2,817 research outputs found
Tensor Networks and Quantum Error Correction
We establish several relations between quantum error correction (QEC) and
tensor network (TN) methods of quantum many-body physics. We exhibit
correspondences between well-known families of QEC codes and TNs, and
demonstrate a formal equivalence between decoding a QEC code and contracting a
TN. We build on this equivalence to propose a new family of quantum codes and
decoding algorithms that generalize and improve upon quantum polar codes and
successive cancellation decoding in a natural way.Comment: Accepted in Phys. Rev. Lett. 8 pages, 9 figure
Quantum Computing with Very Noisy Devices
In theory, quantum computers can efficiently simulate quantum physics, factor
large numbers and estimate integrals, thus solving otherwise intractable
computational problems. In practice, quantum computers must operate with noisy
devices called ``gates'' that tend to destroy the fragile quantum states needed
for computation. The goal of fault-tolerant quantum computing is to compute
accurately even when gates have a high probability of error each time they are
used. Here we give evidence that accurate quantum computing is possible with
error probabilities above 3% per gate, which is significantly higher than what
was previously thought possible. However, the resources required for computing
at such high error probabilities are excessive. Fortunately, they decrease
rapidly with decreasing error probabilities. If we had quantum resources
comparable to the considerable resources available in today's digital
computers, we could implement non-trivial quantum computations at error
probabilities as high as 1% per gate.Comment: 47 page
Blind Detection of Polar Codes
Polar codes were recently chosen to protect the control channel information
in the next-generation mobile communication standard (5G) defined by the 3GPP.
As a result, receivers will have to implement blind detection of polar coded
frames in order to keep complexity, latency, and power consumption tractable.
As a newly proposed class of block codes, the problem of polar-code blind
detection has received very little attention. In this work, we propose a
low-complexity blind-detection algorithm for polar-encoded frames. We base this
algorithm on a novel detection metric with update rules that leverage the a
priori knowledge of the frozen-bit locations, exploiting the inherent
structures that these locations impose on a polar-encoded block of data. We
show that the proposed detection metric allows to clearly distinguish
polar-encoded frames from other types of data by considering the cumulative
distribution functions of the detection metric, and the receiver operating
characteristic. The presented results are tailored to the 5G standardization
effort discussions, i.e., we consider a short low-rate polar code concatenated
with a CRC.Comment: 6 pages, 8 figures, to appear at the IEEE Int. Workshop on Signal
Process. Syst. (SiPS) 201
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