127,393 research outputs found
Introduction to Grassmann Manifolds and Quantum Computation
Geometrical aspects of quantum computing are reviewed elementarily for
non-experts and/or graduate students who are interested in both Geometry and
Quantum Computation.
In the first half we show how to treat Grassmann manifolds which are very
important examples of manifolds in Mathematics and Physics. Some of their
applications to Quantum Computation and its efficiency problems are shown in
the second half. An interesting current topic of Holonomic Quantum Computation
is also covered.
In the Appendix some related advanced topics are discussed.Comment: Latex File, 28 pages, corrected considerably in the process of
refereeing. to appear in Journal of Applied Mathematic
Geometric Quantum Computation on Solid-State Qubits
An adiabatic cyclic evolution of control parameters of a quantum system ends
up with a holonomic operation on the system, determined entirely by the
geometry in the parameter space. The operation is given either by a simple
phase factor (a Berry phase) or a non-Abelian unitary operator depending on the
degeneracy of the eigenspace of the Hamiltonian. Geometric quantum computation
is a scheme to use such holonomic operations rather than the conventional
dynamic operations to manipulate quantum states for quantum information
processing. Here we propose a geometric quantum computation scheme which can be
realized with current technology on nanoscale Josephson-junction networks,
known as a promising candidate for solid-state quantum computer.Comment: 6 figures; to appear in J. Phys.: Condens. Mat
Geometric Quantum Computation
We describe in detail a general strategy for implementing a conditional
geometric phase between two spins. Combined with single-spin operations, this
simple operation is a universal gate for quantum computation, in that any
unitary transformation can be implemented with arbitrary precision using only
single-spin operations and conditional phase shifts. Thus quantum geometrical
phases can form the basis of any quantum computation. Moreover, as the induced
conditional phase depends only on the geometry of the paths executed by the
spins it is resilient to certain types of errors and offers the potential of a
naturally fault-tolerant way of performing quantum computation.Comment: 15 pages, LaTeX, uses cite, eepic, epsfig, graphicx and amsfonts.
Accepted by J. Mod. Op
Physics of computation and light sheet concept in the measurement of (4+n)-dimensional spacetime geometry
We analyze the limits that quantum mechanics imposes on the accuracy to which
-dimensional spacetime geometry can be measured. Using physics of
computation and light sheet concept we derive explicit expressions for quantum
fluctuations and explore their cumulative effects for various spacetime foam
models.Comment: 5 page
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