Licentiatseminarium: Basudha Srivastava

Opponent: Alexandre Graell I Amat (Chalmers, E2)
Examinator: Bernhard Mehlig
Handledare: Mats Granath 
Bihandledare: Anton Frisk Kockum (Chalmers, MC2)

Abstract

Quantum systems are adversely affected by noise due to interactions with the environment. Quantum error correction is a technique that relies on the principle of redundancy to encode logical information in additional qubits to better protect the system against noise, and is required in order to design a viable quantum computer. One of the most popular classes of quantum error-correcting codes are topological stabilizer codes, which use repeated local measurements to detect and correct errors on the code.

In this thesis, we present a novel topological stabilizer code, the XYZ^2 code, which is implemented on a hexagonal grid of qubits and encodes a logical qubit with the help of weight-six and weight-two stabilizer measurements. This code has the advantage of having a quadratic distance (2d^2) for pure Z noise and pure Y noise, where d is the minimum distance of the code that utilizes 2d^2 physical qubits. The code demonstrates high thresholds and reduced logical failure rates for biased noise error models simulated under perfect stabilizer measurement conditions.

We also present a maximum-likelihood decoder for stabilizer codes, called the effective weight and degeneracy (EWD) decoder. The EWD decoder uses Metropolis-based Monte Carlo sampling to find the most likely equivalence class for a given error syndrome, whose implementation depends on the bias of the noise model and is independent of the physical error rate of the qubits. The EWD decoder is a near-optimal decoder that is efficient, fast and can be easily modified to characterize new topological stabilizer codes, such as the XYZ^2 code.