Non-Pauli topological stabilizer codes from twisted quantum doubles

Abstract

It has long been known that long-ranged entangled topological phases can be exploited to protect quantum information against unwanted local errors. Indeed, conditions for intrinsic topological order are reminiscent of criteria for faithful quantum error correction. At the same time, the promise of using general topological orders for practical error correction remains largely unfulfilled to date. In this work, we significantly contribute to establishing such a connection by showing that Abelian twisted quantum double models can be used for quantum error correction. By exploiting the group cohomological data sitting at the heart of these lattice models, we transmute the terms of these Hamiltonians into full-rank, pairwise commuting operators, defining commuting stabilizers. The resulting codes are defined by non-Pauli commuting stabilizers, with local systems that can either be qubits or higher dimensional quantum systems. Thus, this work establishes a new connection between condensed matter physics and quantum information theory, and constructs tools to systematically devise new topological quantum error correcting codes beyond toric or surface code models.

arXiv commentv1: 18 pages, 3 figures, v2: stabilizer group explanation added, calculations and results unchanged, v3: extended last section for submission, v4: minor changes for published version

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Cited by in corpus (11)

• Intrinsic Mixed-state Topological Order
• Pauli stabilizer models of twisted quantum doubles
• Three-dimensional quantum cellular automata from chiral semion surface topological order and beyond
• The XP Stabiliser Formalism: a Generalisation of the Pauli Stabiliser Formalism with Arbitrary Phases
• Fracton Self-Statistics
• Topological error correcting processes from fixed-point path integrals
• Bulk-to-boundary anyon fusion from microscopic models
• Low-overhead non-Clifford fault-tolerant circuits for all non-chiral abelian topological phases
• Many-body quantum catalysts for transforming between phases of matter
• Error-mitigated initialization of surface codes with non-Pauli stabilizers
• Universal fault tolerant quantum computation in 2D without getting tied in knots