Quantum Biased Oracles

Iwama, Kazuo; Kawachi, Akinori; Yamashita, Shigeru

doi:10.2197/ipsjdc.1.461

Cited by 1 publication

(1 citation statement)

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“…12, is not so easy.) Then the group A gates can be deleted one by one from the leftmost one by Rule (6 Fig. 6 which is the canonical form for the initial circuit.…”

Section: Proofmentioning

confidence: 99%

Transformation rules for CNOT-based quantum circuits and their applications

Iwama

Yamashita

2003

New Gener Comput

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This paper introduces a simple but nontrivial set of local transformation rules for designing Control-NOT(CNOT)-based combinatorial circuits. We also provide a proof that the rule set is complete, namely, for any two equivalent circuits, $1 and Sz, there is a sequence of transformations, each of them in the rule set, which changes $1 to $2. Two applications of the rule set are also presented. One is to simulate Resolution with only polynomial overhead by the rule set. Therefore we can conclude that the rule set is reasonably powerful. The other is to reduce the cost of CNOT-based circuits by using the transformations in the rule set. This implies that the rule set might be used for the practical circuit design.Keywords: Quantum Circuit, CNOT Gate, Local Transformation Rules, Proof System. w IntroductionTo realize a quantum algorithm, we need to translate it into an efficient quantum circuit 1~ which is a sequence of elementary quantum operations so called

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“…12, is not so easy.) Then the group A gates can be deleted one by one from the leftmost one by Rule (6 Fig. 6 which is the canonical form for the initial circuit.…”

Section: Proofmentioning

confidence: 99%