Approximate t-Designs in Generic Circuit Architectures
Unitary t-designs are distributions on the unitary group whose first t moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate t-designs. Here we show that these bounds can be extended to...
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| Format: | Article |
| Language: | English |
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American Physical Society
2024-12-01
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| Series: | PRX Quantum |
| Online Access: | http://doi.org/10.1103/PRXQuantum.5.040344 |
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| _version_ | 1850114600778858496 |
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| author | Daniel Belkin James Allen Soumik Ghosh Christopher Kang Sophia Lin James Sud Frederic T. Chong Bill Fefferman Bryan K. Clark |
| author_facet | Daniel Belkin James Allen Soumik Ghosh Christopher Kang Sophia Lin James Sud Frederic T. Chong Bill Fefferman Bryan K. Clark |
| author_sort | Daniel Belkin |
| collection | DOAJ |
| description | Unitary t-designs are distributions on the unitary group whose first t moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate t-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of one-dimensional brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is bounded, the circuit forms an approximate t-design in at most linear depth. We give numerical evidence for a stronger bound that depends only on the number of connected blocks into which the architecture can be divided. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures. |
| format | Article |
| id | doaj-art-d4c114325ea54d28964f709adffbbd5d |
| institution | OA Journals |
| issn | 2691-3399 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | PRX Quantum |
| spelling | doaj-art-d4c114325ea54d28964f709adffbbd5d2025-08-20T02:36:49ZengAmerican Physical SocietyPRX Quantum2691-33992024-12-015404034410.1103/PRXQuantum.5.040344Approximate t-Designs in Generic Circuit ArchitecturesDaniel BelkinJames AllenSoumik GhoshChristopher KangSophia LinJames SudFrederic T. ChongBill FeffermanBryan K. ClarkUnitary t-designs are distributions on the unitary group whose first t moments appear maximally random. Previous work has established several upper bounds on the depths at which certain specific random quantum circuit ensembles approximate t-designs. Here we show that these bounds can be extended to any fixed architecture of Haar-random two-site gates. This is accomplished by relating the spectral gaps of such architectures to those of one-dimensional brickwork architectures. Our bound depends on the details of the architecture only via the typical number of layers needed for a block of the circuit to form a connected graph over the sites. When this quantity is bounded, the circuit forms an approximate t-design in at most linear depth. We give numerical evidence for a stronger bound that depends only on the number of connected blocks into which the architecture can be divided. We also give an implicit bound for nondeterministic architectures in terms of properties of the corresponding distribution over fixed architectures.http://doi.org/10.1103/PRXQuantum.5.040344 |
| spellingShingle | Daniel Belkin James Allen Soumik Ghosh Christopher Kang Sophia Lin James Sud Frederic T. Chong Bill Fefferman Bryan K. Clark Approximate t-Designs in Generic Circuit Architectures PRX Quantum |
| title | Approximate t-Designs in Generic Circuit Architectures |
| title_full | Approximate t-Designs in Generic Circuit Architectures |
| title_fullStr | Approximate t-Designs in Generic Circuit Architectures |
| title_full_unstemmed | Approximate t-Designs in Generic Circuit Architectures |
| title_short | Approximate t-Designs in Generic Circuit Architectures |
| title_sort | approximate t designs in generic circuit architectures |
| url | http://doi.org/10.1103/PRXQuantum.5.040344 |
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