Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks
We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2022-05-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.3.020332 |
| _version_ | 1797681390434648064 |
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| author | ChunJun Cao Brad Lackey |
| author_facet | ChunJun Cao Brad Lackey |
| author_sort | ChunJun Cao |
| collection | DOAJ |
| description | We introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as nonstabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding or encoding circuit. To highlight the framework’s range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct nontrivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a three-dimensional stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the two-dimensional Bacon-Shor code after “dualizing” its tensor-network encoding map. |
| first_indexed | 2024-03-11T23:44:15Z |
| format | Article |
| id | doaj.art-aa9f4dc9fa284e5e9fc8e1fa1779ab83 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-11T23:44:15Z |
| publishDate | 2022-05-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-aa9f4dc9fa284e5e9fc8e1fa1779ab832023-09-19T14:03:53ZengAmerican Physical SocietyPRX Quantum2691-33992022-05-013202033210.1103/PRXQuantum.3.020332Quantum Lego: Building Quantum Error Correction Codes from Tensor NetworksChunJun CaoBrad LackeyWe introduce a flexible and graphically intuitive framework that constructs complex quantum error correction codes from simple codes or states, generalizing code concatenation. More specifically, we represent the complex code constructions as tensor networks built from the tensors of simple codes or states in a modular fashion. Using a set of local moves known as operator pushing, one can derive properties of the more complex codes, such as transversal non-Clifford gates, by tracing the flow of operators in the network. The framework endows a network geometry to any code it builds and is valid for constructing stabilizer codes as well as nonstabilizer codes over qubits and qudits. For a contractible tensor network, the sequence of contractions also constructs a decoding or encoding circuit. To highlight the framework’s range of capabilities and to provide a tutorial, we lay out some examples where we glue together simple stabilizer codes to construct nontrivial codes. These examples include the toric code and its variants, a holographic code with transversal non-Clifford operators, a three-dimensional stabilizer code, and other stabilizer codes with interesting properties. Surprisingly, we find that the surface code is equivalent to the two-dimensional Bacon-Shor code after “dualizing” its tensor-network encoding map.http://doi.org/10.1103/PRXQuantum.3.020332 |
| spellingShingle | ChunJun Cao Brad Lackey Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks PRX Quantum |
| title | Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks |
| title_full | Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks |
| title_fullStr | Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks |
| title_full_unstemmed | Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks |
| title_short | Quantum Lego: Building Quantum Error Correction Codes from Tensor Networks |
| title_sort | quantum lego building quantum error correction codes from tensor networks |
| url | http://doi.org/10.1103/PRXQuantum.3.020332 |
| work_keys_str_mv | AT chunjuncao quantumlegobuildingquantumerrorcorrectioncodesfromtensornetworks AT bradlackey quantumlegobuildingquantumerrorcorrectioncodesfromtensornetworks |