Noisy Approach to Intrinsically Mixed-State Topological Order
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 intrinsically mixed-state topological order (imTO)—topological order that is not expected to occur in the ground state...
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-01-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.6.010313 |
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| author | Ramanjit Sohal Abhinav Prem |
| author_facet | Ramanjit Sohal Abhinav Prem |
| author_sort | Ramanjit Sohal |
| collection | DOAJ |
| description | 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 intrinsically mixed-state topological order (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 topological subsystem codes, 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. |
| format | Article |
| id | doaj-art-a4af9dbbb2a74718a76d32f1d9f702c2 |
| institution | Kabale University |
| issn | 2691-3399 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-a4af9dbbb2a74718a76d32f1d9f702c22025-01-21T17:40:44ZengAmerican Physical SocietyPRX Quantum2691-33992025-01-016101031310.1103/PRXQuantum.6.010313Noisy Approach to Intrinsically Mixed-State Topological OrderRamanjit SohalAbhinav PremWe 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 intrinsically mixed-state topological order (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 topological subsystem codes, 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.http://doi.org/10.1103/PRXQuantum.6.010313 |
| spellingShingle | Ramanjit Sohal Abhinav Prem Noisy Approach to Intrinsically Mixed-State Topological Order PRX Quantum |
| title | Noisy Approach to Intrinsically Mixed-State Topological Order |
| title_full | Noisy Approach to Intrinsically Mixed-State Topological Order |
| title_fullStr | Noisy Approach to Intrinsically Mixed-State Topological Order |
| title_full_unstemmed | Noisy Approach to Intrinsically Mixed-State Topological Order |
| title_short | Noisy Approach to Intrinsically Mixed-State Topological Order |
| title_sort | noisy approach to intrinsically mixed state topological order |
| url | http://doi.org/10.1103/PRXQuantum.6.010313 |
| work_keys_str_mv | AT ramanjitsohal noisyapproachtointrinsicallymixedstatetopologicalorder AT abhinavprem noisyapproachtointrinsicallymixedstatetopologicalorder |