Physics – Quantum Physics
Scientific paper
2002-10-31
Phys. Rev. A, 68(2003), no. 1, July 2003, 012318.
Physics
Quantum Physics
18 pages, 7 figures. Version 2 gives correct credits for the GQC "quantum compiler". Version 3 adds justification for our choi
Scientific paper
10.1103/PhysRevA.68.012318
Quantum circuits currently constitute a dominant model for quantum computation. 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 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 worst-case upper bound of 23 elementary gates, of which at most 4 (CNOT) entail multi-qubit interactions. Our analysis shows that synthesis algorithms suggested in previous work, although more general, entail much larger quantum circuits than ours in the special case of two qubits. One such algorithm 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 and operator theory. They are related to the canonical decomposition of a two-qubit gate with respect to the ``magic basis'' of phase-shifted Bell states, published previously. We further extend this decomposition in terms of elementary gates for quantum computation.
Bullock Stephen S.
Markov Igor L.
No associations
LandOfFree
An Arbitrary Two-qubit Computation In 23 Elementary Gates does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with An Arbitrary Two-qubit Computation In 23 Elementary Gates, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Arbitrary Two-qubit Computation In 23 Elementary Gates will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-432343