127 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
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
Continuous Quantum Error Correction Through Local Operations
We propose local strategies to protect global quantum information. The
protocols, which are quantum error correcting codes for dissipative systems,
are based on environment measurements, direct feedback control and simple
encoding of the logical qubits into physical qutrits whose decaying transitions
are indistinguishable and equally probable. The simple addition of one extra
level in the description of the subsystems allows for local actions to fully
and deterministically protect global resources, such as entanglement. We
present codes for both quantum jump and quantum state diffusion measurement
strategies and test them against several sources of inefficiency. The use of
qutrits in information protocols suggests further characterization of
qutrit-qutrit disentanglement dynamics, which we also give together with simple
local environment measurement schemes able to prevent distillability sudden
death and even enhance entanglement in situations in which our feedback error
correction is not possible.Comment: Accepted for publication in Phys. Rev.
Robust Syndrome Extraction via BCH Encoding
Quantum data-syndrome (QDS) codes are a class of quantum error-correcting
codes that protect against errors both on the data qubits and on the syndrome
itself via redundant measurement of stabilizer group elements. One way to
define a QDS code is to choose a syndrome measurement code, a classical block
code that encodes the syndrome of the underlying quantum code by defining
additional stabilizer measurements. We propose the use of primitive
narrow-sense BCH codes as syndrome measurement codes. We show that these codes
asymptotically require extra measurements, where is the
number of stabilizer generators of the quantum code and is the number of
errors corrected by the BCH code. Previously, the best known general method of
constructing QDS codes out of quantum codes requires extra
measurements. As the number of additional syndrome measurements is a reasonable
metric for the amount of additional time a general QDS code requires, we
conclude that our construction protects against the same number of syndrome
errors with significantly less time overhead
Robust projective measurements through measuring code-inspired observables
Quantum measurements are ubiquitous in quantum information processing tasks,
but errors can render their outputs unreliable. Here, we present a scheme that
implements a robust projective measurement through measuring code-inspired
observables. Namely, given a projective POVM, a classical code and a constraint
on the number of measurement outcomes each observable can have, we construct
commuting observables whose measurement is equivalent to the projective
measurement in the noiseless setting. Moreover, we can correct errors on
the classical outcomes of the observables' measurement if the classical code
corrects errors. Since our scheme does not require the encoding of quantum
data onto a quantum error correction code, it can help construct robust
measurements for near-term quantum algorithms that do not use quantum error
correction. Moreover, our scheme works for any projective POVM, and hence can
allow robust syndrome extraction procedures in non-stabilizer quantum error
correction codes.Comment: 7 pages, 1 figure, 2 column
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