Codes and designs for quantum error correction : some recent developments through combinatorics (Designs, Codes, Graphs and Related Areas)

황규호

Yuichiro Fujiwara

Suppressing the effect of decoherence plays a vital role in the theory of quantum information processing.Despite many skepticisms about its feasibility, the existence of error correction schemes in the quantum do- main was proved in the last century, giving the birth to the field of quantum error correction.Since then, the new field has seen remarkably rapid progress in various directions including experimental realizations of quantum error-correcting codes.While quantum information science draws on many branches of physics, computer science, and mathematics, combinatorics is rapidly becoming an indispensable mathematical tool to the study of quantum error correction.In this note, we review some of the latest developments in quantum error correction where combinatorial design theory and coding theory play the central role.

Roffe, J., Zohren, S., Dominic C. Horsman +1 more

We introduce a new graphical framework for designing quantum error correction codes based on classical principles. A key feature of this graphical language, over previous approaches, is that it is closely related to that of factor graphs or graphical models in classical information theory and machine learning. It enables us to formulate the description of the recently-introduced ‘coherent parity check’ quantum error correction codes entirely within the language of classical information theory. This makes our construction accessible without requiring background in quantum error correction or even quantum mechanics in general. More importantly, this allows for a collaborative interplay where one can design new quantum error correction codes derived from classical codes.

Paul G. Baity, Anuj K. Nayak, Lav R. Varshney +4 more

Radiation impacts are a current challenge with computing on superconducting-based quantum devices because they can lead to widespread correlated errors across the device. Such errors can be problematic for quantum error correction (QEC) codes, which are generally designed to correct independent errors. To address this, we have developed a computational model to simulate the effects of radiation impacts on QEC performance. This is achieved by building from recently developed models of quasiparticle density, mapping radiation-induced qubit error rates onto a quantum error channel and simulation of a simple surface code. We also provide a performance metric to quantify the resilience of a QEC code to radiation impacts. Additionally, we sweep various parameters of chip design to test mitigation strategies for improved QEC performance. Our model approach is holistic, allowing for modular performance testing of error mitigation strategies and chip and code designs.

Zachary P. Bradshaw, Jeffrey J. Dale, Ethan N. Evans

Daniel A. Lidar, Todd A. Brun