Related papers: Pauli stabilizer models of twisted quantum doubles
Tailored topological stabilizer codes in two dimensions have been shown to exhibit high storage threshold error rates and improved subthreshold performance under biased Pauli noise. Three-dimensional (3D) topological codes can allow for…
Quantum many-body scars (QMBS) have attracted considerable interest due to their role in weak ergodicity breaking in many-body systems. We present a general construction that embeds stabilizer states as QMBS of local Hamiltonians. The…
This work uncovers a fundamental connection between doped stabilizer states, a concept from quantum information theory, and the structure of eigenstates in perturbed many-body quantum systems. We prove that for Hamiltonians consisting of a…
We propose a family of explicit geometrically local circuits on a 2-dimensional planar grid of qudits, realizing any abelian non-chiral topological phase as an actively error-corrected fault-tolerant memory. These circuits are constructed…
Despite growing interest in beyond-group symmetries in quantum condensed matter systems, there are relatively few microscopic lattice models explicitly realizing these symmetries, and many phenomena have yet to be studied at the microscopic…
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…
We develop the quantum component of Algebraic Phase Theory by showing that quantum phase, Weyl noncommutativity, and stabiliser codes arise as unavoidable algebraic consequences of Frobenius duality. Working over finite commutative…
Exact quantum codes detecting a prescribed set of Pauli errors are approached through algebraic constructions--stabilizer, codeword-stabilized, permutation-invariant, topological, and related families. Geometrically, exact Pauli detection…
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…
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group…
We construct a family of infinitely many new candidate non-Abelian self-correcting topological quantum memories in $D\geq 5+1$ spacetime dimensions without particle excitations using local commuting non-Pauli stabilizer lattice models and…
We introduce the qudit Noisy Stabilizer Formalism, a framework for efficiently describing the evolution of stabilizer states in prime-power dimensions subject to generalized Pauli-diagonal noise under Clifford operations and generalized…
Nonabelian topological orders host exotic anyons central to quantum computing, yet established realizations rely on case-by-case constructions that are often conceptually involved. In this work, we present a systematic construction of…
Topological codes have many desirable properties that allow fault-tolerant quantum computation with relatively low overhead. A core challenge for these codes, however, is to achieve a low-overhead universal gate set with limited…
Qudits with local dimension $d>2$ can have unique structure and uses that qubits ($d=2$) cannot. Qudit Pauli operators provide a very useful basis of the space of qudit states and operators. We study the structure of the qudit Pauli group…
Perturbation theories provide valuable insights on quantum many-body systems. Systems of interacting particles, like electrons, are often treated perturbatively around exactly solvable Gaussian points. Systems of interacting qubits have…
We construct an exactly soluble Hamiltonian on the D=3 cubic lattice, whose ground state is a topological phase of bosons protected by time reversal symmetry, i.e a symmetry protected topological (SPT) phase. In this model anyonic…
We propose a non-commutative extension of the Pauli stabilizer formalism. The aim is to describe a class of many-body quantum states which is richer than the standard Pauli stabilizer states. In our framework, stabilizer operators are…
We extend the twisted gauge theory model of topological orders in three spatial dimensions to the case where the three spaces have two dimensional boundaries. We achieve this by systematically constructing the boundary Hamiltonians that are…
Motivated by the recent introduction of a $U(1)$-symmetric toric code model, we investigate symmetry-based deformations of topological order by systematically deconstructing the Gauss-law-enforcing star terms of the toric code (TC)…