2,190 research outputs found
Trading classical and quantum computational resources
We propose examples of a hybrid quantum-classical simulation where a
classical computer assisted by a small quantum processor can efficiently
simulate a larger quantum system. First we consider sparse quantum circuits
such that each qubit participates in O(1) two-qubit gates. It is shown that any
sparse circuit on n+k qubits can be simulated by sparse circuits on n qubits
and a classical processing that takes time . Secondly, we
study Pauli-based computation (PBC) where allowed operations are
non-destructive eigenvalue measurements of n-qubit Pauli operators. The
computation begins by initializing each qubit in the so-called magic state.
This model is known to be equivalent to the universal quantum computer. We show
that any PBC on n+k qubits can be simulated by PBCs on n qubits and a classical
processing that takes time . Finally, we propose a purely
classical algorithm that can simulate a PBC on n qubits in a time where . This improves upon the brute-force simulation
method which takes time . Our algorithm exploits the fact that
n-fold tensor products of magic states admit a low-rank decomposition into
n-qubit stabilizer states.Comment: 14 pages, 4 figure
A Subband-Based SVM Front-End for Robust ASR
This work proposes a novel support vector machine (SVM) based robust
automatic speech recognition (ASR) front-end that operates on an ensemble of
the subband components of high-dimensional acoustic waveforms. The key issues
of selecting the appropriate SVM kernels for classification in frequency
subbands and the combination of individual subband classifiers using ensemble
methods are addressed. The proposed front-end is compared with state-of-the-art
ASR front-ends in terms of robustness to additive noise and linear filtering.
Experiments performed on the TIMIT phoneme classification task demonstrate the
benefits of the proposed subband based SVM front-end: it outperforms the
standard cepstral front-end in the presence of noise and linear filtering for
signal-to-noise ratio (SNR) below 12-dB. A combination of the proposed
front-end with a conventional front-end such as MFCC yields further
improvements over the individual front ends across the full range of noise
levels
Syndrome decoding of Reed-Muller codes and tensor decomposition over finite fields
Reed-Muller codes are some of the oldest and most widely studied
error-correcting codes, of interest for both their algebraic structure as well
as their many algorithmic properties. A recent beautiful result of Saptharishi,
Shpilka and Volk showed that for binary Reed-Muller codes of length and
distance , one can correct random errors
in time (which is well beyond the worst-case error
tolerance of ).
In this paper, we consider the problem of `syndrome decoding' Reed-Muller
codes from random errors. More specifically, given the
-bit long syndrome vector of a codeword corrupted in
random coordinates, we would like to compute the
locations of the codeword corruptions. This problem turns out to be equivalent
to a basic question about computing tensor decomposition of random low-rank
tensors over finite fields.
Our main result is that syndrome decoding of Reed-Muller codes (and the
equivalent tensor decomposition problem) can be solved efficiently, i.e., in
time. We give two algorithms for this problem:
1. The first algorithm is a finite field variant of a classical algorithm for
tensor decomposition over real numbers due to Jennrich. This also gives an
alternate proof for the main result of Saptharishi et al.
2. The second algorithm is obtained by implementing the steps of the
Berlekamp-Welch-style decoding algorithm of Saptharishi et al. in
sublinear-time. The main new ingredient is an algorithm for solving certain
kinds of systems of polynomial equations.Comment: 24 page
Decoding by Linear Programming
This paper considers the classical error correcting problem which is
frequently discussed in coding theory. We wish to recover an input vector from corrupted measurements . Here, is an by
(coding) matrix and is an arbitrary and unknown vector of errors. Is it
possible to recover exactly from the data ? We prove that under suitable
conditions on the coding matrix , the input is the unique solution to
the -minimization problem () provided that the support of the vector of
errors is not too large, for some . In short, can be recovered exactly by solving a
simple convex optimization problem (which one can recast as a linear program).
In addition, numerical experiments suggest that this recovery procedure works
unreasonably well; is recovered exactly even in situations where a
significant fraction of the output is corrupted.Comment: 22 pages, 4 figures, submitte
`The frozen accident' as an evolutionary adaptation: A rate distortion theory perspective on the dynamics and symmetries of genetic coding mechanisms
We survey some interpretations and related issues concerning the frozen hypothesis due to F. Crick and how it can be explained in terms of several natural mechanisms involving error correction codes, spin glasses, symmetry breaking and the characteristic robustness of genetic networks. The approach to most of these questions involves using elements of Shannon's rate distortion theory incorporating a semantic system which is meaningful for the relevant alphabets and vocabulary implemented in transmission of the genetic code. We apply the fundamental homology between information source uncertainty with the free energy density of a thermodynamical system with respect to transcriptional regulators and the communication channels of sequence/structure in proteins. This leads to the suggestion that the frozen accident may have been a type of evolutionary adaptation
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