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Local Transition Functions of Quantum Turing Machines
[article]

2000
*
arXiv
*
pre-print

According to Deutsch's formulation, the time evolution

arXiv:quant-ph/9811069v2
fatcat:xdzzddd6ybdirh3sqsvmnn53i4
*of*a*quantum**Turing**machine*is to be determined by the*local**transition**function*. ... In this paper, the*local**transition**functions*are characterized for fully general*quantum**Turing**machines*, including multi-tape*quantum**Turing**machines*, extending the results due to Bernstein and Vazirani ... In Section 5, we will also characterize the*local**transition**functions**of*multi-tape*quantum**Turing**machines*. ...##
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Local Transition Functions of Quantum Turing Machines

2000
*
RAIRO - Theoretical Informatics and Applications
*

According to Deutsch's formulation, the time evolution

doi:10.1051/ita:2000123
fatcat:gsrrdoubizeptolnnufofgafr4
*of*a*quantum**Turing**machine*is to be determined by the*local**transition**function*. ... In this paper, the*local**transition**functions*are characterized for fully general*quantum**Turing**machines*, including multi-tape*quantum**Turing**machines*, extending an earlier attempt due to Bernstein and ... . , m} in the set*of*integers. We call δ the*local**transition**function**of*the*quantum**Turing**machine*Q. ...##
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Some relations between quantum Turing machines and Turing machines
[article]

1999
*
arXiv
*
pre-print

For

arXiv:quant-ph/9912012v2
fatcat:j2tndcdrynavllppx3ua4igyii
*quantum**Turing**machines*we present three elements: Its components, its time evolution operator and its*local**transition**function*. ... The components are related with the components*of*deterministic*Turing**machines*, the time evolution operator is related with the evolution*of*reversible*Turing**machines*and the*local**transition**function*... Introduction First time, David Deutsch [2] described*quantum*TM (*Turing**machine*), he said the computational power*of*a*quantum*TM and an classical (deterministic) one are the same for*functions*from ...##
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A Relative Church-Turing-Deutsch Thesis from Special Relativity and Undecidability
[article]

2022
*
arXiv
*
pre-print

In this work, we construct a relative model

arXiv:2206.06419v1
fatcat:sfc5r3xz65dedjb5a6pzqs2vtm
*of*computation where a computable*local**machine*is simulated by a global, classical*Turing**machine*. ...*quantum*mechanics for a*local**machine*with the same constant-time*local*computational complexity as experienced in our universe. ... So, the perception*of**local*time is at every instance*of*the*transition**function*and only at the*transition**function*. ...##
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Quantum Turing Machines: Local Transition, Preparation, Measurement, and Halting
[article]

1998
*
arXiv
*
pre-print

The

arXiv:quant-ph/9809038v1
fatcat:xs7tk7mpt5e3dpdzw5btazrgeq
*local**transition**functions*are characterized for fully general*quantum**Turing**machines*. ... Foundations*of*the theory*of**quantum**Turing**machines*are investigated. The protocol for the preparation and the measurement*of**quantum**Turing**machines*is discussed. ... The characterization*of*the*transition**functions**of**quantum**Turing**machines*is also discussed. Deutsch 5 required that the*transition**function*should be determined by*local*configurations. ...##
###
Revisiting the simulation of quantum Turing machines by quantum circuits
[article]

2018
*
arXiv
*
pre-print

Yao (1993) proved that

arXiv:1808.01701v1
fatcat:3crjlka52zcj3ihyhk54o7s22m
*quantum**Turing**machines*and uniformly generated*quantum*circuits are polynomially equivalent computational models: t ≥ n steps*of*a*quantum**Turing**machine*running on an input*of*... This analysis reveals that the simulation*of**quantum**Turing**machines*can be performed by*quantum*circuits having depth linear in t, rather than quadratic depth, and can be extended to variants*of**quantum*... Not all*transition**functions**of*this form describe valid*quantum**Turing**machines*; only those*transition**functions*that induce global unitary evolutions, to be discussed shortly, are valid. ...##
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Revisiting the simulation of quantum Turing machines by quantum circuits

2019
*
Proceedings of the Royal Society A
*

Yao's 1995 publication '

doi:10.1098/rspa.2018.0767
pmid:31293355
pmcid:PMC6598068
fatcat:yruhzdqwoffg3pbctqi5gze5ni
*Quantum*circuit complexity' in Proceedings*of*the 34th Annual IEEE Symposium on Foundations*of*Computer Science, pp. 352-361, proved that*quantum**Turing**machines*and*quantum*circuits ... in t, and a polynomial-time uniformly generated family*of**quantum*circuits can be simulated by a*quantum**Turing**machine*running in polynomial time. ... Not all*transition**functions**of*this form describe valid*quantum**Turing**machines*; only those*transition**functions*that induce global unitary evolutions, to be discussed shortly, are valid. ...##
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Halting of Quantum Turing Machines
[chapter]

