Quantum computation and quantum information
Quantum computation and quantum information
Logic Synthesis and Verification Algorithms
Logic Synthesis and Verification Algorithms
Reducing Quantum Computations to Elementary Unitary Operations
Computing in Science and Engineering
Reversible logic circuit synthesis
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Gate-level simulation of quantum circuits
ASP-DAC '03 Proceedings of the 2003 Asia and South Pacific Design Automation Conference
Quantum Information & Computation
Optimal realizations of controlled unitary gates
Quantum Information & Computation
Asymptotically optimal circuits for arbitrary n-qubit diagonal comutations
Quantum Information & Computation
Smaller Two-Qubit Circuits for Quantum Communication and Computation
Proceedings of the conference on Design, automation and test in Europe - Volume 2
Bi-Direction Synthesis for Reversible Circuits
ISVLSI '05 Proceedings of the IEEE Computer Society Annual Symposium on VLSI: New Frontiers in VLSI Design
Synthesis of quantum logic circuits
Proceedings of the 2005 Asia and South Pacific Design Automation Conference
A discrete local invariant for quantum gates
Quantum Information & Computation
A new algorithm for producing quantum circuits using KAK decompositions
Quantum Information & Computation
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Quantum circuits currently constitute a dominant model for quantum computation [14]. Our work addresses the problem of constructing quantum circuits to implement an arbitrary given quantum computation, in the special case of two qubits. We pursue circuits without ancilla qubits and as small a number of elementary quantum gates [1, 9] as possible. Our lower bound for worst-case optimal two-qubit circuits calls for at least 17 gates: 15 one-qubit rotations and 2 CNOTs. To this end, we constructively prove a worstcase upper bound of 23 elementary gates, of which at most 4 (CNOTs) entail multi-qubit interactions. Our analysis shows that previously known synthesis algorithms, although more general, entail much larger quantum circuits than ours in the special case of two qubits. One such algorithm [4] has a worst case of 61 gates of which 18 may be CNOTs. Our techniques rely on the KAK decomposition from Lie theory as well as the polar and spectral (symmetric Shur) matrix decompositions from numerical analysis. They are related to the canonical decomposition of a two-qubit gate with respect to the "magic basis" of phase-shifted Bell states [11, 12]. We extend this decomposition in terms of elementary gates for quantum computation.