883 research outputs found
Entanglement Increases the Error-Correcting Ability of Quantum Error-Correcting Codes
If entanglement is available, the error-correcting ability of quantum codes
can be increased. We show how to optimize the minimum distance of an
entanglement-assisted quantum error-correcting (EAQEC) code, obtained by adding
ebits to a standard quantum error-correcting code, over different encoding
operators. By this encoding optimization procedure, we found several new EAQEC
codes, including a family of [[n, 1, n; n-1]] EAQEC codes for n odd and code
parameters [[7, 1, 5; 2]], [[7, 1, 5; 3]], [[9, 1, 7; 4]], [[9, 1, 7; 5]],
which saturate the quantum singleton bound for EAQEC codes. A random search
algorithm for the encoding optimization procedure is also proposed.Comment: 39 pages, 10 table
The Encoding and Decoding Complexities of Entanglement-Assisted Quantum Stabilizer Codes
Quantum error-correcting codes are used to protect quantum information from
decoherence. A raw state is mapped, by an encoding circuit, to a codeword so
that the most likely quantum errors from a noisy quantum channel can be removed
after a decoding process.
A good encoding circuit should have some desired features, such as low depth,
few gates, and so on. In this paper, we show how to practically implement an
encoding circuit of gate complexity for an
quantum stabilizer code with the help of pairs of maximally-entangled
states. For the special case of an stabilizer code with , the
encoding complexity is , which is previously known to be
. For this suggests that the benefits from shared
entanglement come at an additional cost of encoding complexity.
Finally we discuss decoding of entanglement-assisted quantum stabilizer codes
and extend previously known computational hardness results on decoding quantum
stabilizer codes.Comment: accepted by the 2019 IEEE International Symposium on Information
Theory (ISIT2019
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
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