321 research outputs found
Good Quantum Convolutional Error Correction Codes And Their Decoding Algorithm Exist
Quantum convolutional code was introduced recently as an alternative way to
protect vital quantum information. To complete the analysis of quantum
convolutional code, I report a way to decode certain quantum convolutional
codes based on the classical Viterbi decoding algorithm. This decoding
algorithm is optimal for a memoryless channel. I also report three simple
criteria to test if decoding errors in a quantum convolutional code will
terminate after a finite number of decoding steps whenever the Hilbert space
dimension of each quantum register is a prime power. Finally, I show that
certain quantum convolutional codes are in fact stabilizer codes. And hence,
these quantum stabilizer convolutional codes have fault-tolerant
implementations.Comment: Minor changes, to appear in PR
Degenerate Viterbi decoding
We present a decoding algorithm for quantum convolutional codes that finds
the class of degenerate errors with the largest probability conditioned on a
given error syndrome. The algorithm runs in time linear with the number of
qubits. Previous decoding algorithms for quantum convolutional codes optimized
the probability over individual errors instead of classes of degenerate errors.
Using Monte Carlo simulations, we show that this modification to the decoding
algorithm results in a significantly lower block error rate
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
Description of a quantum convolutional code
We describe a quantum error correction scheme aimed at protecting a flow of
quantum information over long distance communication. It is largely inspired by
the theory of classical convolutional codes which are used in similar
circumstances in classical communication. The particular example shown here
uses the stabilizer formalism, which provides an explicit encoding circuit. An
associated error estimation algorithm is given explicitly and shown to provide
the most likely error over any memoryless quantum channel, while its complexity
grows only linearly with the number of encoded qubits.Comment: 4 pages, uses revtex4. Minor correction in the encoding and decoding
circuit
The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure
Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing
and protecting fragile qubits against the undesirable effects of quantum
decoherence. Similar to classical codes, hashing bound approaching QECCs may be
designed by exploiting a concatenated code structure, which invokes iterative
decoding. Therefore, in this paper we provide an extensive step-by-step
tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided
concatenated quantum codes based on the underlying quantum-to-classical
isomorphism. These design lessons are then exemplified in the context of our
proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the
outer component of a concatenated quantum code. The proposed QIRCC can be
dynamically adapted to match any given inner code using EXIT charts, hence
achieving a performance close to the hashing bound. It is demonstrated that our
QIRCC-based optimized design is capable of operating within 0.4 dB of the noise
limit
Extra Shared Entanglement Reduces Memory Demand in Quantum Convolutional Coding
We show how extra entanglement shared between sender and receiver reduces the
memory requirements for a general entanglement-assisted quantum convolutional
code. We construct quantum convolutional codes with good error-correcting
properties by exploiting the error-correcting properties of an arbitrary basic
set of Pauli generators. The main benefit of this particular construction is
that there is no need to increase the frame size of the code when extra shared
entanglement is available. Then there is no need to increase the memory
requirements or circuit complexity of the code because the frame size of the
code is directly related to these two code properties. Another benefit, similar
to results of previous work in entanglement-assisted convolutional coding, is
that we can import an arbitrary classical quaternary code for use as an
entanglement-assisted quantum convolutional code. The rate and error-correcting
properties of the imported classical code translate to the quantum code. We
provide an example that illustrates how to import a classical quaternary code
for use as an entanglement-assisted quantum convolutional code. We finally show
how to "piggyback" classical information to make use of the extra shared
entanglement in the code.Comment: 7 pages, 1 figure, accepted for publication in Physical Review
Convolutional and tail-biting quantum error-correcting codes
Rate-(n-2)/n unrestricted and CSS-type quantum convolutional codes with up to
4096 states and minimum distances up to 10 are constructed as stabilizer codes
from classical self-orthogonal rate-1/n F_4-linear and binary linear
convolutional codes, respectively. These codes generally have higher rate and
less decoding complexity than comparable quantum block codes or previous
quantum convolutional codes. Rate-(n-2)/n block stabilizer codes with the same
rate and error-correction capability and essentially the same decoding
algorithms are derived from these convolutional codes via tail-biting.Comment: 30 pages. Submitted to IEEE Transactions on Information Theory. Minor
revisions after first round of review
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