Fetching the paper…
Reading the bibliography…
We present a complete classification of all possible sets of classical reversible gates acting on bits, in terms of which reversible transformations they generate, assuming swaps and ancilla bits are available for free.
The two-valued iterative systems of mathematical logic
E. L. Post · 1941
Earlier work this paper cites.
r-universal reversible logic gates
A. De Vos and L. Storme · 1941
Earlier work this paper cites.
Irreversibility and heat generation in the computing process
R. Landauer · 1961
Earlier work this paper cites.
The Art of Computer Programming, Volume 1, 2nd edition
D. E. Knuth · 1969
Earlier work this paper cites.
Orthogonal matrices over finite fields
J. MacWilliams · 1969
Earlier work this paper cites.
Logical reversibility of computation
C. H. Bennett · 1973
Earlier work this paper cites.
Reversible computing
T. Toffoli · 1980
Earlier work this paper cites.
Conservative logic
E. Fredkin and T. Toffoli · 1982
Earlier work this paper cites.
Computing algebraic formulas with a constant number of registers
M. Ben-Or and R. Cleve · 1988
Earlier work this paper cites.
Any nonlinear one-to-one binary logic gate suffices for computation
S. Lloyd · 1992
Earlier work this paper cites.
Elementary gates for quantum computation
A. Barenco, C. H. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. Smolin, and H. Weinfurter · 1995
Cited alongside, same era.
Algorithmic problems in varieties
O. G. Kharlampovich and M. V. Sapir · 1995
Cited alongside, same era.
Class of quantum error-correcting codes saturating the quantum Hamming bound
D. Gottesman · 1996
Cited alongside, same era.
Universal affine classification of Boolean functions
I. Strazdins · 1997
Cited alongside, same era.
Power of one bit of quantum information
E. Knill and R. Laflamme · 1998
Cited alongside, same era.
Fast parallel circuits for the quantum Fourier transform
R. Cleve and J. Watrous · 2000
Cited alongside, same era.
On universality of general reversible multiple-valued logic gates
P. Kerntopf, M. A. Perkowski, and M. Khan · 2004
Later among the works it cites.
Classification and universality of reversible logic elements with one-bit memory
K. Morita, T. Ogiro, K. Tanaka, and H. Kato · 2005
Later among the works it cites.
Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory
D. Lau · 2006
Later among the works it cites.
The computational complexity of linear optics
S. Aaronson and A. Arkhipov · 2011
Later among the works it cites.
Synthesis and optimization of reversible circuits–a survey
M. Saeedi and I. L. Markov · 2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Encoded universality in physical implementations of a quantum computer
D. Bacon, J. Kempe, D. P. DiVincenzo, D. A. Lidar, and K. B. Whaley · 2001
Cited alongside, same era.
Both Toffoli and controlled-NOT need little help to do universal quantum computation
Y. Shi · 2002
Cited alongside, same era.
Synthesis of reversible logic circuits
V. V. Shende, A. K. Prasad, I. L. Markov, and J. P. Hayes · 2003
Cited alongside, same era.
Improved simulation of stabilizer circuits
S. Aaronson and D. Gottesman · 2004
Cited alongside, same era.
S. Aaronson and A. Bouland · 2014
Later among the works it cites.
Complexity classification of local Hamiltonian problems
T. Cubitt and A. Montanaro · 2014
Later among the works it cites.
Answer to CS Theory StackExchange question on “classifying reversible gates”
E. Jeřábek · 2014
Later among the works it cites.
Reversible Gate Classifier, 2015
L. Schaefer · 2015
Closest in time.