1,741 research outputs found
Implementation of the Five Qubit Error Correction Benchmark
The smallest quantum code that can correct all one-qubit errors is based on
five qubits. We experimentally implemented the encoding, decoding and
error-correction quantum networks using nuclear magnetic resonance on a five
spin subsystem of labeled crotonic acid. The ability to correct each error was
verified by tomography of the process. The use of error-correction for
benchmarking quantum networks is discussed, and we infer that the fidelity
achieved in our experiment is sufficient for preserving entanglement.Comment: 6 pages with figure
Approximate quantum error correction for generalized amplitude damping errors
We present analytic estimates of the performances of various approximate
quantum error correction schemes for the generalized amplitude damping (GAD)
qubit channel. Specifically, we consider both stabilizer and nonadditive
quantum codes. The performance of such error-correcting schemes is quantified
by means of the entanglement fidelity as a function of the damping probability
and the non-zero environmental temperature. The recovery scheme employed
throughout our work applies, in principle, to arbitrary quantum codes and is
the analogue of the perfect Knill-Laflamme recovery scheme adapted to the
approximate quantum error correction framework for the GAD error model. We also
analytically recover and/or clarify some previously known numerical results in
the limiting case of vanishing temperature of the environment, the well-known
traditional amplitude damping channel. In addition, our study suggests that
degenerate stabilizer codes and self-complementary nonadditive codes are
especially suitable for the error correction of the GAD noise model. Finally,
comparing the properly normalized entanglement fidelities of the best
performant stabilizer and nonadditive codes characterized by the same length,
we show that nonadditive codes outperform stabilizer codes not only in terms of
encoded dimension but also in terms of entanglement fidelity.Comment: 44 pages, 8 figures, improved v
Global entanglement in multiparticle systems
We define a polynomial measure of multiparticle entanglement which is
scalable, i.e., which applies to any number of spin-1/2 particles. By
evaluating it for three particle states, for eigenstates of the one dimensional
Heisenberg antiferromagnet and on quantum error correcting code subspaces, we
illustrate the extent to which it quantifies global entanglement. We also apply
it to track the evolution of entanglement during a quantum computation.Comment: 9 pages, plain TeX, 1 PostScript figure included with epsf.tex
(ignore the under/overfull \vbox error messages); for related work see
http://math.ucsd.edu/~dmeyer/research.html or
http://www.math.ucsd.edu/~nwallach
Optimum Quantum Error Recovery using Semidefinite Programming
Quantum error correction (QEC) is an essential element of physical quantum
information processing systems. Most QEC efforts focus on extending classical
error correction schemes to the quantum regime. The input to a noisy system is
embedded in a coded subspace, and error recovery is performed via an operation
designed to perfectly correct for a set of errors, presumably a large subset of
the physical noise process. In this paper, we examine the choice of recovery
operation. Rather than seeking perfect correction on a subset of errors, we
seek a recovery operation to maximize the entanglement fidelity for a given
input state and noise model. In this way, the recovery operation is optimum for
the given encoding and noise process. This optimization is shown to be
calculable via a semidefinite program (SDP), a well-established form of convex
optimization with efficient algorithms for its solution. The error recovery
operation may also be interpreted as a combining operation following a quantum
spreading channel, thus providing a quantum analogy to the classical diversity
combining operation.Comment: 7 pages, 3 figure
Against Quantum Noise
This is a brief description of how to protect quantum states from dissipation
and decoherence that arise due to uncontrolled interactions with the
environment. We discuss recoherence and stabilisation of quantum states based
on two techniques known as "symmetrisation" and "quantum error correction". We
illustrate our considerations with the most popular quantum-optical model of
the system-environment interaction, commonly used to describe spontaneous
emission, and show the benefits of quantum error correction in this case.Comment: 12 pages. Presented at the International Conference "Quantum Optics
IV", Jaszowiec, Poland, June 17-24 1997. An introductory overview of quantum
dissipation and error correction. Late submission to the archive due to
requests and the limited availability of the journa
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