White Dots do Matter: Rewriting Reversible Logic Circuits

Soeken, Mathias; Thomsen, Michael Kirkedal

doi:10.1007/978-3-642-38986-3_16

Cited by 34 publications

(26 citation statements)

References 18 publications

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“…The results from optimizing benchmark functions are promising, whereas computationally, it is not feasible to obtain all templates even with three lines before template matching starts. Relating our findings in template matching with mixedpolarity Toffoli gates to the results of[16] can help to devise a better understanding of template matching and estimate the number of total templates, but also…”

mentioning

confidence: 74%

“…In fact, the technique described in [13] considers sequences of gates that share the same target line and can therefore be effeciently reduced using ESOP minimzation as demonstrated in [15]. In fact, all optimization approaches that take negative controls into account are instances of rewriting according to the elementary rules presented in [16]. This also explains the huge number of templates when considering negative controls and justifies a dynamic matching approach as presented in this paper.…”

Section: Introductionmentioning

confidence: 89%

“…These rules origin from previous work in which only postive control lines were considered. By allowing negative control lines for the circuit description, one gains more flexibility [16].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Template Matching with Mixed-Polarity Toffoli Gates

Rahman

Soeken

Dueck

2015

2015 IEEE International Symposium on Multiple-Valued Logic

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The Toffoli gate, as originally proposed, had only positive controls. It has been shown that mixed polarity controlled Toffoli gates can be efficiently implemented. In fact, their quantum cost is the same as for positive controlled gates in most cases. Thus it is advantageous to consider circuits with mixed polarity Toffoli gates. Template matching has been successfully used to reduce the number of Toffoli gates in reversible circuits. Little work on templates with mixed polarity gates has been reported. Unfortunately, the number of potential templates increases dramatically, if mixed polarity is introduced. Here we propose a dynamic template matching algorithm that takes templates with few lines and dynamically extends the lines to find matches. Experimental results show that the proposed approach has a significant impact on reducing the total number of gates (57% in the best case) in circuits.

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confidence: 74%

Section: Introductionmentioning

confidence: 89%

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Dynamic Template Matching with Mixed-Polarity Toffoli Gates

Rahman

Soeken

Dueck

2015

2015 IEEE International Symposium on Multiple-Valued Logic

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“…Standard gate-based compilation is a well studied subject [4,10,18,23,51]. Practical techniques have been developed to improve the standard gate-based compilation from the reversible logic level down to the technology level, including studies of hand optimization, discrete [34,35] and continuous [38] template matching, and rule-based rewriting [37,53]. Template matching methods achieved impressive gate reduction on small and intermediate-scale circuits, though they are limited by having to manually search for new template rules for each specific gate library (for example, there is no library for iSWAP gates).…”

Section: Related Workmentioning

confidence: 99%

Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers

Shi

Leung

Gokhale

et al. 2019

Proceedings of the Twenty-Fourth International Conference on Architectural Support for Programming Languages and Operating Syst

100

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Recent developments in engineering and algorithms have made real-world applications in quantum computing possible in the near future. Existing quantum programming languages and compilers use a quantum assembly language composed of 1-and 2-qubit (quantum bit) gates. Quantum compiler frameworks translate this quantum assembly to electric signals (called control pulses) that implement the specified computation on specific physical devices. However, there is a mismatch between the operations defined by the 1-and 2-qubit logical ISA and their underlying physical implementation, so the current practice of directly translating logical instructions into control pulses results in inefficient, high-latency programs. To address this inefficiency, we propose a universal quantum compilation methodology that aggregates multiple logical operations into larger units that manipulate up to 10 qubits at a time. Our methodology then optimizes these aggregates by (1) finding commutative intermediate operations that result in more efficient schedules and (2) creating custom control pulses optimized for the aggregate (instead of individual 1-and 2-qubit operations). Compared to the standard gate-based compilation, the proposed approach realizes a deeper vertical integration of high-level quantum software and low-level, physical quantum hardware. We evaluate our approach on important near-term quantum applications on simulations of superconducting Permission to make digital

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“…The circuits for p and q consist each of at most n NOT gates. First, we move the circuit for p to the right of F by switching the polarities of the controls on lines i if p i " 1 [17], leading to an updated circuit F 1 of the same size. Using the identities…”

Section: Application To Reversible Circuitsmentioning

confidence: 99%

Enumeration of Reversible Functions and Its Application to Circuit Complexity

Soeken

Abdessaied

Micheli

2016

Reversible Computation

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Abstract. We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying linear and affine transformations to inputs and outputs. We apply the results to reversible circuits and prove that minimum circuit realizations of functions in the same equivalence class differ at most in a linear number of gates in presence of negation and permutation and at most in a quadratic number of gates in presence of linear and affine transformations.

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White Dots do Matter: Rewriting Reversible Logic Circuits

Cited by 34 publications

References 18 publications

Dynamic Template Matching with Mixed-Polarity Toffoli Gates

Dynamic Template Matching with Mixed-Polarity Toffoli Gates

Optimized Compilation of Aggregated Instructions for Realistic Quantum Computers

Enumeration of Reversible Functions and Its Application to Circuit Complexity

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