4,168 research outputs found
On Protected Realizations of Quantum Information
There are two complementary approaches to realizing quantum information so
that it is protected from a given set of error operators. Both involve encoding
information by means of subsystems. One is initialization-based error
protection, which involves a quantum operation that is applied before error
events occur. The other is operator quantum error correction, which uses a
recovery operation applied after the errors. Together, the two approaches make
it clear how quantum information can be stored at all stages of a process
involving alternating error and quantum operations. In particular, there is
always a subsystem that faithfully represents the desired quantum information.
We give a definition of faithful realization of quantum information and show
that it always involves subsystems. This justifies the "subsystems principle"
for realizing quantum information. In the presence of errors, one can make use
of noiseless, (initialization) protectable, or error-correcting subsystems. We
give an explicit algorithm for finding optimal noiseless subsystems. Finding
optimal protectable or error-correcting subsystems is in general difficult.
Verifying that a subsystem is error-correcting involves only linear algebra. We
discuss the verification problem for protectable subsystems and reduce it to a
simpler version of the problem of finding error-detecting codes.Comment: 17 page
Schrodinger cat animated on a quantum computer
We present a quantum algorithm which allows to simulate chaos-assisted
tunneling in deep semiclassical regime on existing quantum computers. This
opens new possibilities for investigation of macroscopic quantum tunneling and
realization of semiclassical Schr\"odinger cat oscillations. Our numerical
studies determine the decoherence rate induced by noisy gates for these
oscillations and propose a suitable parameter regime for their experimental
implementation.Comment: research at Quantware MIPS Center http://www.quantware.ups-tlse.fr ;
revtex, 4 pages, 4 figure
Stabilizer states and Clifford operations for systems of arbitrary dimensions, and modular arithmetic
We describe generalizations of the Pauli group, the Clifford group and
stabilizer states for qudits in a Hilbert space of arbitrary dimension d. We
examine a link with modular arithmetic, which yields an efficient way of
representing the Pauli group and the Clifford group with matrices over the
integers modulo d. We further show how a Clifford operation can be efficiently
decomposed into one and two-qudit operations. We also focus in detail on
standard basis expansions of stabilizer states.Comment: 10 pages, RevTe
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