Quantum Circuit Simplification Using Templates

Maslov, Dmitri; Young, Cho Eun; Miller, David M.; Dueck, Gerhard W.

doi:10.1109/date.2005.249

Cited by 87 publications

(103 citation statements)

References 16 publications

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“…Table I shows the quantum cost for a selection of Toffoli and Fredkin gate configurations as introduced in [32] and further optimized in [29] and [33]. As can be seen, gates of larger size are considerably more expensive than gates of smaller size.…”

Section: Definitionmentioning

confidence: 99%

SyReC: a programming language for synthesis of reversible circuits

Wille¹,

Offermann²,

Drechsler³

2010

2010 Forum on Specification &Amp; Design Languages (FDL 2010)

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Abstract-Reversible logic serves as a basis for emerging technologies like quantum computing and additionally has applications in low-power design. In particular, since traditional technologies like CMOS are going to reach their limits in the near future, reversible logic has been established as a promising alternative. Thus, in the last years this area started to become intensely studied by researchers. In particular, how to efficiently synthesize complex reversible circuits is an important question. So far, only synthesis approaches are available that rely on Boolean function representations, like e.g. truth tables or decision diagrams.In this paper, we propose the programming language SyReC that allows to specify and afterwards to automatically synthesize reversible circuits. Using an existing programming language for reversible software design as basis, we introduce new concepts, operations, and restrictions allowing the specification of reversible hardware. Furthermore, a hierarchical approach is presented that automatically transforms the respective statements and operations of the new programming language into a reversible circuit. Experiments show that with the proposed method, complex circuits can be easily specified and synthesized while with previous approaches this often is not possible due to the limits caused by truth tables or decision diagrams.

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Section: Definitionmentioning

confidence: 99%

SyReC: a programming language for synthesis of reversible circuits

Wille¹,

Offermann²,

Drechsler³

2010

2010 Forum on Specification &Amp; Design Languages (FDL 2010)

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“…In addition, for n ≥ 7, a C n−2 NOT gate can be simulated by 24n − 88 elementary gates with no auxiliary bits if there is at least one positive control [7,10]. On the other hand, for a C n−2 NOT with only negative controls, four additional elementary gates are required [10].…”

Section: Preliminariesmentioning

confidence: 99%

“…Consider a circuit of size n. For (n ≥ 5), a C m NOT gate (m ∈ {3, 4, · · · , n/2 }) can be simulated by 12m − 22 elementary gates if at least one positive control is available; otherwise, two extra elementary gates are required [7,10]. In addition, for n ≥ 7, a C n−2 NOT gate can be simulated by 24n − 88 elementary gates with no auxiliary bits if there is at least one positive control [7,10].…”

Section: Preliminariesmentioning

confidence: 99%

“…The gates NOT, CNOT, controlled-V, and controlled-V + (with positive controls) have been efficiently simulated in some quantum computer technologies [16]. These gates are considered as elementary gates for reversible Boolean functions [7,17]. The number of elementary gates required for simulating a given gate is called quantum cost.…”

Section: Preliminariesmentioning

confidence: 99%

“…In this scenario, a realization is found from a given specification first and then, further optimizations are applied in a post-processing step to improve various cost metrics (e.g., quantum cost). Local transformation [4], templates matching [5][6][7][8], and data-structure-based optimization [9] were used to simplify synthesized circuits in the past.…”

Section: Introductionmentioning

confidence: 99%

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Rule-based optimization of reversible circuits

Arabzadeh¹,

Saeedi²,

Zamani³

2010

2010 15th Asia and South Pacific Design Automation Conference (ASP-DAC)

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Abstract-Reversible logic has applications in various research areas including lowpower design and quantum computation. In this paper, a rule-based optimization approach for reversible circuits is proposed which uses both negative and positive control Toffoli gates during the optimization. To this end, a set of rules for removing NOT gates and optimizing sub-circuits with common-target gates are proposed. To evaluate the proposed approach, the best-reported synthesized circuits and the results of a recent synthesis algorithm which uses both negative and positive controls are used. Our experiments reveal the potential of the proposed approach in optimizing synthesized circuits.

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