Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
SIAM Journal on Computing
Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Quantum computation and quantum information
Quantum computation and quantum information
Data structures and algorithms for simplifying reversible circuits
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Exact sat-based toffoli network synthesis
Proceedings of the 17th ACM Great Lakes symposium on VLSI
ISVLSI '07 Proceedings of the IEEE Computer Society Annual Symposium on VLSI
Bi-Directional Synthesis of 4-Bit Reversible Circuits
The Computer Journal
Synthesis of reversible logic circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
An Algorithm for Synthesis of Reversible Logic Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Synthesis and optimization of reversible circuits—a survey
ACM Computing Surveys (CSUR)
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Optimal synthesis of reversible functions is a non-trivial problem. One of the major limiting factors in computing such circuits is the sheer number of reversible functions. Even restricting synthesis to 4-bit reversible functions results in a complexity explosion (16! ≈ 244 functions). The output of such a search alone, counting only the space required to list Toffoli gates for every function, would require over 100 terabytes of storage. In this paper, we present an algorithm, that synthesizes an optimal circuit for any 4-bit reversible specification. We employ several techniques to make the problem tractable. We report results from several experiments, including synthesis of random 4-bit permutations, optimal synthesis of all 4-bit linear reversible circuits, synthesis of existing benchmark functions, and distribution of optimal circuits. Our results have important implications for the design and optimization of quantum circuits, testing circuit synthesis heuristics, and performing experiments in the area of quantum information processing.