15,010 research outputs found
LEDAkem: a post-quantum key encapsulation mechanism based on QC-LDPC codes
This work presents a new code-based key encapsulation mechanism (KEM) called
LEDAkem. It is built on the Niederreiter cryptosystem and relies on
quasi-cyclic low-density parity-check codes as secret codes, providing high
decoding speeds and compact keypairs. LEDAkem uses ephemeral keys to foil known
statistical attacks, and takes advantage of a new decoding algorithm that
provides faster decoding than the classical bit-flipping decoder commonly
adopted in this kind of systems. The main attacks against LEDAkem are
investigated, taking into account quantum speedups. Some instances of LEDAkem
are designed to achieve different security levels against classical and quantum
computers. Some performance figures obtained through an efficient C99
implementation of LEDAkem are provided.Comment: 21 pages, 3 table
Analysing correlated noise on the surface code using adaptive decoding algorithms
Laboratory hardware is rapidly progressing towards a state where quantum
error-correcting codes can be realised. As such, we must learn how to deal with
the complex nature of the noise that may occur in real physical systems. Single
qubit Pauli errors are commonly used to study the behaviour of error-correcting
codes, but in general we might expect the environment to introduce correlated
errors to a system. Given some knowledge of structures that errors commonly
take, it may be possible to adapt the error-correction procedure to compensate
for this noise, but performing full state tomography on a physical system to
analyse this structure quickly becomes impossible as the size increases beyond
a few qubits. Here we develop and test new methods to analyse blue a particular
class of spatially correlated errors by making use of parametrised families of
decoding algorithms. We demonstrate our method numerically using a diffusive
noise model. We show that information can be learnt about the parameters of the
noise model, and additionally that the logical error rates can be improved. We
conclude by discussing how our method could be utilised in a practical setting
blue and propose extensions of our work to study more general error models.Comment: 19 pages, 8 figures, comments welcome; v2 - minor typos corrected
some references added; v3 - accepted to Quantu
Enhanced Feedback Iterative Decoding of Sparse Quantum Codes
Decoding sparse quantum codes can be accomplished by syndrome-based decoding
using a belief propagation (BP) algorithm.We significantly improve this
decoding scheme by developing a new feedback adjustment strategy for the
standard BP algorithm. In our feedback procedure, we exploit much of the
information from stabilizers, not just the syndrome but also the values of the
frustrated checks on individual qubits of the code and the channel model.
Furthermore we show that our decoding algorithm is superior to belief
propagation algorithms using only the syndrome in the feedback procedure for
all cases of the depolarizing channel. Our algorithm does not increase the
measurement overhead compared to the previous method, as the extra information
comes for free from the requisite stabilizer measurements.Comment: 10 pages, 11 figures, Second version, To be appeared in IEEE
Transactions on Information Theor
Quantum Error Correction beyond the Bounded Distance Decoding Limit
In this paper, we consider quantum error correction over depolarizing
channels with non-binary low-density parity-check codes defined over Galois
field of size . The proposed quantum error correcting codes are based on
the binary quasi-cyclic CSS (Calderbank, Shor and Steane) codes. The resulting
quantum codes outperform the best known quantum codes and surpass the
performance limit of the bounded distance decoder. By increasing the size of
the underlying Galois field, i.e., , the error floors are considerably
improved.Comment: To appear in IEEE Transactions on Information Theor
Upper Bounds on the Rate of Low Density Stabilizer Codes for the Quantum Erasure Channel
Using combinatorial arguments, we determine an upper bound on achievable
rates of stabilizer codes used over the quantum erasure channel. This allows us
to recover the no-cloning bound on the capacity of the quantum erasure channel,
R is below 1-2p, for stabilizer codes: we also derive an improved upper bound
of the form : R is below 1-2p-D(p) with a function D(p) that stays positive for
0 < p < 1/2 and for any family of stabilizer codes whose generators have
weights bounded from above by a constant - low density stabilizer codes.
We obtain an application to percolation theory for a family of self-dual
tilings of the hyperbolic plane. We associate a family of low density
stabilizer codes with appropriate finite quotients of these tilings. We then
relate the probability of percolation to the probability of a decoding error
for these codes on the quantum erasure channel. The application of our upper
bound on achievable rates of low density stabilizer codes gives rise to an
upper bound on the critical probability for these tilings.Comment: 32 page
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