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Perfect computational equivalence between quantum turing machines and finitely generated uniform quantum circuit families
, 2008
"... 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 previously introduced the class of uniform QCFs based on an infinite set of elementary gates, which has been shown to be c ..."
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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 previously introduced the class of uniform QCFs based on an infinite set of elementary gates, which has been shown to be computationally equivalent to the polynomial-time QTMs (with appropriate restriction of amplitudes) up to bounded error simulation. This result implies that the complexity class BQP introduced by Bernstein and Vazirani for QTMs equals its counterpart for uniform QCFs. However, the complexity classes ZQP and EQP for QTMs do not appear to equal their counterparts for uniform QCFs. In this paper, we introduce a subclass of uniform QCFs, the finitely generated uniform QCFs, based on finite number of elementary gates and show that the class of finitely generated uniform QCFs is perfectly equivalent to the class of polynomial-time QTMs; they can exactly simulate each other. This naturally implies that BQP as well as ZQP and EQP equal the corresponding complexity classes of the finitely generated uniform QCFs. 1
Synthesis of quantum circuits in Linear Nearest Neighbor model using Positive Davio Lattices
, 2011
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Algorithmic Quantum Channel Simulation
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, 2015
"... Quantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations and applications of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been ..."
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Quantum simulation, which is generically the task to employ quantum computers to simulate quantum physical models, has been one of the most significant motivations and applications of quantum computing. Quantum dynamics, unitary or nonunitary Markovian dynamics driven by local interactions, has been proved to be efficiently simulatable on quantum computers. Extending the underlying models in quantum computation and quantum simulation from unitary to general nonunitary evolution, and from continuous-time to discrete-time evo-lution is essential not only for quantum simulation of more general processes, e.g., dissipative processes with evident non-Markovian effects, but also for developing alternative quantum computing models and algorithms. In this thesis, we explore quantum simulation problems mainly from the following three themes. First, we extend quantum simulation framework of Hamiltonian-driven evolution to quan-tum simulation of quantum channels, combined with the scheme of algorithmic simulation that accepts a promised simulation accuracy, hence algorithmic quantum channel simulation. Our simulation scheme contains a classical preprocessing part, i.e. a classical algorithm for
NTT Communication Science Laboratories, Nippon Telegraph and Telephone Corporation
, 2005
"... using KAK decompositions ..."
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NTT Communication Science Laboratories, NTT Corporation
, 2005
"... using KAK decompositions ..."
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