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The bulk-boundary correspondence is a hallmark feature of topological phases of matter. Nonetheless, our understanding of the correspondence remains incomplete for phases with intrinsic topological order, and is nearly entirely lacking for…
We show how to obtain concrete constructions of homological quantum codes based on tilings of 2D surfaces with constant negative curvature (hyperbolic surfaces). This construction results in two-dimensional quantum codes whose tradeoff of…
We present a full quantum error correcting procedure with the semion code: an off-shell extension of the double semion model. We construct open strings operators that recover the quantum memory from arbitrary errors and closed string…
Surface codes describe quantum memory stored as a global property of interacting spins on a surface. The state space is fixed by a complete set of quasi-local stabilizer operators and the code dimension depends on the first homology group…
Typical topological systems undergo a topological phase transition in the presence of a strong enough perturbation. In this paper, we propose an adjustable frustrated Toric code with a "topological line" at which no phase transition happens…
The toric code can be constructed as a gauge theory of finite groups on oriented two dimensional lattices. Here we construct analogous models with the gauge fields belonging to groupoids, which are categories where every morphism has an…
We investigate topological order on fractal geometries embedded in $n$ dimensions. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a…
We explain how gapped quantum spin liquids, both conventional and 'fractonic', may be unambiguously diagnosed experimentally using the technique of multidimensional coherent spectroscopy. 'Conventional' gapped quantum spin liquids (e.g.…
We describe a superconducting circuit consisting of a Josephson junction in parallel with a quantum phase slip wire, which implements a Hamiltonian that is periodic in both charge and flux. This Hamiltonian is exactly diagonalisable in a…
We present a family of quantum error-correcting codes that support a universal set of transversal logic gates using only local operations on a two-dimensional array of physical qubits. The construction is a subsystem version of color codes…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
We propose a set of constraints on the ground-state wavefunctions of fracton phases, which provide a possible generalization of the string-net equations used to characterize topological orders in two spatial dimensions. Our constraint…
We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which…
The two-dimensional color code is an alternative to the toric code that encodes more logical qubits while maintaining crucial features of the $\mathbb{Z}_2\times\mathbb{Z}_2$ toric code in the long wavelength limit. However its short range…
A variety of past research on superconducting qubits shows that these devices exhibit considerable variation and thus cannot be accurately depicted by a uniform noise model. To combat this often unrealistic picture of homogeneous noise in…
Gauge theories form the foundation of the Standard Model of particle physics. These theories can exhibit confinement, where charged particles only occur in bound states, connected by flux strings whose energy grows linearly with separation.…
We first present a useful characterization of additive (stabilizer) quantum error-correcting codes. Then we present several examples of We first present a useful characterization of additive (stabilizer) quantum error--correcting codes.…
The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher…
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits…
We consider the problem of describing the typical (possibly) non-linear code of minimum distance bounded from below over a large alphabet. We concentrate on block codes with the Hamming metric and on subspace codes with the injection…