STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
SIAM Journal on Computing
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Strengths and Weaknesses of Quantum Computing
SIAM Journal on Computing
SIAM Journal on Computing
On Quantum Computation with Some Restricted Amplitudes
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Halting of Quantum Turing Machines
UMC '02 Proceedings of the Third International Conference on Unconventional Models of Computation
Polynomial time quantum computation with advice
Information Processing Letters
Quantum branching programs and space-bounded nonuniform quantum complexity
Theoretical Computer Science
Classically controlled quantum computation
Mathematical Structures in Computer Science
Uniformity of quantum circuit families for error-free algorithms
Theoretical Computer Science
ACM SIGACT News
On generalized quantum turing machine and its language classes
MATH'07 Proceedings of the 11th WSEAS International Conference on Applied Mathematics
Quantum Information Processing
On a measurement-free quantum lambda calculus with classical control
Mathematical Structures in Computer Science
Quantum implicit computational complexity
Theoretical Computer Science
Hi-index | 5.23 |
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 efficiently simulating multi-tape QTMs. 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 to one another as computing models implementing not only Monte Carlo algorithms but also exact (or error-free) ones