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Quantum Circuit Complexity
, 1993
"... We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum compu ..."
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Cited by 320 (1 self)
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We study a complexity model of quantum circuits analogous to the standard (acyclic) Boolean circuit model. It is shown that any function computable in polynomial time by a quantum Turing machine has a polynomialsize quantum circuit. This result also enables us to construct a universal quantum
Quantum circuits with mixed states
 in Proc. 30th STOC
, 1998
"... Current formal models for quantum computation deal only with unitary gates operating on “pure quantum states”. In these models it is difficult or impossible to deal formally with several central issues: measurements in the middle of the computation; decoherence and noise, using probabilistic subrout ..."
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Cited by 142 (7 self)
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subroutines, and more. It turns out, that the restriction to unitary gates and pure states is unnecessary. In this paper we generalize the formal model of quantum circuits to a model in which the state can be a general quantum state, namely a mixed state, or a “density matrix”, and the gates can be general
Parallelization of Restricted Quantum Circuits
"... Quantum circuits are proposed as a parallel model of quantum computation by Deutsch [3], in which computing devices, called quantum gates, are connected acyclicly. Here we are concerned with parallelization of quantum circuits by using ancillae (i.e., auxiliary quantum bits). By parallelization of q ..."
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Quantum circuits are proposed as a parallel model of quantum computation by Deutsch [3], in which computing devices, called quantum gates, are connected acyclicly. Here we are concerned with parallelization of quantum circuits by using ancillae (i.e., auxiliary quantum bits). By parallelization
Approximation by Quantum Circuits
 and 68Q9529 at http://www.c3.lanl.gov/laces, Los Alamos National Laboratory
, 1995
"... In a recent preprint by Deutsch et al. [5] the authors suggest the possibility of polynomial approximability of arbitrary unitary operations on n qubits by 2qubit unitary operations. We address that comment by proving strong lower bounds on the approximation capabilities of gqubit unitary operati ..."
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Cited by 39 (5 self)
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operations for fixed g. We consider approximation of unitary operations on subspaces as well as approximation of states and of density matrices by quantum circuits in several natural metrics. The ability of quantum circuits to probabilistically solve decision problem and guess checkable functions
Efficient quantum circuits for . . .
, 2002
"... We present two methods for the construction of quantum circuits for quantum errorcorrecting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit has ..."
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We present two methods for the construction of quantum circuits for quantum errorcorrecting codes (QECC). The underlying quantum systems are tensor products of subsystems (qudits) of equal dimension which is a prime power. For a QECC encoding k qudits into n qudits, the resulting quantum circuit
Automated Design of Quantum Circuits
, 1999
"... Abstract. In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of a sequence of quantum gate operations. To date, such designs have either been found by hand or by exh ..."
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Cited by 20 (1 self)
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Abstract. In order to design a quantum circuit that performs a desired quantum computation, it is necessary to find a decomposition of the unitary matrix that represents that computation in terms of a sequence of quantum gate operations. To date, such designs have either been found by hand
Efficient Universal Quantum Circuits
"... Abstract. We define and construct efficient depthuniversal and almostsizeuniversal quantum circuits. Such circuits can be viewed as generalpurpose simulators for central quantum circuit classes and used to capture the computational power of the simulated class. For depth we construct universal ..."
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Cited by 4 (0 self)
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Abstract. We define and construct efficient depthuniversal and almostsizeuniversal quantum circuits. Such circuits can be viewed as generalpurpose simulators for central quantum circuit classes and used to capture the computational power of the simulated class. For depth we con
Universal Quantum Circuits
"... Abstract. We define and construct efficient depthuniversal and almostsizeuniversal quantum circuits. Such circuits can be viewed as generalpurpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated. For depth w ..."
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Cited by 1 (0 self)
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Abstract. We define and construct efficient depthuniversal and almostsizeuniversal quantum circuits. Such circuits can be viewed as generalpurpose simulators for central classes of quantum circuits and can be used to capture the computational power of the circuit class being simulated. For depth
Selftesting of quantum circuits
 In Proceedings of 33rd ICALP, Lecture Notes in Computer Science
, 2006
"... Abstract. We prove that a quantum circuit together with measurement apparatuses and EPR sources can be selftested, i.e. fully verified without any reference to some trusted set of quantum devices. To achieve our goal we define the notions of simulation and equivalence. Using these two concepts, we ..."
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Cited by 14 (2 self)
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Abstract. We prove that a quantum circuit together with measurement apparatuses and EPR sources can be selftested, i.e. fully verified without any reference to some trusted set of quantum devices. To achieve our goal we define the notions of simulation and equivalence. Using these two concepts, we
Compiling Quantum Circuits . . .
, 2003
"... The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2 n ×2 n unitary matrices into efficient circuits of (n −1).controlled singlequbit and (n−1)controlledNOT gates. We first present a general algebraic optim ..."
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The design and optimization of quantum circuits is central to quantum computation. This paper presents new algorithms for compiling arbitrary 2 n ×2 n unitary matrices into efficient circuits of (n −1).controlled singlequbit and (n−1)controlledNOT gates. We first present a general algebraic
Results 1  10
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1,995