# Quantum Error Correction with Reflexive Stabilizer Codes and Cayley Graphs

@article{Vandermolen2021QuantumEC, title={Quantum Error Correction with Reflexive Stabilizer Codes and Cayley Graphs}, author={Robert Vandermolen and Duncan Wright}, journal={ArXiv}, year={2021}, volume={abs/2110.08414} }

Long distance communication of digital data, whether through a physical medium or a broadcast signal, is often subjected to noise. To deliver data reliably through noisy communication channels, one must use codes that can detect and correct the particular noise of the channel. For transmission of classical data, error correcting schemes can be as simple as the sending of replicates. For quantum data, and in tandem the development of machines that can process quantum data, quantum error…

## References

SHOWING 1-10 OF 26 REFERENCES

A Theory of Quantum Error-Correcting Codes

- Physics
- 1996

Quantum Error Correction will be necessary for preserving coherent states against noise and other unwanted interactions in quantum computation and communication. We develop a general theory of…

Good quantum error-correcting codes exist.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1996

The techniques investigated in this paper can be extended so as to reduce the accuracy required for factorization of numbers large enough to be difficult on conventional computers appears to be closer to one part in billions.

Multiple-particle interference and quantum error correction

- Physics, MathematicsProceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
- 1996

The concept of multiple-particle interference is discussed, using insights provided by the classical theory of error correcting codes. This leads to a discussion of error correction in a quantum…

Quantum Error Correction Via Codes Over GF(4)

- Mathematics, Computer ScienceIEEE 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.

Mixed-state entanglement and quantum error correction.

- Physics, MedicinePhysical review. A, Atomic, molecular, and optical physics
- 1996

It is proved that an EPP involving one-way classical communication and acting on mixed state M (obtained by sharing halves of Einstein-Podolsky-Rosen pairs through a channel) yields a QECC on \ensuremath{\chi} with rate Q=D, and vice versa, and it is proved Q is not increased by adding one- way classical communication.

Theory of fault-tolerant quantum computation

- Physics
- 1998

In order to use quantum error-correcting codes to improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a…

Automated error correction in IBM quantum computer and explicit generalization

- Computer Science, MathematicsQuantum Inf. Process.
- 2018

An automated error correction code is experimentally realized and the nondestructive discrimination of GHZ states in IBM 5-qubit quantum computer is demonstrated and generalize the investigated code for maximally entangled n-qudit case.

Perfect Quantum Error Correcting Code.

- Physics, MathematicsPhysical review letters
- 1996

A quantum error correction code which protects a qubit of information against general one qubit errors and encode the original state by distributing quantum information over five qubits, the minimal number required for this task.

Synthesis of Logical Clifford Operators via Symplectic Geometry

- Computer Science, Mathematics2018 IEEE International Symposium on Information Theory (ISIT)
- 2018

A mathematical framework for synthesizing physical circuits that implement logical Clifford operators for stabilizer codes, and a proof of concept synthesis of universal Clifford gates for the well-known $k(k+1)/2) code is provided.

Quantum computing cryptography: Finding cryptographic Boolean functions with quantum annealing by a 2000 qubit D-wave quantum computer

- Mathematics, Physics
- 2020

This work shows how to codify super-exponential cryptographic problems into quantum annealers and paves the way for reaching quantum supremacy with an adequately designed chip.