Classically estimating observables of noiseless quantum circuits
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arXiv
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| Autori principali: | , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909902745632768 |
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| author | Angrisani, Armando Schmidhuber, Alexander Rudolph, Manuel S. Cerezo, M. Holmes, Zoë Huang, Hsin-Yuan |
| author_facet | Angrisani, Armando Schmidhuber, Alexander Rudolph, Manuel S. Cerezo, M. Holmes, Zoë Huang, Hsin-Yuan |
| contents | We present a classical algorithm based on Pauli propagation for estimating expectation values of arbitrary observables on random unstructured quantum circuits across all circuit architectures and depths, including those with all-to-all connectivity. We prove that for any architecture where each circuit layer is randomly sampled from a distribution invariant under single-qubit rotations, our algorithm achieves a small error $\varepsilon$ on all circuits except for a small fraction $δ$. The computational time is polynomial in qubit count and circuit depth for any small constant $\varepsilon, δ$, and quasi-polynomial for inverse-polynomially small $\varepsilon, δ$. Our results show that estimating observables of quantum circuits exhibiting chaotic and locally scrambling behavior is classically tractable across all geometries. We further conduct numerical experiments beyond our average-case assumptions, demonstrating the potential utility of Pauli propagation methods for simulating real-time dynamics and finding low-energy states of physical Hamiltonians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_01706 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Classically estimating observables of noiseless quantum circuits Angrisani, Armando Schmidhuber, Alexander Rudolph, Manuel S. Cerezo, M. Holmes, Zoë Huang, Hsin-Yuan Quantum Physics Computational Complexity Mathematical Physics We present a classical algorithm based on Pauli propagation for estimating expectation values of arbitrary observables on random unstructured quantum circuits across all circuit architectures and depths, including those with all-to-all connectivity. We prove that for any architecture where each circuit layer is randomly sampled from a distribution invariant under single-qubit rotations, our algorithm achieves a small error $\varepsilon$ on all circuits except for a small fraction $δ$. The computational time is polynomial in qubit count and circuit depth for any small constant $\varepsilon, δ$, and quasi-polynomial for inverse-polynomially small $\varepsilon, δ$. Our results show that estimating observables of quantum circuits exhibiting chaotic and locally scrambling behavior is classically tractable across all geometries. We further conduct numerical experiments beyond our average-case assumptions, demonstrating the potential utility of Pauli propagation methods for simulating real-time dynamics and finding low-energy states of physical Hamiltonians. |
| title | Classically estimating observables of noiseless quantum circuits |
| topic | Quantum Physics Computational Complexity Mathematical Physics |
| url | https://arxiv.org/abs/2409.01706 |