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}
}
  • J. Watrous
  • Published 1995
  • Mathematics, Computer Science
  • Proceedings of IEEE 36th Annual Foundations of Computer Science
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… Expand
View on IEEE
cs.uwaterloo.ca
170 Citations
Highly Influential Citations
8
Background Citations
63
Methods Citations
31
Results Citations
2

170 Citations

Citation Type

Citation Type

An Introduction to Quantum Cellular Automata
Computer scientists have invented a plethora of fascinating machines to study. They are called computational models, and they come in many strange and varied shapes: Turing machines, register… Expand
A Decision Procedure for Unitary Linear Quantum Cellular Automata
TLDR
An efficient algorithm to decide if a linear quantum cellular automaton is unitary is given and the complexity of the algorithm is O(n(3r-1)/(r+1) = O( n3) in the algebraic computational model if the automaton has a continuous neighborhood of size r, where n is the size of the input. Expand
A universal quantum cellular automaton
We will prove the existence of a universal quantum cellular automaton. Such qca are defined as the quantum-mechanical pendant of classical one-dimensional cellular automata. As is the case with… Expand
An overview of quantum computation models: quantum automata
TLDR
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. Expand
Reversible quantum cellular automata
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… Expand
WHEN IS A QUANTUM CELLULAR AUTOMATON A QUANTUM LATTICE GAS AUTOMATON
Quantum cellular automata (QCA) are models of quantum computation of particular interest from the point of view of quantum simulation. Quantum lattice gas automata (QLGA - equivalently partitioned… Expand
A decision procedure for unitary linear quantum cellular automata
  • C. Dürr, M. Santha
  • Mathematics, Computer Science
  • Proceedings of 37th Conference on Foundations of Computer Science
  • 1996
TLDR
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. Expand
An overview of quantum cellular automata
  • P. Arrighi
  • Physics, Computer Science
  • Natural Computing
  • 2019
TLDR
An overview of quantum cellular automata theory is given, with particular focus on structure results; computability and universality results; and quantum simulation results. Expand
Reversibility and quantum coherence in one-dimensional quantum cellular automata
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… Expand
Discrete Time Quantum Lattice Systems
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… Expand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 12 REFERENCES
Quantum complexity theory
TLDR
This dissertation proves that relative to an oracle chosen uniformly at random, the class NP cannot be solved on a quantum Turing machine in time $o(2\sp{n/2}).$ and gives evidence suggesting that quantum Turing Machines cannot efficiently solve all of NP. Expand
Computation universality of one-dimensional reversible (injective) cellular automata
A reversible cellular automaton (CA) is a "backward deterministic" CA, i. e_, every configuration of it has at most one predecessor. Toffoli showed that a two-dimensional reversible cellular… Expand
Quantum theory, the Church–Turing principle and the universal quantum computer
  • D. Deutsch
  • Mathematics
  • Proceedings 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… Expand
Quantum Circuit Complexity
  • A. Yao
  • Mathematics, Computer Science
  • FOCS
  • 1993
TLDR
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. Expand
Algorithms for quantum computation: discrete logarithms and factoring
  • P. Shor
  • Mathematics, Computer Science
  • Proceedings 35th Annual Symposium on Foundations of Computer Science
  • 1994
TLDR
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. Expand
The Quantum Theory
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,… Expand
Simulating physics with computers
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… Expand
Quantum Circuit Complexity , Proc . 34 thAnn
  • Quantum Complexity Theory , Proc . 25 th Ann . ACM Symp . on Theory of Computing
  • 1993
An introduction to hilbert space
A n Introduction to Hilbert Space, Canibridge
  • 1988
...
1
2
...