Implications of electronics constraints for solid-state quantum error correction and quantum circuit failure probability

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.

Probabilities of Failure for Quantum Error Correction

Mixed-state entanglement and quantum error correction.

Entanglement purification protocols (EPP) and quantum errorcorrecting codes (QECC) provide two ways of protecting quantum states from interaction with the environment. In an EPP, perfectly entangled pure states are extracted, with some yield D, from a bipartite mixed state M ; with a QECC, an arbitrary quantum state |ξ〉 can be transmitted at some rate Q through a noisy channel χ without degrada...

Implications of ignorance for quantum-error-correction thresholds

Quantum error-correcting codes have a distance parameter, conveying the minimum number of single spin errors that could cause error correction to fail. However, the success thresholds of the finite per-qubit error rate that have been proven for the likes of the toric code require them to work well beyond this limit. We argue that, without the assumption of being below the distance limit, the su...

Quantum Steganography and Quantum Error-Correction

xiv Chapter 1: Introduction 1 1.1 A Brief History of Quantum Information Science . . . . . . . . . . . . . . 1 1.2 Thesis Organization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Chapter 2: Quantum Stabilizer Codes 9 2.1 The Stabilizer Formalism . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Quantum Error-Correction . . . . . . . . . . . . . . . . . . . . . . . ....