Reversible logic circuit synthesis

Reversible or information-lossless circuits have applications in digital signal processing, communication, computer graphics and cryptography. They are also a fundamental requirement in the emerging field of quantum computation. We investigate the synthesis of reversible circuits that employ a minimum number of gates and contain no redundant input-output line-pairs (temporary storage channels). We prove constructively that every even permutation can be implemented without temporary storage using NOT, CNOT and TOFFOLI gates. We describe an algorithm for the synthesis of optimal circuits and study the reversible functions on three wires, reporting distributions of circuit sizes. Finally, in an application important to quantum computing, we synthesize oracle circuits for Grover's search algorithm, and show a significant improvement over a previously proposed synthesis algorithm.

[1]  Anas N. Al-Rabadi,et al.  A General Decomposition for Reversible Logic , 2001 .

[2]  Yahiko Kambayashi,et al.  Transformation rules for designing CNOT-based quantum circuits , 2002, DAC '02.

[3]  Kozo Kinoshita,et al.  Conservative Logic Elements and Their Universality , 1979, IEEE Transactions on Computers.

[4]  Martin Rötteler,et al.  Quantum Algorithms: Applicable Algebra and Quantum Physics , 2001 .

[5]  Eugene L. Lawler,et al.  An Approach to Multilevel Boolean Minimization , 1964, JACM.

[6]  Tommaso Toffoli,et al.  Reversible Computing , 1980, ICALP.

[7]  Charles H. Bennett,et al.  Logical reversibility of computation , 1973 .

[8]  Yongwook Chung,et al.  A Practical Method of Constructing Quantum Combinational Logic Circuits , 1999 .

[9]  Ruby B. Lee,et al.  Architectural enhancements for fast subword permutations with repetitions in cryptographic applications , 2001, Proceedings 2001 IEEE International Conference on Computer Design: VLSI in Computers and Processors. ICCD 2001.

[10]  Thomas F. Knight,et al.  Asymptotically Zero Energy Split-Level Charge Recovery Logic , 1994 .

[11]  Pawel Kerntopf.  A COMPARISON OF LOGICAL EFFICIENCY OF REVERSIBLE AND CONVENTIONAL GATES , 2000 .

[12]  Tad Hogg,et al.  TOOLS FOR QUANTUM ALGORITHMS , 1999 .

[13]  Richard Phillips Feynman,et al.  Quantum mechanical computers , 1984, Feynman Lectures on Computation.

[14]  Birger Raa,et al.  INSTITUTE OF PHYSICS PUBLISHING JOURNAL OF PHYSICS A: MATHEMATICAL AND GENERAL J. Phys. A: Math. Gen. 35 (2002) 7063–7078 PII: S0305-4470(02)34943-6 Generating the group of reversible logic gates , 2022 .

[15]  Mikhail J. Atallah,et al.  Algorithms and Theory of Computation Handbook , 2009, Chapman & Hall/CRC Applied Algorithms and Data Structures series.

[16]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[17]  Ruby B. Lee,et al.  Bit permutation instructions for accelerating software cryptography , 2000, Proceedings IEEE International Conference on Application-Specific Systems, Architectures, and Processors.

[18]  Leo Storme,et al.  Group Theoretical Aspects of Reversible Logic Gates , 1999, J. Univers. Comput. Sci..

[19]  Lov K. Grover.  A framework for fast quantum mechanical algorithms , 1997, STOC '98.

[20]  Luciano Serafini,et al.  Toward an architecture for quantum programming , 2001, ArXiv.

[21]  Andris Ambainis,et al.  ROM-based computation: quantum versus classical , 2002, Quantum Inf. Comput..