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Smaller Two-Qubit Circuits for Quantum Communication and Computation



V V. Shende, I L. Markov, Stephen Bullock


We show how to implement an arbitrary two-qubit unitary operation using any of several quantum gate libraries with small a priori upper bounds on gate counts.Using quantum circuit identities, we improve an earlier lower bound of 17 elementary gates by Bullock and Markov to 18, and their upper bound of 23 elementary gates to 18. We also improve upon the generic circuit with six CNOT gates by Zhang et al. (our circuit uses three), and that by Vidal and Dawson with 11 basic gates (we use 10).We study the performance of our synthesis procedures on two-qubit operators that are useful in quantum algorithms and communication protocols. With additional work, we find small circuits and improve upon previously known circuits in some cases.
Proceedings Title
DATE (Design, Automation, and Test in Europe) Conference paper
Paris, France
Conference Dates
February 16, 2004
Conference Location
Paris, 1, FR
Conference Title
Design Automation Conference


circuit synthesis, quantum circuit


Shende, V. , Markov, I. and Bullock, S. (2003), Smaller Two-Qubit Circuits for Quantum Communication and Computation, DATE (Design, Automation, and Test in Europe) Conference paper, Paris, 1, FR, [online], (Accessed June 24, 2024)


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Created March 19, 2003, Updated October 12, 2021