2002
*
Lecture Notes in Computer Science
*

Foundations

doi:10.1007/3-540-45833-6_6
fatcat:u5grwj2wyva47aakptn5jcbqva
*of*the theory*of**quantum**Turing**machines*are investigated. The*local**transition**functions*are characterized for fully general*quantum**Turing**machines*. ... Foundational problems on the preparation and the measurement*of**quantum**Turing**machines*are discussed. ... Section 3 discusses the characterization*of*the*transition**functions**of**quantum**Turing**machines*. Deutsch [5] required that the*transition**function*should be determined by*local*configurations. ...##
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On the Universality of Memcomputing Machines

2018
*
IEEE Transactions on Neural Networks and Learning Systems
*

UMMs have been shown to be

doi:10.1109/tnnls.2018.2872676
fatcat:uoudhhq74raybe6atpf5zkeghy
*Turing*-complete, namely they can simulate any*Turing**machine*. ... We show that UMMs can simulate both types*of**machines*, hence they are both "liquid-" or "reservoir-complete" and "*quantum*-complete". ... The difference between the "possible" and "actual"*transition**functions*will be formalized in section IV-C. 2)*Turing**Machine*as Example: For a*Turing**machine*, after the*machine*is coded, the*transition*...##
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Turing machines based on unsharp quantum logic

2012
*
Electronic Proceedings in Theoretical Computer Science
*

In this paper, we consider

doi:10.4204/eptcs.95.17
fatcat:doo7m5bfafa4vntax2ubv4jkuq
*Turing**machines*based on unsharp*quantum*logic. ... For a lattice-ordered*quantum*multiple-valued (MV) algebra E, we introduce E-valued non-deterministic*Turing**machines*(ENTMs) and E-valued deterministic*Turing**machines*(EDTMs). ... Deutsch proposed*quantum**Turing**machines*from a*quantum*mechanics point*of*view [2] and Perdrix generalized this to observable*quantum**Turing**machines*[10] . ...##
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Theory of quantum computation
[article]

2000
*
arXiv
*
pre-print

Short review article on

arXiv:quant-ph/0010057v1
fatcat:dtfszyoygbbydc5dtqljv4bp44
*quantum*computation accepted for Supplement III, Encyclopaedia*of*Mathematics (publication expected Summer 2001). See also http://www.wkap.nl/series.htm/ENM ... Thus the*functions*computable by*quantum**Turing**machines*are the same as those computable by classical*Turing**machines*. Article by E. H. Knill and M. A. ... In particular, for formal studies*of*complexity, many researchers use various versions*of**quantum**Turing**machines*, while*quantum*random access*machines*or*quantum*networks (also known as*quantum*circuits ...##
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Size-driven quantum phase transitions

2017
*
Proceedings of the National Academy of Sciences of the United States of America
*

The resulting effect may be viewed as a new type

doi:10.1073/pnas.1705042114
pmid:29259107
pmcid:PMC5776787
fatcat:n5kdwzdj5rgutcuahumc2unweq
*of**quantum*phase*transition*that is driven by the size*of*the system rather than by an external field or coupling strength. ... Starting from a minimal case with spins*of*dimension 6 and threshold lattice size 15 x 15, we show that the latter grows faster than any computable*function*with increasing*local*spin dimension. ... The*transition*threshold N d = Nc+2 for this model is thus given simply by the horizontal pattern period.*Turing**Machine*Tiling. ...##
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Determining acceptance possibility for a quantum computation is hard for the polynomial hierarchy

1999
*
Proceedings of the Royal Society A
*

value at the end

doi:10.1098/rspa.1999.0485
fatcat:jhzu3u4kyvf2dptulz3p4gvyn4
*of*a*quantum*computation. ... This result is achieved by showing that the complexity class NQP*of*Adleman, Demarrais, and Huang 1], a*quantum*analog*of*NP, is equal to the counting class coC = P. ... The work*of*S. Homer was supported in part by the NSF under grant NSF-CCR-94-00229. The work*of*R. Pruim was done while visiting the Computer Science Department at Boston University. W e thank C. ...##
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Quantum circuit design for universal distribution using a superposition of classical automata
[article]

2022
*
arXiv
*
pre-print

The precise

arXiv:2006.00987v2
fatcat:ga7lgbhrdnctnecg3oayhi367a
*quantum*circuit design that allows executing a superposition*of*programs, along with a superposition*of*inputs as in the standard*quantum**Turing**machine*formulation, is presented. ... This is the first time, a superposition*of*classical automata is implemented on the circuit model*of**quantum*computation, having the corresponding mechanistic parts*of*a classical*Turing**machine*. ... QTM that exhibit*local*causal behavior can be mapped to such a*transition**function*. ...##
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Universality and programmability of quantum computers
[article]

2007
*
arXiv
*
pre-print

Much

arXiv:0710.3329v2
fatcat:5o7tvnl25nepraohyo3wcp75ye
*of*the writing about*quantum*logic circuits and*quantum**Turing**machines*has shown how these*machines*can simulate an arbitrary unitary transformation on a finite number*of*qubits. ...*Quantum**Turing**machines*form a class closely related to deterministic and probabilistic*Turing**machines*and one might hope to find a universal*machine*in this class. ... A TM has a finite list*of*instructions, or*transition*rules, describing its operation. There is at most one*transition*rule for each combination*of*cell content ...
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