Matrix Decompositions and Quantum Circuit Design
Stephen Bullock
Information Technology Laboratory, Mathematical and Computational Sciences Division
Wednesday, September 15, 2004 15:00-16:00,
NIST North (820), Room 145
Gaithersburg
Wednesday, September 15, 2004 13:00-14:00,
Room 4511
Boulder
Abstract:
Quantum computations are in particular closed-system evolutions of the state space of n quantum bits.
As such, they may be represented by 2n by 2n unitary matrices.
A quantum circuit specifies a quantum computation by breaking the entire evolution into a sequence of simple operations
applied to only one or two quantum bits at a time.
Recent research has seen advances on the problem of constructing circuits given a target unitary matrix.
The talk surveys these results, paying particular attention to the use of matrix decompositions as a technique.
The canonical decomposition of Duer-Vidal-Cirac in the two-qubit case and the Cosine-Sine Decomposition (CSD) play a prominent role.
Time permitting, theoretical results showing that the size of the universal circuit for the CSD may not be improved by more than a factor of two
will be discussed.
Speaker Bio:
Stephen S. Bullock graduated with a Ph.D. in Mathematics from Cornell University in May 2000 and spent three years as a professor
in the Mathematics Department of the University of Michigan before joining MCSD as an NRC Research Associate in July 2003.
His current research interests are quantum circuit design and multi-partite entanglement theory,
with published results appearing in Quantum Information and Computation, Physical Review A,
Proceedings of the Design Automation Conference, and Journal of Mathematical Physics.
Presentation Slides:
PDF (Slides),
PDF (Additional Materials)
Contact: P. M. KetchamNote: Visitors from outside NIST must contact
Robin Bickel; (301) 975-3668;
at least 24 hours in advance.
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