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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.13855 |
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| _version_ | 1866912715464769536 |
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| author | Simon, William A. Love, Peter J. |
| author_facet | Simon, William A. Love, Peter J. |
| contents | Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme that does not increase the number of arbitrary rotations for symmetric Trotterizations, which applies to second-order and higher Suzuki-Trotter decompositions. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to resource estimates in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations dominate the $T$-cost of fault-tolerant implementations of quantum simulation. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_13855 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Halving the Cost of Controlled Time-Evolution Simon, William A. Love, Peter J. Quantum Physics Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme that does not increase the number of arbitrary rotations for symmetric Trotterizations, which applies to second-order and higher Suzuki-Trotter decompositions. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to resource estimates in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations dominate the $T$-cost of fault-tolerant implementations of quantum simulation. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation. |
| title | Halving the Cost of Controlled Time-Evolution |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2511.13855 |