Results 1  10
of
65
Elementary Gates for Quantum Computation
, 1995
"... We show that a set of gates that consists of all onebit quantum gates (U(2)) and the twobit exclusiveor gate (that maps Boolean values (x,y) to (x,x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We in ..."
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Cited by 198 (11 self)
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We show that a set of gates that consists of all onebit quantum gates (U(2)) and the twobit exclusiveor gate (that maps Boolean values (x,y) to (x,x⊕y)) is universal in the sense that all unitary operations on arbitrarily many bits n (U(2 n)) can be expressed as compositions of these gates. We investigate the number of the above gates required to implement other gates, such as generalized DeutschToffoli gates, that apply a specific U(2) transformation to one input bit if and only if the logical AND of all remaining input bits is satisfied. These gates play a central role in many proposed constructions of quantum computational networks. We derive upper and lower bounds on the exact number of elementary gates required to build up a variety of two and threebit quantum gates, the asymptotic number required for nbit DeutschToffoli gates, and make some observations about the number required for arbitrary nbit unitary operations.
Automaton Logic
 International Journal of Theoretical Physics
, 1996
"... The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1 ..."
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Cited by 79 (47 self)
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The experimental logic of Moore and Mealy type automata is investigated. key words: automaton logic; partition logic; comparison to quantum logic; intrinsic measurements 1
Information and Computation: Classical and Quantum Aspects
 REVIEWS OF MODERN PHYSICS
, 2001
"... Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely ..."
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Cited by 23 (2 self)
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Quantum theory has found a new field of applications in the realm of information and computation during the recent years. This paper reviews how quantum physics allows information coding in classically unexpected and subtle nonlocal ways, as well as information processing with an efficiency largely surpassing that of the present and foreseeable classical computers. Some outstanding aspects of classical and quantum information theory will be addressed here. Quantum teleportation, dense coding, and quantum cryptography are discussed as a few samples of the impact of quanta in the transmission of information. Quantum logic gates and quantum algorithms are also discussed as instances of the improvement in information processing by a quantum computer. We provide finally some examples of current experimental
Quantum Circuits: Fanout, Parity, and Counting
 In Los Alamos Preprint archives
, 1999
"... Abstract. We propose definitions of QAC 0, the quantum analog of the classical class AC 0 of constantdepth circuits with AND and OR gates of arbitrary fanin, and QACC 0 [q], where nary MODq gates are also allowed. We show that it is possible to make a ‘cat ’ state on n qubits in constant depth if ..."
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Cited by 17 (1 self)
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Abstract. We propose definitions of QAC 0, the quantum analog of the classical class AC 0 of constantdepth circuits with AND and OR gates of arbitrary fanin, and QACC 0 [q], where nary MODq gates are also allowed. We show that it is possible to make a ‘cat ’ state on n qubits in constant depth if and only if we can construct a parity or MOD2 gate in constant depth; therefore, any circuit class that can fan out a qubit to n copies in constant depth also includes QACC 0 [2]. In addition, we prove the somewhat surprising result that parity or fanout allows us to construct MODq gates in constant depth for any q, so QACC 0 [2] = QACC 0. Since ACC 0 [p] ̸ = ACC 0 [q] whenever p and q are mutually prime, QACC 0 [2] is strictly more powerful than its classical counterpart, as is QAC 0 when fanout is allowed. 1
Twoqubit projective measurements are universal for quantum computation
"... Nielsen showed in quantph/0108020 that universal quantum computation can be performed using projective measurements, quantum memory, and preparation of the 0 〉 state. Furthermore, 4qubit measurements are sufficient. Fenner and Zhang showed in quantph/0111077 that 3qubit measurements are suffici ..."
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Cited by 16 (0 self)
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Nielsen showed in quantph/0108020 that universal quantum computation can be performed using projective measurements, quantum memory, and preparation of the 0 〉 state. Furthermore, 4qubit measurements are sufficient. Fenner and Zhang showed in quantph/0111077 that 3qubit measurements are sufficient. We prove that 2qubit measurements are sufficient, closing the gap between the upper and lower bound of the number of qubits to be measured jointly. We conclude with some open questions. 1 Introduction and previous work Studying the resources required for universal quantum computation is important not only for its realization but also for our theoretical understanding of what makes it so powerful. In the predominant standard quantum circuit model [1], it suffices to prepare the 0 〉 state, to measure individual qubits in the computation basis, and to well approximate any unitary gate. Any unitary gate
Counting, Fanout, And The Complexity Of Quantum Acc
, 2002
"... q are distinct primes, QACC[q] is strictly more powerful than its classical counterpart, as is QAC 0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upp ..."
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Cited by 15 (2 self)
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q are distinct primes, QACC[q] is strictly more powerful than its classical counterpart, as is QAC 0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We dene classes of languages closely related to QACC[2] and show that restricted versions of them can be simulated by polynomialsize circuits. With further restrictions, language classes related to QACC[2] operators can be simulated by classical threshold circuits of polynomial size and constant depth. Keywords: quantum computation, quantum & circuit complexity, threshold circuit Communicated by : R Cleve & J Watrous 1. Introduction Advances in quantum computation
Results on twobit gate design for quantum computers
 Proceedings of the Workshop on Physics and Computation, PhysComp ’94 (Los Alamitos: IEEE Comp. Soc
, 1994
"... We present numerical results which show how twobit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a particular sequence of exactly five twobit gates. An arbitrar ..."
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Cited by 14 (2 self)
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We present numerical results which show how twobit logic gates can be used in the design of a quantum computer. We show that the Toffoli gate, which is a universal gate for all classical reversible computation, can be implemented using a particular sequence of exactly five twobit gates. An arbitrary threebit unitary gate, which can be used to build up any arbitrary quantum computation, can be implemented exactly with six twobit gates. The ease of implementation of any particular quantum operation is dependent upon a very nonclassical feature of the operation, its exact quantum phase factor. 1
Classical simulation of noninteractingfermion quantum circuits
 Phys. Rev. A
"... We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [1] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend ..."
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Cited by 14 (1 self)
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We show that a class of quantum computations that was recently shown to be efficiently simulatable on a classical computer by Valiant [1] corresponds to a physical model of noninteracting fermions in one dimension. We give an alternative proof of his result using the language of fermions and extend the result to noninteracting fermions with arbitrary pairwise interactions, where gates can be conditioned on outcomes of complete von Neumann measurements in the computational basis on other fermionic modes in the circuit. This last result is in remarkable contrast with the case of noninteracting bosons where universal quantum computation can be achieved by allowing gates to be conditioned on classical bits [2].