On the CNOT-cost of TOFFOLI gates

T. Toffoli, Reversible Computing, MIT Technical Report

1980

Earlier work this paper cites.

D. P. DiVincenzo and J. A. Smolin, Results on two-bit gate design for quantum computers, Proc. of the Workshop on Physics and Computation

1994

Earlier work this paper cites.

N. Margolus, Simple quantum gates, Unpublished manuscript (circa 1994)

1994

Earlier work this paper cites.

History and generality of the CS decomposition,

C. C. Paige and M. Wei, · 1994

Earlier work this paper cites.

Elementary gates for quantum computation,

A. Barenco, C. Bennett, R. Cleve, D. P. DiVincenzo, N. Margolus, P. Shor, T. Sleator, J. A. Smolin, and H. Weinfurter, · 1995

Earlier work this paper cites.

A. W. Knapp, Lie Groups Beyond an Introduction

1996

Earlier work this paper cites.

D.P. DiVincenzo, Quantum gates and circuits. Proc. R. Soc. Lond. A

1998

Earlier work this paper cites.

M. Lewenstein, B. Kraus, J. I. Cirac, and P. Horodecki, Optimization of entanglement witnesses, PRA

2000

Earlier work this paper cites.

Quantum Computation and Quantum Information

M. A. Nielsen and I. L. Chuang, · 2000

Cited alongside, same era.

N. Khaneja and S. J. Glaser, Cartan decomposition of SU(n) and control of spin systems, Chem. Physics

2001

Cited alongside, same era.

Yu. G. Makhlin, Nonlocal properties of two-qubit gates and mixed states and optimizations of quantum computations, QIP

2002

Cited alongside, same era.

D. Maslov and G. W. Dueck. IEE Electronics Letters

2003

Cited alongside, same era.

G. Song and A. Klappenecker, Optimal realizations of controlled unitary gates, QIC

2003

Cited alongside, same era.

J. Zhang, J. Vala, K. B. Whaley, and S. Sastry, A geometric theory of non-local two-qubit operations, PRA

2003

Cited alongside, same era.

Quantum circuits for general multiqubit gates,

M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa, · 2004

Later among the works it cites.

CNOT-optimal circuits for generic two-qubit operators, PRA

V. V. Shende, I. L. Markov, and S. S. Bullock, · 2004

Later among the works it cites.

Recognizing small-circuit structure in two-qubit operators

V. V. Shende, S. S. Bullock, and I. L. Markov, · 2004

Later among the works it cites.

G. Song and A. Klappenecker, The simplified Toffoli gate implementation by Margolus is optimal, QIC

2004

Later among the works it cites.

F. Vatan and C. Williams, Optimal quantum circuits for general two-qubit gates, PRA

2004

Later among the works it cites.

A universal quantum circuit for two-qubit transformations with three CNOT gates,

G. Vidal and C. M. Dawson, · 2004