Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines

Details Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines

1999-06-25

arxiv.org/abs/quant-ph/9906095v3

Theor.Comput.Sci. 276 (2002) 147-181

Physics

Quantum Physics

34 pages, LaTeX, revised and extended, to appear in Theoret. Comput. Sci

Scientific paper

Deutsch proposed two sorts of models of quantum computers, quantum Turing machines (QTMs) and quantum circuit families (QCFs). In this paper we explore the computational powers of these models and re-examine the claim of the computational equivalence of these models often made in the literature without detailed investigations. For this purpose, we formulate the notion of the codes of QCFs and the uniformity of QCFs by the computability of the codes. Various complexity classes are introduced for QTMs and QCFs according to constraints on the error probability of algorithms or transition amplitudes. Their interrelations are examined in detail. For Monte Carlo algorithms, it is proved that the complexity classes based on uniform QCFs are identical with the corresponding classes based on QTMs. However, for Las Vegas algorithms, it is still open whether the two models are equivalent. We indicate the possibility that they are not equivalent. In addition, we give a complete proof of the existence of a universal QTM simulating multi-tape QTMs efficiently. We also examine the simulation of various types of QTMs such as multi-tape QTMs, single tape QTMs, stationary, normal form QTMs (SNQTMs), and QTMs with the binary tapes. As a result, we show that these QTMs are computationally equivalent one another as computing models implementing not only Monte Carlo algorithms but exact (or error-free) ones.

Affiliated with

Also associated with

No associations

Rating

Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Computational Complexity of Uniform Quantum Circuit Families and Quantum Turing Machines will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-508246