相关论文: Self-dual random-plaquette gauge model and the qua…

In this paper, we apply the method of Fourier transform and basis rewriting developed in arXiv:1910.13441 for the two-dimensional quantum double model of topological orders to the three-dimensional gauge theory model (with a gauge group…

Standard approaches to quantum error correction (QEC) require active maintenance using measurements and classical processing. Passive QEC, by contrast, has so far been established only in unphysical spatial dimensions. Here, we give an…

This paper presents a method for achieving equilibrium in the ISING Hamiltonian when confronted with unevenly distributed charges on an irregular grid. Employing (Multi-Edge) QC-LDPC codes and the Boltzmann machine, our approach involves…

We describe a computationally-efficient heuristic algorithm based on a renormalization-group procedure which aims at solving the problem of finding minimal surface given its boundary (curve) in any hypercubic lattice of dimension $D>2$. We…

We analyze several high dimensional generalizations of the toric code at nonzero temperature. We find that in large enough dimension, there can be a distinct separation between the critical temperature $T_c$, given by thermodynamic…

Given a two-dimensional quantum lattice model with an abelian gauge theory interpretation, we investigate a duality operation that amounts to gauging its invertible 1-form symmetry, followed by gauging the resulting 0-form symmetry in a…

We relate two classical dualities in low-dimensional quantum field theory: Kramers-Wannier duality of the Ising and related lattice models in $2$ dimensions, with electromagnetic duality for finite gauge theories in $3$ dimensions. The…

Higher rank gauge theories are generalizations of electromagnetism where, in addition to overall charge conservation, there is also conservation of higher rank multipoles such as the total dipole moment. In this work we study a four…

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 correction. We demonstrate that symmetry can lead to…

Fracton models provide examples of novel gapped quantum phases of matter that host intrinsically immobile excitations and therefore lie beyond the conventional notion of topological order. Here, we calculate optimal error thresholds for…

We derive the moduli dependent threshold corrections to gauge couplings in toroidal orbifold compactifications. The underlying six dimensional torus lattice of the heterotic string theory is not assumed ---as in previous calculations--- to…

We explore topological defects in the 4-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. This theory has 1-form $\mathbb{Z}_{2}$ center symmetry as well as the Kramers-Wannier-Wegner (KWW) duality. We construct the KWW duality…

Topological subsystem codes in three spatial dimensions allow for quantum error correction with no time overhead, even in the presence of measurement noise. The physical origins of this single-shot property remain elusive, in part due to…

The $SU(2){-}$gauged custodial two-Higgs-doublet model, which shares the same global-symmetry properties with the standard model, is studied non-perturbatively on the lattice. The additional Higgs doublet enlarges the scalar spectrum and…

Quantum computers are predicted to utilize quantum states to perform memory and to process tasks far faster than those of conventional classical computers. In this paper we show a new road towards building fault tolerance quantum computer…

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a $2+1$-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting…

In the quantum simulation of lattice gauge theories, gauge symmetry can be either fixed or encoded as a redundancy of the Hilbert space. While gauge-fixing reduces the number of qubits, keeping the gauge redundancy can provide code space to…

We investigate the stability of the topological phase of the toric code model in the presence of a uniform magnetic field by means of variational and high-order series expansion approaches. We find that when this perturbation is strong…

We investigate the effects of quenched bond randomness on the critical properties of the two-dimensional ferromagnetic Ising model embedded in a triangular lattice. The system is studied in both the pure and disordered versions by the same…

In this chapter we discuss aspects of the quantum critical behavior that occurs at a quantum phase transition separating a topological phase from a conventionally ordered one. We concentrate on a family of quantum lattice models, namely…