3,889 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
Effects of noise on quantum error correction algorithms
It has recently been shown that there are efficient algorithms for quantum
computers to solve certain problems, such as prime factorization, which are
intractable to date on classical computers. The chances for practical
implementation, however, are limited by decoherence, in which the effect of an
external environment causes random errors in the quantum calculation. To combat
this problem, quantum error correction schemes have been proposed, in which a
single quantum bit (qubit) is ``encoded'' as a state of some larger number of
qubits, chosen to resist particular types of errors. Most such schemes are
vulnerable, however, to errors in the encoding and decoding itself. We examine
two such schemes, in which a single qubit is encoded in a state of qubits
while subject to dephasing or to arbitrary isotropic noise. Using both
analytical and numerical calculations, we argue that error correction remains
beneficial in the presence of weak noise, and that there is an optimal time
between error correction steps, determined by the strength of the interaction
with the environment and the parameters set by the encoding.Comment: 26 pages, LaTeX, 4 PS figures embedded. Reprints available from the
authors or http://eve.physics.ox.ac.uk/QChome.htm
Benchmarking quantum control methods on a 12-qubit system
In this letter, we present an experimental benchmark of operational control
methods in quantum information processors extended up to 12 qubits. We
implement universal control of this large Hilbert space using two complementary
approaches and discuss their accuracy and scalability. Despite decoherence, we
were able to reach a 12-coherence state (or 12-qubits pseudo-pure cat state),
and decode it into an 11 qubit plus one qutrit labeled observable pseudo-pure
state using liquid state nuclear magnetic resonance quantum information
processors.Comment: 11 pages, 4 figures, to be published in PR
Experimental Implementation of a Codeword Stabilized Quantum Code
A five-qubit codeword stabilized quantum code is implemented in a seven-qubit
system using nuclear magnetic resonance (NMR). Our experiment implements a good
nonadditive quantum code which encodes a larger Hilbert space than any
stabilizer code with the same length and capable of correcting the same kind of
errors. The experimentally measured quantum coherence is shown to be robust
against artificially introduced errors, benchmarking the success in
implementing the quantum error correction code. Given the typical decoherence
time of the system, our experiment illustrates the ability of coherent control
to implement complex quantum circuits for demonstrating interesting results in
spin qubits for quantum computing
Iterative Optimization of Quantum Error Correcting Codes
We introduce a convergent iterative algorithm for finding the optimal coding
and decoding operations for an arbitrary noisy quantum channel. This algorithm
does not require any error syndrome to be corrected completely, and hence also
finds codes outside the usual Knill-Laflamme definition of error correcting
codes. The iteration is shown to improve the figure of merit "channel fidelity"
in every step.Comment: 5 pages, 2 figures, REVTeX 4; stability of algorithm include
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