Adaptive quantum codes: constructions, applications and fault tolerance

TL;DR

This paper introduces adaptive quantum error correction codes tailored to specific noise models, proposing a numerical optimization construction, demonstrating high-fidelity quantum information transmission, and establishing fault-tolerance thresholds.

Contribution

It presents a new numerical method for constructing noise-adapted quantum codes, applies these codes to quantum communication, and analyzes their fault-tolerance capabilities.

Findings

Proposed a fast numerical optimization algorithm for code construction.

Achieved high-fidelity quantum information transmission over a spin chain.

Established a lower bound on fault-tolerance threshold for adaptive codes.

Abstract

A major obstacle towards realizing a practical quantum computer is the noise that arises due to system-environment interactions. While it is very well known that quantum error correction (QEC) provides a way to protect against errors that arise due to the noise affecting the system, a perfect quantum code requires atleast five physical qubits to observe a noticeable improvement over the no-QEC scenario. However, in cases where the noise structure in the system is already known, it might be more useful to consider quantum codes that are adapted to specific noise models. It is already known in the literature that such codes are resource efficient and perform on par with the standard codes. In this spirit, we address the following questions concerning such adaptive quantum codes in this thesis. (a) Construction: Given a noise model, we propose a simple and fast numerical optimization algorithm to search for good quantum codes. (b) Application: As a simple application of noise-adapted codes, we propose an adaptive QEC protocol that allows transmission of quantum information from one site to the other over a 1-d spin chain with high fidelity. (c) Fault-tolerance: Finally, we address the question of whether such noise-adapted QEC protocols can be made fault-tolerant starting with a [[4,1]] code and obtain a rigorous lower bound on threshold.