88 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
Schemes for Parallel Quantum Computation Without Local Control of Qubits
Typical quantum computing schemes require transformations (gates) to be
targeted at specific elements (qubits). In many physical systems, direct
targeting is difficult to achieve; an alternative is to encode local gates into
globally applied transformations. Here we demonstrate the minimum physical
requirements for such an approach: a one-dimensional array composed of two
alternating 'types' of two-state system. Each system need be sensitive only to
the net state of its nearest neighbors, i.e. the number in state 1 minus the
number in state 2. Additionally, we show that all such arrays can perform quite
general parallel operations. A broad range of physical systems and interactions
are suitable: we highlight two potential implementations.Comment: 12 pages + 3 figures. Several small corrections mad
Efficient Computations of Encodings for Quantum Error Correction
We show how, given any set of generators of the stabilizer of a quantum code,
an efficient gate array that computes the codewords can be constructed. For an
n-qubit code whose stabilizer has d generators, the resulting gate array
consists of O(n d) operations, and converts k-qubit data (where k = n - d) into
n-qubit codewords.Comment: 16 pages, REVTeX, 3 figures within the tex
Decoherence of geometric phase gates
We consider the effects of certain forms of decoherence applied to both
adiabatic and non-adiabatic geometric phase quantum gates. For a single qubit
we illustrate path-dependent sensitivity to anisotropic noise and for two
qubits we quantify the loss of entanglement as a function of decoherence.Comment: 4 pages, 3 figure
Quantum Convolutional Error Correction Codes
I report two general methods to construct quantum convolutional codes for
quantum registers with internal states. Using one of these methods, I
construct a quantum convolutional code of rate 1/4 which is able to correct one
general quantum error for every eight consecutive quantum registers.Comment: To be reported in the 1st NASA Conf. on Quantum Comp., uses
llncs.sty, 12 page
Optimal correction of concatenated fault-tolerant quantum codes
We present a method of concatenated quantum error correction in which
improved classical processing is used with existing quantum codes and
fault-tolerant circuits to more reliably correct errors. Rather than correcting
each level of a concatenated code independently, our method uses information
about the likelihood of errors having occurred at lower levels to maximize the
probability of correctly interpreting error syndromes. Results of simulations
of our method applied to the [[4,1,2]] subsystem code indicate that it can
correct a number of discrete errors up to half of the distance of the
concatenated code, which is optimal.Comment: 7 pages, 2 figures, published versio
Loading of a Rb magneto-optic trap from a getter source
We study the properties of a Rb magneto-optic trap loaded from a commercial
getter source which provides a large flux of atoms for the trap along with the
capability of rapid turn-off necessary for obtaining long trap lifetimes. We
have studied the trap loading at two different values of background pressure to
determine the cross-section for Rb--N collisions to be 3.5(4)x10^{-14} cm^2
and that for Rb--Rb collisions to be of order 3x10^{-13} cm^2. At a background
pressure of 1.3x10^{-9} torr, we load more than 10^8 atoms into the trap with a
time constant of 3.3 s. The 1/e lifetime of trapped atoms is 13 s limited only
by background collisions.Comment: 5 pages, 5 figure
Quantum Stabilizer Codes and Classical Linear Codes
We show that within any quantum stabilizer code there lurks a classical
binary linear code with similar error-correcting capabilities, thereby
demonstrating new connections between quantum codes and classical codes. Using
this result -- which applies to degenerate as well as nondegenerate codes --
previously established necessary conditions for classical linear codes can be
easily translated into necessary conditions for quantum stabilizer codes.
Examples of specific consequences are: for a quantum channel subject to a
delta-fraction of errors, the best asymptotic capacity attainable by any
stabilizer code cannot exceed H(1/2 + sqrt(2*delta*(1-2*delta))); and, for the
depolarizing channel with fidelity parameter delta, the best asymptotic
capacity attainable by any stabilizer code cannot exceed 1-H(delta).Comment: 17 pages, ReVTeX, with two figure
Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
We describe the use of composite rotations to combat systematic errors in
single qubit quantum logic gates and discuss three families of composite
rotations which can be used to correct off-resonance and pulse length errors.
Although developed and described within the context of NMR quantum computing
these sequences should be applicable to any implementation of quantum
computation.Comment: 6 pages RevTex4 including 4 figures. Will submit to Phys. Rev.
Quantum disentanglers
It is not possible to disentangle a qubit in an unknown state from a
set of (N-1) ancilla qubits prepared in a specific reference state . That
is, it is not possible to {\em perfectly} perform the transformation
. The question is then how well we can do? We consider a number of
different methods of extracting an unknown state from an entangled state formed
from that qubit and a set of ancilla qubits in an known state. Measuring the
whole system is, as expected, the least effective method. We present various
quantum ``devices'' which disentangle the unknown qubit from the set of ancilla
qubits. In particular, we present the optimal universal disentangler which
disentangles the unknown qubit with the fidelity which does not depend on the
state of the qubit, and a probabilistic disentangler which performs the perfect
disentangling transformation, but with a probability less than one.Comment: 8 pages, 1 eps figur
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