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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.04240 |
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| _version_ | 1866917903075377152 |
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| author | Watson, James D. |
| author_facet | Watson, James D. |
| contents | The quantum stochastic drift protocol, also known as qDRIFT, has become a popular algorithm for implementing time-evolution of quantum systems using randomised compiling. In this work we develop qFLO, a higher order randomised algorithm for time-evolution. To estimate an observable expectation value at time $T$ to precision $ε$, we show it is sufficient to use circuit depths of $O(T^2\log(1/ε))$ -- an exponential improvement over standard qDRIFT requirements with respect to $ε$. The protocol achieves this using $O(1/ε^2)$ repeated runs of the standard qDRIFT protocol combined with classical post-processing in the form of Richardson extrapolation. Notably, it requires no ancillary qubits or additional control gates making it especially promising for near-term quantum devices. Furthermore, it is well-conditioned and inherits many desirable properties of randomly compiled simulation methods, including circuit depths that do not explicitly depend on the number of terms in the Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04240 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Randomly Compiled Quantum Simulation with Exponentially Reduced Circuit Depths Watson, James D. Quantum Physics The quantum stochastic drift protocol, also known as qDRIFT, has become a popular algorithm for implementing time-evolution of quantum systems using randomised compiling. In this work we develop qFLO, a higher order randomised algorithm for time-evolution. To estimate an observable expectation value at time $T$ to precision $ε$, we show it is sufficient to use circuit depths of $O(T^2\log(1/ε))$ -- an exponential improvement over standard qDRIFT requirements with respect to $ε$. The protocol achieves this using $O(1/ε^2)$ repeated runs of the standard qDRIFT protocol combined with classical post-processing in the form of Richardson extrapolation. Notably, it requires no ancillary qubits or additional control gates making it especially promising for near-term quantum devices. Furthermore, it is well-conditioned and inherits many desirable properties of randomly compiled simulation methods, including circuit depths that do not explicitly depend on the number of terms in the Hamiltonian. |
| title | Randomly Compiled Quantum Simulation with Exponentially Reduced Circuit Depths |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.04240 |