Classically estimating observables of noiseless quantum circuits

• URL: http://arxiv.org/abs/2409.01706v2
• Date: Tue, 12 Aug 2025 12:42:04 GMT
• Title: Classically estimating observables of noiseless quantum circuits
• Authors: Armando Angrisani, Alexander Schmidhuber, Manuel S. Rudolph, M. Cerezo, Zoë Holmes, Hsin-Yuan Huang,
• Abstract summary: We present a classical algorithm for estimating expectation values of arbitrary observables on random unstructured quantum circuits.<n>Our results show that estimating observables of quantum circuits exhibiting chaotic and locally scrambling behavior is classically tractable across all geometries.
• Score: 36.688706661620905
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\delta$. The computational time is polynomial in qubit count and circuit depth for any small constant $\varepsilon, \delta$, and quasi-polynomial for inverse-polynomially small $\varepsilon, \delta$. 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.

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