech is. I do not intend in any way to suggest what should be in this meeting as a keynote of the subjects or…
A n Introduction to Hilbert Space, Canibridge
- 1988