Quantum circuits with mixed states

Aharonov, Dorit; Kitaev, Alexei; Nisan, Noam

doi:10.1145/276698.276708

Cited by 350 publications

(587 citation statements)

References 16 publications

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“…The dual forms of 5.2(1)-5.1 (8) hold for the connective ∨. The following theorem sums up some basic arguments that hold for the genuine quantum computational connectives.…”

Section: Logical Argumentsmentioning

confidence: 91%

Holistic logical arguments in quantum computation

Chiara

Giuntini

Leporini

et al. 2016

Mathematica Slovaca

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Abstract. Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way. The characteristic holistic features of the quantum theoretic formalism (which play an essential role in entanglement-phenomena) can be used in order to develop a holistic version of the quantum computational semantics. In contrast with the compositional character of most standard semantic approaches, meanings of formulas are here dealt with as global abstract objects that determine the contextual meanings of the formulas' components (from the whole to the parts). We present a survey of the most significant logical arguments that are valid or that are possibly violated in the framework of this semantics. Some logical features that may appear prima facie strange seem to reflect pretty well informal arguments that are currently used in our rational activity.

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“…The dual forms of 5.2(1)-5.1 (8) hold for the connective ∨. The following theorem sums up some basic arguments that hold for the genuine quantum computational connectives.…”

Section: Logical Argumentsmentioning

confidence: 91%

Holistic logical arguments in quantum computation

Chiara

Giuntini

Leporini

et al. 2016

Mathematica Slovaca

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show abstract

“…Since non-unitary and unitary quantum circuits are equivalent in computational power [6], it is sufficient to treat only unitary quantum circuits, which justifies the above definition. For avoiding unnecessary complication, however, the descriptions of procedures may include non-unitary operations in the subsequent sections.…”

Section: Quantum Circuitsmentioning

confidence: 92%

Quantum Merlin-Arthur Proof Systems: Are Multiple Merlins More Helpful to Arthur?

Kobayashi

Matsumoto

Yamakami

2003

Algorithms and Computation

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This paper introduces quantum "multiple-Merlin"-Arthur proof systems in which Arthur receives multiple quantum proofs that are unentangled with each other. Although classical multi-proof systems are obviously equivalent to classical single-proof systems (i.e., usual Merlin-Arthur proof systems), it is unclear whether or not quantum multi-proof systems collapse to quantum single-proof systems (i.e., usual quantum Merlin-Arthur proof systems). This paper presents a necessary and sufficient condition under which the number of quantum proofs is reducible to two. It is also proved that, in the case of perfect soundness, using multiple quantum proofs does not increase the power of quantum Merlin-Arthur proof systems. * A preliminary version of this paper has appeared in

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“…We assume that a < b < 1 2 . Let n 0 ∈ N the first natural such that 1 2 n 0 ≤ a. Let n 1 ∈ N such that 1 2 n 1 ≤ 1 4 min{b−a, a− 1 2 n 0 }.…”

Section: = ¬0mentioning

confidence: 99%