# Avoiding coherent errors with rotated concatenated stabilizer codes

@article{Ouyang2020AvoidingCE,
title={Avoiding coherent errors with rotated concatenated stabilizer codes},
author={Yingkai Ouyang},
journal={npj Quantum Information},
year={2020},
volume={7},
pages={1-7}
}
• Yingkai Ouyang
• Published 1 October 2020
• Computer Science, Physics
• npj Quantum Information
Coherent errors, which arise from collective couplings, are a dominant form of noise in many realistic quantum systems, and are more damaging than oft considered stochastic errors. Here, we propose integrating stabilizer codes with constant-excitation codes by code concatenation. Namely, by concatenating an [[ n ,  k ,  d ]] stabilizer outer code with dual-rail inner codes, we obtain a [[2 n ,  k ,  d ]] constant-excitation code immune from coherent phase errors and also equivalent to a Pauli…
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## References

SHOWING 1-10 OF 50 REFERENCES
Permutation-Invariant Constant-Excitation Quantum Codes for Amplitude Damping
• Physics, Computer Science
IEEE Transactions on Information Theory
• 2020
The purpose of this paper is to give constant-excitation quantum codes that not only correct amplitude damping errors, but are also immune against permutations of their underlying modes.
High Performance Single-Error-Correcting Quantum Codes for Amplitude Damping
• Computer Science
IEEE Transactions on Information Theory
• 2011
These codes are nonadditive and most modestly outperform the best possible additive codes in terms of encoded dimension and are of the codeword stabilized (CWS) type, conceptually simple encoding and decoding circuits are available.
Detected-jump-error-correcting quantum codes, quantum error designs, and quantum computation
• Computer Science
• 2002
The construction of a family of one detected jump-error correcting quantumcodes is shown and the optimal redundancy, encoding and recovery as well as general properties ofdetected jump- error correcting quantum codes are discussed.
Stabilizer Slicing: Coherent Error Cancellations in Low-Density Parity-Check Stabilizer Codes.
• Physics
Physical review letters
• 2018
This Letter demonstrates that coherent noise is preferable to stochastic noise within certain code and gate implementations when the coherence is utilized effectively.
Optimal and efficient decoding of concatenated quantum block codes
These Monte Carlo results using the five-qubit and Steane's code on a depolarizing channel demonstrate significant advantages of the message-passing algorithms in two respects: Optimal decoding increases by as much as 94% the error threshold below which the error correction procedure can be used to reliably send information over a noisy channel.
Theory of quantum error-correcting codes
• Computer Science
• 1997
A general theory of quantum error correction based on encoding states into larger Hilbert spaces subject to known interactions is developed and necessary and sufficient conditions for the perfect recovery of an encoded state after its degradation by an interaction are obtained.
Quantum Error Correction Via Codes Over GF(4)
• Computer Science, Physics
IEEE Trans. Inf. Theory
• 1998
In the present paper the problem of finding quantum-error-correcting codes is transformed into one of finding additive codes over the field GF(4) which are self-orthogonal with respect to a certain trace inner product.
Bosonic quantum codes for amplitude damping
• Physics, Computer Science
• 1997
This work demonstrates alternative codes that correct just amplitude damping errors that allow, for example, a $t=1$, $k=1$ code using effectively $n=4.6$.
Approximate quantum error correction can lead to better codes
• Computer Science
• 1997
We present relaxed criteria for quantum error correction that are useful when the specific dominant quantum noise process is known. As an example, we provide a four-bit code that corrects for a