Noisy Approach to Intrinsically Mixed-State Topological Order

Journal Article · 20 January 2025 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.6.010313 · OSTI ID:2504247

Sohal, Ramanjit ; Prem, Abhinav

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed state can display (imTO)—topological order that is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, “gauging out” anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and , which can appear as anomalous surface states of three-dimensional topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or nonmodular topological order. We argue that a partial classification of imTO is given in terms of nonmodular braided-fusion categories. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0009988
• OSTI ID: 2504247
• Journal Information: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 1 Vol. 6; ISSN 2691-3399; ISSN PQRUAG
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English