To use quantum systems for technological applications one first needs to preserve their
coherence for macroscopic time scales, even at finite temperature. Quantum error correction …

We present a family of local quantum channels whose steady states exhibit stable mixed-
state symmetry-protected topological (SPT) order. Motivated by recent experimental …

Historically, noise in superconducting circuits has been considered an obstacle to be
removed. A large fraction of the research effort in designing superconducting circuits has …

We prove that the quantum Gibbs states of spin systems above a certain threshold
temperature are approximate quantum Markov networks, meaning that the conditional …

This book presents a self-consistent review of quantum computation with topological
quantum codes. The book covers everything required to understand topological fault …

A self-correcting quantum memory can store and protect quantum information for a time that
increases without bound with the system size and without the need for active error …

While topological quantum computation is intrinsically fault-tolerant at zero temperature, it
loses its topological protection at any finite temperature. We present a scheme to protect the …

A physical realization of self-correcting quantum code would be profoundly useful for
constructing a quantum computer. In this theoretical work, we provide a partial solution to …

Active error decoding and correction of topological quantum codes—in particular the toric
code—remains one of the most viable routes to large scale quantum information processing …

We examine two proposals for marginally-self-correcting quantum memory: the cubic code
by Haah and the welded code by Michnicki. In particular, we prove explicitly that they are …