Elementary Quantum Gate Realizations for Multiple-Control Toffoli Gates

AbstractAny unitary operation in quantum information processing can be implemented via a sequence of simpler steps — quantum gates. However, actual implementation of a quantum gate is always imperfect and takes a finite time. Therefore, searching for a short sequence of gates — efficient quantum circuit for a given operation, is an important task. We contribute to this issue by proposing optimization of the well-known universal procedure proposed by Barenco et al. [Phys. Rev. A 52, 3457 (1995)]. We also created a computer program which realizes both Barenco’s decomposition and the proposed optimization. Furthermore, our optimization can be applied to any quantum circuit containing generalized Toffoli gates, including basic quantum gate circuits.

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Low quantum cost realization of generalized peres and toffoli gates with multiple-control signals

2013 13th IEEE International Conference on Nanotechnology (IEEE-NANO 2013) ◽

10.1109/nano.2013.6721034 ◽

2013 ◽

Cited By ~ 8

Author(s):

Marek Szyprowski ◽

Pawel Kerntopf

Keyword(s):

Quantum Cost ◽

Multiple Control ◽

Control Signals ◽

Toffoli Gates

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Improved Decomposition of Multiple-Control Ternary Toffoli Gates Using Muthukrishnan-Stroud Quantum Gates

Reversible Computation - Lecture Notes in Computer Science ◽

10.1007/978-3-319-59936-6_16 ◽

2017 ◽

pp. 202-213 ◽

Cited By ~ 3

Author(s):

P. Mercy Nesa Rani ◽

Abhoy Kole ◽

Kamalika Datta ◽

Indranil Sengupta

Keyword(s):

Quantum Gates ◽

Multiple Control ◽

Toffoli Gates

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Primitive quantum gate realizations of multiple-controlled Toffoli gates

16th Int'l Conf. Computer and Information Technology ◽

10.1109/iccitechn.2014.6997380 ◽

2014 ◽

Cited By ~ 1

Author(s):

Mozammel H. A. Khan

Keyword(s):

Quantum Gate ◽

Toffoli Gates

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Reversible logic synthesis by quantum rotation gates

Quantum Information and Computation ◽

10.26421/qic13.9-10-3 ◽

2013 ◽

Vol 13 (9&10) ◽

pp. 771-792

Author(s):

Afshin Abdollahi ◽

Mehdi Saeedi ◽

Massoud Pedram

Keyword(s):

Logic Synthesis ◽

Canonical Representation ◽

Reversible Logic ◽

Boolean Logic ◽

Decision Diagrams ◽

Multiple Control ◽

Decomposition Approach ◽

Binary Decision ◽

Gate Count ◽

Toffoli Gates

A rotation-based synthesis framework for reversible logic is proposed. We develop a canonical representation based on binary decision diagrams and introduce operators to manipulate the developed representation model. Furthermore, a recursive functional bi-decomposition approach is proposed to automatically synthesize a given function. While Boolean reversible logic is particularly addressed, our framework constructs intermediate quantum states that may be in superposition, hence we combine techniques from reversible Boolean logic and quantum computation. {The proposed approach results in quadratic gate count for multiple-control Toffoli gates without ancillae, linear depth for quantum carry-ripple adder, and $O(n\log^2 n)$ size for quantum multiplexer.

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