1,580 research outputs found
A Unified and Generalized Approach to Quantum Error Correction
We present a unified approach to quantum error correction, called operator
quantum error correction. This scheme relies on a generalized notion of
noiseless subsystems that is not restricted to the commutant of the interaction
algebra. We arrive at the unified approach, which incorporates the known
techniques -- i.e. the standard error correction model, the method of
decoherence-free subspaces, and the noiseless subsystem method -- as special
cases, by combining active error correction with this generalized noiseless
subsystem method. Moreover, we demonstrate that the quantum error correction
condition from the standard model is a necessary condition for all known
methods of quantum error correction.Comment: 5 page
NP-hardness of decoding quantum error-correction codes
Though the theory of quantum error correction is intimately related to the
classical coding theory, in particular, one can construct quantum error
correction codes (QECCs) from classical codes with the dual containing
property, this does not necessarily imply that the computational complexity of
decoding QECCs is the same as their classical counterparts. Instead, decoding
QECCs can be very much different from decoding classical codes due to the
degeneracy property. Intuitively, one expect degeneracy would simplify the
decoding since two different errors might not and need not be distinguished in
order to correct them. However, we show that general quantum decoding problem
is NP-hard regardless of the quantum codes being degenerate or non-degenerate.
This finding implies that no considerably fast decoding algorithm exists for
the general quantum decoding problems, and suggests the existence of a quantum
cryptosystem based on the hardness of decoding QECCs.Comment: 5 pages, no figure. Final version for publicatio
Algebraic and information-theoretic conditions for operator quantum error-correction
Operator quantum error-correction is a technique for robustly storing quantum
information in the presence of noise. It generalizes the standard theory of
quantum error-correction, and provides a unified framework for topics such as
quantum error-correction, decoherence-free subspaces, and noiseless subsystems.
This paper develops (a) easily applied algebraic and information-theoretic
conditions which characterize when operator quantum error-correction is
feasible; (b) a representation theorem for a class of noise processes which can
be corrected using operator quantum error-correction; and (c) generalizations
of the coherent information and quantum data processing inequality to the
setting of operator quantum error-correction.Comment: 4 page
Quantum error correction benchmarks for continuous weak parity measurements
We present an experimental procedure to determine the usefulness of a
measurement scheme for quantum error correction (QEC). A QEC scheme typically
requires the ability to prepare entangled states, to carry out multi-qubit
measurements, and to perform certain recovery operations conditioned on
measurement outcomes. As a consequence, the experimental benchmark of a QEC
scheme is a tall order because it requires the conjuncture of many elementary
components. Our scheme opens the path to experimental benchmarks of individual
components of QEC. Our numerical simulations show that certain parity
measurements realized in circuit quantum electrodynamics are on the verge of
being useful for QEC
Preparing ground states of quantum many-body systems on a quantum computer
Preparing the ground state of a system of interacting classical particles is
an NP-hard problem. Thus, there is in general no better algorithm to solve this
problem than exhaustively going through all N configurations of the system to
determine the one with lowest energy, requiring a running time proportional to
N. A quantum computer, if it could be built, could solve this problem in time
sqrt(N). Here, we present a powerful extension of this result to the case of
interacting quantum particles, demonstrating that a quantum computer can
prepare the ground state of a quantum system as efficiently as it does for
classical systems.Comment: 7 pages, 1 figur
The structure of preserved information in quantum processes
We introduce a general operational characterization of information-preserving
structures (IPS) -- encompassing noiseless subsystems, decoherence-free
subspaces, pointer bases, and error-correcting codes -- by demonstrating that
they are isometric to fixed points of unital quantum processes. Using this, we
show that every IPS is a matrix algebra. We further establish a structure
theorem for the fixed states and observables of an arbitrary process, which
unifies the Schrodinger and Heisenberg pictures, places restrictions on
physically allowed kinds of information, and provides an efficient algorithm
for finding all noiseless and unitarily noiseless subsystems of the process
Large-scale patterns in trematode richness and infection levels in marine crustacean hosts
Little is known about the patterns of variation in parasitism in marine hosts. Trematodes, the dominant parasites in intertidal systems, are transmitted from their first intermediate hosts (snails) to a range of second intermediate hosts, including crustaceans. Using published studies of trematode infections in crustacean hosts, we investigated general patterns of variation in trematode species richness and infection levels (i.e. percentage of hosts infected and mean number of individual parasites per host). Since the production and release of infective stages in snails is strongly temperature dependent, we also investigated a potential decrease in trematode infection levels with increasing latitude (as a proxy for decreasing temperature). Trematode species richness in the crustacean hosts was generally low (mostly 1 or 2), and infection levels were moderate. However, there were differences among taxa in some groups, particularly among brachyuran crabs, which showed significantly higher values than in other groups. For amphipods, which were the only well-studied group across a large range of latitudes, we found negative correlations between latitude and the trematode species richness or measures of infection level considered here. These relationships persisted after correction of the potentially confounding effects of sampling effort, host body size and host generic identity (as a control for phylogenetic influences). We discuss these findings in light of environmental mediation of parasite transmission, in particular with respect to the probably fundamental role of temperature in driving the output of trematode infective stages in marine systems
Simulating Particle Dispersions in Nematic Liquid-Crystal Solvents
A new method is presented for mesoscopic simulations of particle dispersions
in nematic liquid crystal solvents. It allows efficient first-principle
simulations of the dispersions involving many particles with many-body
interactions mediated by the solvents. A simple demonstration is shown for the
aggregation process of a two dimentional dispersion.Comment: 5 pages, 5 figure
Optimal and Efficient Decoding of Concatenated Quantum Block Codes
We consider the problem of optimally decoding a quantum error correction code
-- that is to find the optimal recovery procedure given the outcomes of partial
"check" measurements on the system. In general, this problem is NP-hard.
However, we demonstrate that for concatenated block codes, the optimal decoding
can be efficiently computed using a message passing algorithm. We compare the
performance of the message passing algorithm to that of the widespread
blockwise hard decoding technique. Our Monte Carlo results using the 5 qubit
and Steane's code on a depolarizing channel demonstrate significant advantages
of the message passing algorithms in two respects. 1) Optimal decoding
increases by as much as 94% the error threshold below which the error
correction procedure can be used to reliably send information over a noisy
channel. 2) For noise levels below these thresholds, the probability of error
after optimal decoding is suppressed at a significantly higher rate, leading to
a substantial reduction of the error correction overhead.Comment: Published versio
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