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 suggest concrete models for self-correcting quantum memory by reporting examples of
local stabilizer codes in 3D that have no string logical operators. Previously known local …

The construction of a quantum computer remains a fundamental scientific and technological
challenge because of the influence of unavoidable noise. Quantum states and operations …

We analyze the performance of a quantum computer architecture combining a small
processor and a storage unit. By focusing on integer factorization, we show a reduction by …

We propose a new model of quantum computation comprised of low-weight measurement
sequences that simultaneously encode logical information, enable error correction, and …

Color codes are topological stabilizer codes with unusual transversality properties. Here I
show that their group of transversal gates is optimal and only depends on the spatial …

Estimating and reducing the overhead of fault-tolerance (FT) schemes is a crucial step
toward realizing scalable quantum computers. Of particular interest are schemes based on …

We present simple lattice realizations of symmetry-protected topological phases with q-form
global symmetries where charged excitations have q spatial dimensions. Specifically, we …

The topological color code and the toric code are two leading candidates for realizing fault-
tolerant quantum computation. Here we show that the color code on a d-dimensional closed …

We present a unifying framework to study physical systems which exhibit topological
quantum order (TQO). The major guiding principle behind our approach is that of …