A fast quantum mechanical algorithm for database search
STOC '96 Proceedings of the twenty-eighth 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
SIAM Journal on Computing
Complexity limitations on Quantum computation
Journal of Computer and System Sciences
Parallelization, amplification, and exponential time simulation of quantum interactive proof systems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Quantum computation and quantum information
Quantum computation and quantum information
Computational complexity of uniform quantum circuit families and quantum Turing machines
Theoretical Computer Science
An improved quantum Fourier transform algorithm and applications
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Fast parallel circuits for the quantum Fourier transform
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Fault-tolerant quantum computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Quantum Information Processing
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In order to establish the computational equivalence between quantum Turing machines (QTMs) and quantum circuit families (QCFs) using Yao's quantum circuit simulation of QTMs, we have previously introduced the class of uniform QCFs based on an infinite set of elementary gates, which has been shown to be computationally equivalent to polynomial-time QTMs up to bounded error simulation. However, the complexity classes ZQP and EQP introduced by Bernstein and Vazirani for QTMs do not appear to equal their counterparts for uniform QCFs. Recently, we have introduced a subclass of uniform QCFs, the class of finitely generated uniform QCFs, and showed that they are perfectly equivalent to the class of polynomial-time QTMs in the sense that both classes can be exactly simulated with each other. Here, we further investigate the power of uniform QCFs comparing with that of finitely generated uniform QCFs in detail. We obtain the following results: (i) If a permutation Mf: |x)〉 ↦ |f(x)〉 can be implemented with zero error by a uniform QCF, then both f and f-1 can be exactly computed by uniform QCFs. (ii) The quantum Fourier transform (QFT) of any order cannot be implemented with zero error by any finitely generated uniform QCF, while it has been shown, in contrast, by Mosca and Zalka that the QFT of any order can be exactly implemented by a uniform QCF.