ITLApplied  Computational Mathematics Division
ACMD Seminar Series
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Quantum Computations and Unitary Matrix Decompositions

Stephen Bullock
Mathematical and Computational Sciences Division

Tuesday, September 23, 2003 15:00-16:00,
Room 145, NIST North (820)
Tuesday, September 23, 2003 13:00-14:00,
Room 4550

Abstract: Data states within a quantum computer are mathematically modelled by vectors of complex numbers, and a given quantum computation acts on each data state by applying a fixed unitary matrix. Thus, matrix decompositions which factor a unitary matrix provide an automated procedure for dividing a quantum computation into multiple, hopefully simpler subcomputations. This talk opens by describing how the QR and Cosine-Sine decompositions may be applied to the problem of constructing quantum logic circuits. We continue to discuss the canonical decomposition of 4x4 unitaries developed in the physics literature, which allows for generically optimal logic circuits for two-qubit computations. The conclusion will briefly outline some new unitary matrix decompositions optimized for quantum computation. Future work hopes these will be explicitly computable in up to 12 qubits (classically,) but numerical obstacles arise.
Contact: A. J. Kearsley

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Last updated: 2011-01-12.