2011/03/31 by Oleg Golubitsky, Dmitri Maslov · 1 citation
Computer Science · Physics and Astronomy · #Algorithm #Benchmark (surveying) #Computer science #Cryptography and Data Security #Electronic circuit #Function (biology) #Heuristics #Quantum #Quantum Computing Algorithms and Architecture #Quantum computer #Quantum gate #Quantum-Dot Cellular Automata #Reversible computing #Toffoli gate #cs.ET #quant-ph
paper · pdf · doi:10.1109/tc.2011.144
published as IEEE Transactions on Computers, 61(9):1341-1353, September 2012 · arXiv admin note: substantial text overlap with arXiv:1003.1914
openalex publication_date 2011/08/03 · arxiv created 2012/01/31 · arxiv updated 2012/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Optimal synthesis of reversible functions is a nontrivial 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 huge search space (16! ≈ 244functions). 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 two algorithms: one, that synthesizes an optimal circuit for any 4-bit reversible specification, and another that synthesizes all optimal implementations. We employ several techniques to make the problem tractable. We report results from several experiments, including synthesis of all optimal 4-bit permutations, synthesis of random 4-bit permutations, optimal synthesis of all 4-bit linear reversible circuits, and synthesis of existing benchmark functions; we compose a list of the hardest permutations to synthesize, and show distribution of optimal circuits. We further illustrate that our proposed approach may be extended to accommodate physical constraints via reporting LNN-optimal reversible circuits. Our results have important implications in the design and optimization of reversible and quantum circuits, testing circuit synthesis heuristics, and performing experiments in the area of quantum information processing.