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)
Gaithersburg
Tuesday, September 23, 2003 13:00-14:00,
Room 4550
Boulder
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. KearsleyNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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