2,747 research outputs found
Ability of stabilizer quantum error correction to protect itself from its own imperfection
The theory of stabilizer quantum error correction allows us to actively
stabilize quantum states and simulate ideal quantum operations in a noisy
environment. It is critical is to correctly diagnose noise from its syndrome
and nullify it accordingly. However, hardware that performs quantum error
correction itself is inevitably imperfect in practice. Here, we show that
stabilizer codes possess a built-in capability of correcting errors not only on
quantum information but also on faulty syndromes extracted by themselves.
Shor's syndrome extraction for fault-tolerant quantum computation is naturally
improved. This opens a path to realizing the potential of stabilizer quantum
error correction hidden within an innocent looking choice of generators and
stabilizer operators that have been deemed redundant.Comment: 9 pages, 3 tables, final accepted version for publication in Physical
Review A (v2: improved main theorem, slightly expanded each section,
reformatted for readability, v3: corrected an error and typos in the proof of
Theorem 2, v4: edited language
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
Correction of Data and Syndrome Errors by Stabilizer Codes
Performing active quantum error correction to protect fragile quantum states
highly depends on the correctness of error information--error syndromes. To
obtain reliable error syndromes using imperfect physical circuits, we propose
the idea of quantum data-syndrome (DS) codes that are capable of correcting
both data qubits and syndrome bits errors. We study fundamental properties of
quantum DS codes and provide several CSS-type code constructions of quantum DS
codes.Comment: 2 figures. This is a short version of our full paper (in preparation
Quantum convolutional data-syndrome codes
We consider performance of a simple quantum convolutional code in a
fault-tolerant regime using several syndrome measurement/decoding strategies
and three different error models, including the circuit model.Comment: Abstract submitted for The 20th IEEE International Workshop on Signal
Processing Advances in Wireless Communications (SPAWC 2019
Fault-Tolerant Thresholds for Encoded Ancillae with Homogeneous Errors
I describe a procedure for calculating thresholds for quantum computation as
a function of error model given the availability of ancillae prepared in
logical states with independent, identically distributed errors. The thresholds
are determined via a simple counting argument performed on a single qubit of an
infinitely large CSS code. I give concrete examples of thresholds thus
achievable for both Steane and Knill style fault-tolerant implementations and
investigate their relation to threshold estimates in the literature.Comment: 14 pages, 5 figures, 3 tables; v2 minor edits, v3 completely revised,
submitted to PR
Efficient fault-tolerant quantum computing
Fault tolerant quantum computing methods which work with efficient quantum
error correcting codes are discussed. Several new techniques are introduced to
restrict accumulation of errors before or during the recovery. Classes of
eligible quantum codes are obtained, and good candidates exhibited. This
permits a new analysis of the permissible error rates and minimum overheads for
robust quantum computing. It is found that, under the standard noise model of
ubiquitous stochastic, uncorrelated errors, a quantum computer need be only an
order of magnitude larger than the logical machine contained within it in order
to be reliable. For example, a scale-up by a factor of 22, with gate error rate
of order , is sufficient to permit large quantum algorithms such as
factorization of thousand-digit numbers.Comment: 21 pages plus 5 figures. Replaced with figures in new format to avoid
problem
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