Related papers: Topological quantum color code model on infinite l…
In this work, we consider 2D $\mathbb{Z}_2$ topologically ordered phases ($\mathbb{Z}_2$ toric code and the modified surface code) on a simple hyperbolic lattice. Introducing a 2D lattice consisting of the product of a 1D Cayley tree and a…
This is a note from a series of lectures at Encuentro Colombiano de Computacion Cuantica, Universidad de los Andes, Bogota, Colombia, 2015. The purpose is to introduce additive quantum error correcting codes, with emphasis on the use of…
Topological order, the hallmark of fractional quantum Hall states, is primarily defined in terms of ground-state degeneracy on higher-genus manifolds, e.g. the torus. We investigate analytically and numerically the smooth crossover between…
We study parallel fault-tolerant quantum computing for families of homological quantum low-density parity-check (LDPC) codes defined on 3-manifolds with constant or almost-constant encoding rate. We derive generic formula for a transversal…
Quantum error correction is a crucial technology for fault tolerant quantum computing. On superconducting platforms, hardware defects in large scale quantum processors can disrupt the regular lattice structure of topological codes and…
The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…
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…
We construct toric codes on various high-dimensional manifolds. Assuming a conjecture in geometry we find families of quantum CSS stabilizer codes on $N$ qubits with logarithmic weight stabilizers and distance $N^{1-\epsilon}$ for any…
In recent years, there have been many studies on local stabilizer codes. Under the assumption of translation and scale invariance Yoshida classified such codes. His result implies that translation invariant 2D color codes are equivalent to…
Topological phases of matter provide a flexible platform to engineer unconventional quantum excitations in quantum materials. Beyond single particle topological matter, in systems with strong quantum many-body correlations, many-body…
The physical realization of $\mathbb Z_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We predict that this phase of matter can be realized in a two-dimensional array of Rydberg atoms…
We use the topological entanglement entropy (TEE) as an efficient tool to fully characterize the Abelian phase of a $\mathbb{Z}_2 \times \mathbb{Z}_2$ spin liquid emerging as the ground state of topological color code (TCC), which is a…
Stabilizer codes lie at the heart of modern quantum-error-correcting codes (QECC). Of particular importance is a class called Calderbank-Shor-Steane (CSS) codes, which includes many important examples such as toric codes, color codes, and…
Accuracy thresholds of quantum error correcting codes, which exploit topological properties of systems, defined on two different arrangements of qubits are predicted. We study the topological color codes on the hexagonal lattice and on the…
The Kitaev surface-code model is the most studied example of a topologically ordered phase and typically involves four-spin interactions on a two-dimensional surface. A universal signature of this phase is topological entanglement entropy…
We study topological phases of time-reversal invariant singlet superconductors in three spatial dimensions. In these particle-hole symmetric systems the topological phases are characterized by an even-numbered winding number $\nu$. At a…
Quantum loop models are well studied objects in the context of lattice gauge theories and topological quantum computing. They usually carry long range entanglement that is captured by the topological entanglement entropy. I consider…
Engineering synthetic dimensions, where the physics of additional spatial dimensions is simulated within the internal states of a quantum system, allows the realisation of phenomena not otherwise accessible in experiments. Ultracold…
Enhancing robustness of topological orders against perturbations is one of the main goals in topological quantum computing. Since the kinetic of excitations is in conflict with the robustness of topological orders, any mechanism that…
We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry, where $G$ is a finite group. We provide projection operators for its quasiparticles content as irreducible…