1,749 research outputs found
Overhead and noise threshold of fault-tolerant quantum error correction
Fault tolerant quantum error correction (QEC) networks are studied by a
combination of numerical and approximate analytical treatments. The probability
of failure of the recovery operation is calculated for a variety of CSS codes,
including large block codes and concatenated codes. Recent insights into the
syndrome extraction process, which render the whole process more efficient and
more noise-tolerant, are incorporated. The average number of recoveries which
can be completed without failure is thus estimated as a function of various
parameters. The main parameters are the gate (gamma) and memory (epsilon)
failure rates, the physical scale-up of the computer size, and the time t_m
required for measurements and classical processing. The achievable computation
size is given as a surface in parameter space. This indicates the noise
threshold as well as other information. It is found that concatenated codes
based on the [[23,1,7]] Golay code give higher thresholds than those based on
the [[7,1,3]] Hamming code under most conditions. The threshold gate noise
gamma_0 is a function of epsilon/gamma and t_m; example values are
{epsilon/gamma, t_m, gamma_0} = {1, 1, 0.001}, {0.01, 1, 0.003}, {1, 100,
0.0001}, {0.01, 100, 0.002}, assuming zero cost for information transport. This
represents an order of magnitude increase in tolerated memory noise, compared
with previous calculations, which is made possible by recent insights into the
fault-tolerant QEC process.Comment: 21 pages, 12 figures, minor mistakes corrected and layout improved,
ref added; v4: clarification of assumption re logic gate
Context, spacetime loops, and the interpretation of quantum mechanics
Three postulates are discussed: first that well-defined properties cannot be
assigned to an isolated system, secondly that quantum unitary evolution is
atemporal, and thirdly that some physical processes are never reversed. It is
argued that these give useful insight into quantum behaviour. The first
postulate emphasizes the fundamental role in physics of interactions and
correlations, as opposed to internal properties of systems. Statements about
physical interactions can only be framed in a context of further interactions.
This undermines the possibility of objectivity in physics. However, quantum
mechanics retains objectivity through the combination of the second and third
postulates. A rule is given for determining the circumstances in which physical
evolution is non-unitary. This rule appeals to the absence of spacetime loops
in the future evolution of a set of interacting systems. A single universe
undergoing non-unitary evolution is a viable interpretation.Comment: 19 pages. For special issue of J.Phys.A, "The Quantum Universe", on
the occasion of 70th birthday of Professor Giancarlo Ghirard
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