An Extended approach for Mapping Reversible Circuits to Quantum Circuits using NCV-|v1〉library

Fast equivalence -- checking for quantum circuits

Quantum Information and Computation ◽

10.26421/qic10.9-10-1 ◽

2010 ◽

Vol 10 (9&10) ◽

pp. 721-734

Author(s):

Shigeru Yamashita ◽

Igor L. Markov

Keyword(s):

Formal Verification ◽

Quantum Algorithms ◽

Quantum Circuits ◽

Equivalence Checking ◽

Sat Solvers ◽

Reversible Circuits ◽

Verification Tools ◽

Verification Methodology ◽

Verification Techniques ◽

Factoring Algorithm

We perform formal verification of quantum circuits by integrating several techniques specialized to particular classes of circuits. Our verification methodology is based on the new notion of a reversible miter that allows one to leverage existing techniques for simplification of quantum circuits. For reversible circuits which arise as runtime bottlenecks of key quantum algorithms, we develop several verification techniques and empirically compare them. We also combine existing quantum verification tools with the use of SAT-solvers. Experiments with circuits for Shor's number-factoring algorithm, containing thousands of gates, show improvements in efficiency by four orders of magnitude.

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Improving the mapping of reversible circuits to quantum circuits using multiple target lines

2013 18th Asia and South Pacific Design Automation Conference (ASP-DAC) ◽

10.1109/aspdac.2013.6509587 ◽

2013 ◽

Cited By ~ 31

Author(s):

R. Wille ◽

M. Soeken ◽

C. Otterstedt ◽

R. Drechsler

Keyword(s):

Quantum Circuits ◽

Multiple Target ◽

Reversible Circuits

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Technology Mapping of Reversible Circuits to Clifford+T Quantum Circuits

2016 IEEE 46th International Symposium on Multiple-Valued Logic (ISMVL) ◽

10.1109/ismvl.2016.33 ◽

2016 ◽

Cited By ~ 17

Author(s):

Nabila Abdessaied ◽

Matthew Amy ◽

Mathias Soeken ◽

Rolf Drechsler

Keyword(s):

Quantum Circuits ◽

Technology Mapping ◽

Reversible Circuits

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Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits

Synthesis Lectures on Digital Circuits and Systems ◽

10.2200/s00856ed1v01y201805dcs054 ◽

2018 ◽

Vol 13 (1) ◽

pp. 1-125 ◽

Cited By ~ 1

Author(s):

Alexis De Vos ◽

Stijn De Baerdemacker ◽

Yvan Van Rentergem

Keyword(s):

Quantum Circuits ◽

Reversible Circuits

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Optimization of Reversible Circuits Using Toffoli Decompositions with Negative Controls

Symmetry ◽

10.3390/sym13061025 ◽

2021 ◽

Vol 13 (6) ◽

pp. 1025

Author(s):

Mariam Gado ◽

Ahmed Younes

Keyword(s):

Symmetric Group ◽

Permutation Group ◽

Building Blocks ◽

Quantum Circuits ◽

Quantum Computers ◽

Quantum Cost ◽

Reversible Circuits ◽

Negative Controls ◽

Target Qubit

The synthesis and optimization of quantum circuits are essential for the construction of quantum computers. This paper proposes two methods to reduce the quantum cost of 3-bit reversible circuits. The first method utilizes basic building blocks of gate pairs using different Toffoli decompositions. These gate pairs are used to reconstruct the quantum circuits where further optimization rules will be applied to synthesize the optimized circuit. The second method suggests using a new universal library, which provides better quantum cost when compared with previous work in both cost015 and cost115 metrics; this proposed new universal library “Negative NCT” uses gates that operate on the target qubit only when the control qubit’s state is zero. A combination of the proposed basic building blocks of pairs of gates and the proposed Negative NCT library is used in this work for synthesis and optimization, where the Negative NCT library showed better quantum cost after optimization compared with the NCT library despite having the same circuit size. The reversible circuits over three bits form a permutation group of size 40,320 (23!), which is a subset of the symmetric group, where the NCT library is considered as the generators of the permutation group.

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An Extended Approach for Generating Unitary Matrices for Quantum Circuits

Computers Materials & Continua ◽

10.32604/cmc.2020.07483 ◽

2020 ◽

Vol 62 (3) ◽

pp. 1413-1421

Author(s):

Zhiqiang Li ◽

Wei Zhang ◽

Gaoman Zhang ◽

Juan Dai ◽

Jiajia Hu ◽

...

Keyword(s):

Quantum Circuits ◽

Unitary Matrices ◽

Extended Approach

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Using negated control signals in quantum computing circuits

Facta universitatis - series Electronics and Energetics ◽

10.2298/fuee1103423m ◽

2011 ◽

Vol 24 (3) ◽

pp. 423-435 ◽

Cited By ~ 6

Author(s):

Claudio Moraga

Keyword(s):

Quantum Computing ◽

Control Variable ◽

Quantum Circuits ◽

Quantum Cost ◽

Schematic Representation ◽

Control Signals ◽

Reversible Circuits ◽

Mixed Polarity

White dots have been used in the schematic representation of reversible circuits to indicate that a control variable has to be inverted to become active. The present paper argues that the use of negated control signals may also offer advantages for the realization, by reducing the number of elementary components. In the case of quantum circuits, this contributes to reduce the quantum cost. It is shown that mixed polarity Reed Muller expressions, possibly extended with Boolean disjunctions, are very helpful to design quantum computing circuits including negated control signals.

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