Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes
The Gottesman-Kitaev-Preskill (GKP) error-correcting code encodes a finite-dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we introduce a new subsystem decomposition for GKP codes that we...
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-02-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.5.010331 |
| _version_ | 1827343569271128064 |
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| author | Mackenzie H. Shaw Andrew C. Doherty Arne L. Grimsmo |
| author_facet | Mackenzie H. Shaw Andrew C. Doherty Arne L. Grimsmo |
| author_sort | Mackenzie H. Shaw |
| collection | DOAJ |
| description | The Gottesman-Kitaev-Preskill (GKP) error-correcting code encodes a finite-dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we introduce a new subsystem decomposition for GKP codes that we call the stabilizer subsystem decomposition, analogous to the usual approach to quantum stabilizer codes. The decomposition has the defining property that a partial trace over the nonlogical stabilizer subsystem is equivalent to an ideal decoding of the logical state, distinguishing it from previous GKP subsystem decompositions. We describe how to decompose arbitrary states across the subsystem decomposition using a set of transformations that move between the decompositions of different GKP codes. Besides providing a convenient theoretical view on GKP codes, such a decomposition is also of practical use. We use the stabilizer subsystem decomposition to efficiently simulate noise acting on single-mode GKP codes, and in contrast to more conventional Fock basis simulations, we are able to consider essentially arbitrarily large photon numbers for realistic noise channels, such as loss and dephasing. |
| first_indexed | 2024-03-07T22:32:08Z |
| format | Article |
| id | doaj.art-eb8c35a483aa4911969739c79a8c1079 |
| institution | Directory Open Access Journal |
| issn | 2691-3399 |
| language | English |
| last_indexed | 2024-03-07T22:32:08Z |
| publishDate | 2024-02-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj.art-eb8c35a483aa4911969739c79a8c10792024-02-23T15:17:37ZengAmerican Physical SocietyPRX Quantum2691-33992024-02-015101033110.1103/PRXQuantum.5.010331Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill CodesMackenzie H. ShawAndrew C. DohertyArne L. GrimsmoThe Gottesman-Kitaev-Preskill (GKP) error-correcting code encodes a finite-dimensional logical space in one or more bosonic modes, and has recently been demonstrated in trapped ions and superconducting microwave cavities. In this work we introduce a new subsystem decomposition for GKP codes that we call the stabilizer subsystem decomposition, analogous to the usual approach to quantum stabilizer codes. The decomposition has the defining property that a partial trace over the nonlogical stabilizer subsystem is equivalent to an ideal decoding of the logical state, distinguishing it from previous GKP subsystem decompositions. We describe how to decompose arbitrary states across the subsystem decomposition using a set of transformations that move between the decompositions of different GKP codes. Besides providing a convenient theoretical view on GKP codes, such a decomposition is also of practical use. We use the stabilizer subsystem decomposition to efficiently simulate noise acting on single-mode GKP codes, and in contrast to more conventional Fock basis simulations, we are able to consider essentially arbitrarily large photon numbers for realistic noise channels, such as loss and dephasing.http://doi.org/10.1103/PRXQuantum.5.010331 |
| spellingShingle | Mackenzie H. Shaw Andrew C. Doherty Arne L. Grimsmo Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes PRX Quantum |
| title | Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes |
| title_full | Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes |
| title_fullStr | Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes |
| title_full_unstemmed | Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes |
| title_short | Stabilizer Subsystem Decompositions for Single- and Multimode Gottesman-Kitaev-Preskill Codes |
| title_sort | stabilizer subsystem decompositions for single and multimode gottesman kitaev preskill codes |
| url | http://doi.org/10.1103/PRXQuantum.5.010331 |
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