96 citations · 446 across the 36 of their papers we have counts for
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Quantum Data-Syndrome Codes
Alexei Ashikhmin, Ching-Yi Lai, Todd A. Brun
Performing active quantum error correction to protect fragile quantum states highly depends on the correctness of error information--error syndromes. To obtain reliable error syndr…
Quantum convolutional data-syndrome codes
Weilei Zeng, Alexei Ashikhmin, Michael Woolls +1
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, i…
Fidelity Lower Bounds for Stabilizer and CSS Quantum Codes
Alexei Ashikhmin
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find th…
Asymptotically Good Quantum Codes
A. Ashikhmin, S. Litsyn, M. A. Tsfasman
Using algebraic geometry codes we give a polynomial construction of quantum codes with asymptotically non-zero rate and relative distance.
Nonbinary Quantum Stabilizer Codes
Alexei Ashikhmin, Emanuel Knill
We define and show how to construct nonbinary quantum stabilizer codes. Our approach is based on nonbinary error bases. It generalizes the relationship between selforthogonal codes…
Quantum Error Detection II: Bounds
A. Ashikhmin, A. Barg, E. Knill +1
In Part II we show that there exist quantum codes whose probability of undetected error falls exponentially with the length of the code and derive bounds on this exponent.The lower…