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Local Transition Functions of Quantum Turing Machines [article]

Masanao Ozawa, Harumichi Nishimura
2000 arXiv   pre-print
According to Deutsch's formulation, the time evolution 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.  ... 
arXiv:quant-ph/9811069v2 fatcat:xdzzddd6ybdirh3sqsvmnn53i4

Local Transition Functions of Quantum Turing Machines

Masanao Ozawa, Harumichi Nishimura
2000 RAIRO - Theoretical Informatics and Applications  
According to Deutsch's formulation, the time evolution 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.  ... 
doi:10.1051/ita:2000123 fatcat:gsrrdoubizeptolnnufofgafr4

Some relations between quantum Turing machines and Turing machines [article]

Andrés Sicard, Mario Vélez
1999 arXiv   pre-print
For 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  ... 
arXiv:quant-ph/9912012v2 fatcat:j2tndcdrynavllppx3ua4igyii

A Relative Church-Turing-Deutsch Thesis from Special Relativity and Undecidability [article]

Blake Wilson, Ethan Dickey, Vaishnavi Iyer, Sabre Kais
2022 arXiv   pre-print
In this work, we construct a relative model 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.  ... 
arXiv:2206.06419v1 fatcat:sfc5r3xz65dedjb5a6pzqs2vtm

Quantum Turing Machines: Local Transition, Preparation, Measurement, and Halting [article]

Masanao Ozawa
1998 arXiv   pre-print
The 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.  ... 
arXiv:quant-ph/9809038v1 fatcat:xs7tk7mpt5e3dpdzw5btazrgeq

Revisiting the simulation of quantum Turing machines by quantum circuits [article]

Abel Molina, John Watrous
2018 arXiv   pre-print
Yao (1993) proved that 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.  ... 
arXiv:1808.01701v1 fatcat:3crjlka52zcj3ihyhk54o7s22m

Revisiting the simulation of quantum Turing machines by quantum circuits

Abel Molina, John Watrous
2019 Proceedings of the Royal Society A  
Yao's 1995 publication '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.  ... 
doi:10.1098/rspa.2018.0767 pmid:31293355 pmcid:PMC6598068 fatcat:yruhzdqwoffg3pbctqi5gze5ni

Halting of Quantum Turing Machines [chapter]

Masanao Ozawa
2002 Lecture Notes in Computer Science  
Foundations 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.  ... 
doi:10.1007/3-540-45833-6_6 fatcat:u5grwj2wyva47aakptn5jcbqva

On the Universality of Memcomputing Machines

Yan Ru Pei, Fabio L. Traversa, Massimiliano Di Ventra
2018 IEEE Transactions on Neural Networks and Learning Systems  
UMMs have been shown to be 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  ... 
doi:10.1109/tnnls.2018.2872676 fatcat:uoudhhq74raybe6atpf5zkeghy

Turing machines based on unsharp quantum logic

Yun Shang, Xian Lu, Ruqian Lu
2012 Electronic Proceedings in Theoretical Computer Science  
In this paper, we consider 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] .  ... 
doi:10.4204/eptcs.95.17 fatcat:doo7m5bfafa4vntax2ubv4jkuq

Theory of quantum computation [article]

E. H. Knill, M. A. Nielsen
2000 arXiv   pre-print
Short review article on 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  ... 
arXiv:quant-ph/0010057v1 fatcat:dtfszyoygbbydc5dtqljv4bp44

Size-driven quantum phase transitions

Johannes Bausch, Toby S. Cubitt, Angelo Lucia, David Perez-Garcia, Michael M. Wolf
2017 Proceedings of the National Academy of Sciences of the United States of America  
The resulting effect may be viewed as a new type 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.  ... 
doi:10.1073/pnas.1705042114 pmid:29259107 pmcid:PMC5776787 fatcat:n5kdwzdj5rgutcuahumc2unweq

Determining acceptance possibility for a quantum computation is hard for the polynomial hierarchy

S. Fenner, F. Green, S. Homer, R. Pruim
1999 Proceedings of the Royal Society A  
value at the end 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.  ... 
doi:10.1098/rspa.1999.0485 fatcat:jhzu3u4kyvf2dptulz3p4gvyn4

Quantum circuit design for universal distribution using a superposition of classical automata [article]

Aritra Sarkar, Zaid Al-Ars, Koen Bertels
2022 arXiv   pre-print
The precise 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.  ... 
arXiv:2006.00987v2 fatcat:ga7lgbhrdnctnecg3oayhi367a

Universality and programmability of quantum computers [article]

Willem Fouche', Johannes Heidema, Glyn Jones, Petrus H. Potgieter
2007 arXiv   pre-print
Much 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  ... 
arXiv:0710.3329v2 fatcat:5o7tvnl25nepraohyo3wcp75ye
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