QUANTUM ERROR-CORRECTION FOR SPATIALLY CORRELATED ERRORS

Quantum Error Correction of Time-correlated Errors

The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting a single error per error correction cycle. Yet, time-correlated error are common for physical implementations of quantum systems; an error corrected during the previous cycle may reoccur in the next cycle due to physical processes specific for each physical implementation of...

Quantum error correction for continuously detected errors

Quantum Error Correction in correlated quantum noise

The superiority of quantum computation over conventional computation relies on the fact that a quantumbit (qubit) register can be in the superposition of a very large number of classical computational states. At the same time, maintaining coherence of this highly superpositional state poses also the main obstacle for the realization of a quantum computer. For a small number of qubits this diffi...

Quantum Error-Correction Codes on Abelian Groups

We prove a general form of bit flip formula for the quantum Fourier transform on finite abelian groups and use it to encode some general CSS codes on these groups.

Modeling coherent errors in quantum error correction

Analysis of quantum error correcting codes is typically done using a stochastic, Pauli channel error model for describing the noise on physical qubits. However, it was recently found that coherent errors (systematic rotations) on physical data qubits result in both physical and logical error rates that differ significantly from those predicted by a Paulimodel. Herewe examine the accuracy of the...