Decomposing a permutation into a conjugated tensor product
ISSAC '97 Proceedings of the 1997 international symposium on Symbolic and algebraic computation
Quantum automata and quantum grammars
Theoretical Computer Science
Transformation rules for designing CNOT-based quantum circuits
Proceedings of the 39th annual Design Automation Conference
Quantum computation and quantum information
Quantum computation and quantum information
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
A reversible carry-look-ahead adder using control gates
Integration, the VLSI Journal
A transformation based algorithm for reversible logic synthesis
Proceedings of the 40th annual Design Automation Conference
Bit Permutation Instructions for Accelerating Software Cryptography
ASAP '00 Proceedings of the IEEE International Conference on Application-Specific Systems, Architectures, and Processors
Architectural techniques for accelerating subword permutations with repetitions
IEEE Transactions on Very Large Scale Integration (VLSI) Systems - Special section on the 2001 international conference on computer design (ICCD)
Improved bounds for the approximate QFT
WISICT '04 Proceedings of the winter international synposium on Information and communication technologies
Principles and Practices of Interconnection Networks
Principles and Practices of Interconnection Networks
A new heuristic algorithm for reversible logic synthesis
Proceedings of the 41st annual Design Automation Conference
A polynomial-time approximation algorithm for the permanent of a matrix with nonnegative entries
Journal of the ACM (JACM)
Charge-Recovery Computing on Silicon
IEEE Transactions on Computers
A Family of Logical Fault Models for Reversible Circuits
ATS '05 Proceedings of the 14th Asian Test Symposium on Asian Test Symposium
Architectural implications of quantum computing technologies
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Data structures and algorithms for simplifying reversible circuits
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Six Synthesis Methods for Reversible Logic
Open Systems & Information Dynamics
Techniques for the synthesis of reversible Toffoli networks
ACM Transactions on Design Automation of Electronic Systems (TODAES)
A novel synthesis algorithm for reversible circuits
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Checking equivalence of quantum circuits and states
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Reversible logic synthesis with Fredkin and Peres gates
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Bi-Directional Synthesis of 4-Bit Reversible Circuits
The Computer Journal
Reversible computing and cellular automata—A survey
Theoretical Computer Science
Principles of a reversible programming language
Proceedings of the 5th conference on Computing frontiers
RevLib: An Online Resource for Reversible Functions and Reversible Circuits
ISMVL '08 Proceedings of the 38th International Symposium on Multiple Valued Logic
Quantified synthesis of reversible logic
Proceedings of the conference on Design, automation and test in Europe
Fast Bit Gather, Bit Scatter and Bit Permutation Instructions for Commodity Microprocessors
Journal of Signal Processing Systems
Equivalence Checking of Reversible Circuits
ISMVL '09 Proceedings of the 2009 39th International Symposium on Multiple-Valued Logic
BDD-based synthesis of reversible logic for large functions
Proceedings of the 46th Annual Design Automation Conference
Recent progress in quantum algorithms
Communications of the ACM
Exact multiple-control toffoli network synthesis with SAT techniques
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Electronic Notes in Theoretical Computer Science (ENTCS)
A library-based synthesis methodology for reversible logic
Microelectronics Journal
Quantum Circuit Simulation
Reducing Reversible Circuit Cost by Adding Lines
ISMVL '10 Proceedings of the 2010 40th IEEE International Symposium on Multiple-Valued Logic
Reducing the number of lines in reversible circuits
Proceedings of the 47th Design Automation Conference
Synthesis of the optimal 4-bit reversible circuits
Proceedings of the 47th Design Automation Conference
Reversible circuit synthesis using a cycle-based approach
ACM Journal on Emerging Technologies in Computing Systems (JETC)
Rule-based optimization of reversible circuits
Proceedings of the 2010 Asia and South Pacific Design Automation Conference
Area-Efficient Multipliers Based on Multiple-Radix Representations
IEEE Transactions on Computers
Synthesis of fredkin-toffoli reversible networks
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Synthesis of quantum circuits for linear nearest neighbor architectures
Quantum Information Processing
An efficient conversion of quantum circuits to a linear nearest neighbor architecture
Quantum Information & Computation
Block-based quantum-logic synthesis
Quantum Information & Computation
Fast equivalence-checking for quantum circuits
Quantum Information & Computation
Quantum addition circuits and unbounded fan-out
Quantum Information & Computation
The quantum fourier transform on a linear nearest neighbor architecture
Quantum Information & Computation
Optimal synthesis of linear reversible circuits
Quantum Information & Computation
On the CNOT-cost of TOFFOLI gates
Quantum Information & Computation
An O(m2)-depth quantum algorithm for the elliptic curve discrete logarithm problem over GF(2m)a
Quantum Information & Computation
Implementation of Shor's algorithm on a linear nearest neighbour qubit array
Quantum Information & Computation
A fast quantum circuit for addition with few qubits
Quantum Information & Computation
Group theory based synthesis of binary reversible circuits
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Constant-optimized quantum circuits for modular multiplication and exponentiation
Quantum Information & Computation
Synthesis of reversible logic circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Reversible cascades with minimal garbage
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Toffoli network synthesis with templates
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Synthesis of quantum-logic circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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
Quantum Circuit Simplification and Level Compaction
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Reversible Circuit Optimization Via Leaving the Boolean Domain
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Method for Automatic Program Inversion Based on LR(0) Parsing
Fundamenta Informaticae - Program Transformation: Theoretical Foundations and Basic Techniques. Part 1
Constant-optimized quantum circuits for modular multiplication and exponentiation
Quantum Information & Computation
Reversible logic synthesis of k-input, m-output lookup tables
Proceedings of the Conference on Design, Automation and Test in Europe
Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures
Proceedings of the 50th Annual Design Automation Conference
Reversible logic synthesis by quantum rotation gates
Quantum Information & Computation
Line ordering of reversible circuits for linear nearest neighbor realization
Quantum Information Processing
RMDDS: Reed-muller decision diagram synthesis of reversible logic circuits
ACM Journal on Emerging Technologies in Computing Systems (JETC)
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Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, postsynthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms—search based, cycle based, transformation based, and BDD based—as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.