ESOP-based Toffoli Gate Cascade Generation

Fazel, K.; Thornton, Mitchell A.; Rice, Jacqueline E.

doi:10.1109/pacrim.2007.4313212

Cited by 161 publications

(135 citation statements)

References 4 publications

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“…Although synthesis and optimization approaches which create circuits composed of negatively controlled Toffoli gates already exist (e.g. ESOP-based synthesis [16][17][18] or QMDD-based synthesis [19]), they often just exploited the structure of the respective function representation. More precisely, in ESOP-based synthesis, negative control lines are just applied as they allow for a straight-forward realization of negative literals.…”

Section: Motivation and General Ideamentioning

confidence: 99%

“…realizations obtained by various synthesis approaches. However, our evaluations showed that the proposed methodology is particularly suited for circuits derived by ESOP-based synthesis [16][17][18]. Here, the targets lines are usually assumed to be placed on certain output lines, while control lines are usually placed on the separate input lines.…”

Section: Algorithmmentioning

confidence: 99%

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Exploiting Negative Control Lines in the Optimization of Reversible Circuits

Datta

Rathi

Wille

et al. 2013

Reversible Computation

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Abstract. The development of approaches for synthesis and optimization of reversible circuits received significant attention in the past. This is partly due to the increasing emphasis on low power design methodologies, and partly motivated by recent works in quantum computation. While most of them relied on a gate library composed of multiple-control Toffoli (MCT) gates with positive control lines, some initial works also exist which additionally incorporate negative control lines. This usually leads to smaller circuits with respect to the number of gates as well as the corresponding quantum costs. However, despite these benefits, negative control lines have hardly been considered in post-synthesis optimization of reversible circuits so far. In this paper, we address this issue. We are presenting an optimization scheme inspired by template matching which explicitly makes use of negative control lines. Experimental evaluations demonstrate that exploiting negative control lines in fact lead to a reduction in the number of gates and the quantum costs by up to 60% and 25%, respectively.

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Section: Motivation and General Ideamentioning

confidence: 99%

Section: Algorithmmentioning

confidence: 99%

Exploiting Negative Control Lines in the Optimization of Reversible Circuits

Datta

Rathi

Wille

et al. 2013

Reversible Computation

View full text Add to dashboard Cite

show abstract

“…Motivated by this, researchers have developed several synthesis approaches [1][2][3][4][5]. Many quantum algorithms are often described by means of a structured quantum circuit in which only the representation of Boolean components differs.…”

Section: Introductionmentioning

confidence: 99%

Reducing the Depth of Quantum Circuits Using Additional Circuit Lines

Abdessaied

Wille

Soeken

et al. 2013

Reversible Computation

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Abstract. The synthesis of Boolean functions, as they are found in many quantum algorithms, is usually conducted in two steps. First, the function is realized in terms of a reversible circuit followed by a mapping into a corresponding quantum realization. During this process, the number of lines and the quantum costs of the resulting circuits have mainly been considered as optimization objectives thus far. However, beyond that also the depth of a quantum circuit is vital. Although first synthesis approaches that consider depth have recently been introduced, the majority of design methods did not consider this metric. In this paper, we introduce an optimization approach aiming for the reduction of depth in the process of mapping a reversible circuit into a quantum circuit. For this purpose, we present an improved (local) mapping of single gates as well as a (global) optimization scheme considering the whole circuit. In both cases, we incorporate the idea of exploiting additional circuit lines which are used in order to split a chain of serial gates. Our optimization techniques enable a concurrent application of gates which significantly reduces the depth of the circuit. Experiments show that reductions of approx. 40% on average can be achieved when following this scheme.

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“…1-b) vc ( If there is no connection to a with color c, the oracle returns the unique label invalid. In [6], this unique value is all 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 2-cycles for black edges: (7,16), (8,17), (9,15), (11,19), (12,22), (13,18), (14,20). In general, one needs l C k NOT gates to implement each minterm where l is the number of bits with value 1 in the binary representation of the minterm.…”

Section: Quantum Walk On Binary Welded Treementioning

confidence: 99%

Reversible Logic Synthesis of k-Input, m-Output Lookup Tables

Shafaei

Saeedi

Pedram

2013

Design, Automation &Amp; Test in Europe Conference &Amp; Exhibition (DATE), 2013

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Abstract-Improving circuit realization of known quantum algorithms by CAD techniques has benefits for quantum experimentalists. In this paper, we address the problem of synthesizing a given k-input, m-output lookup table (LUT) by a reversible circuit. This problem has interesting applications in the Shor's number-factoring algorithm and in quantum walk on sparse graphs. For LUT synthesis, our approach targets the number of control lines in multiple-control Toffoli gates to reduce synthesis cost. To achieve this, we propose a multi-level optimization technique for reversible circuits to benefit from shared cofactors. To reuse output qubits and/or zero-initialized ancillae, we uncompute intermediate cofactors. Our simulations reveal that the proposed LUT synthesis has a significant impact on reducing the size of modular exponentiation circuits for Shor's quantum factoring algorithm, oracle circuits in quantum walk on sparse graphs, and the well-known MCNC benchmarks.

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ESOP-based Toffoli Gate Cascade Generation

Cited by 161 publications

References 4 publications

Exploiting Negative Control Lines in the Optimization of Reversible Circuits

Exploiting Negative Control Lines in the Optimization of Reversible Circuits

Reducing the Depth of Quantum Circuits Using Additional Circuit Lines

Reversible Logic Synthesis of k-Input, m-Output Lookup Tables

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