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Real-time operator evolution in two and three dimensions via sparse Pauli dynamics
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We study real-time operator evolution using sparse Pauli dynamics, a recently developed method for simulating expectation values of quantum circuits. On the examples of energy and charge diffusion in 1D spin chains and sudden quench dynamics in the 2D transverse-field Ising model, it is shown that this approach can compete with state-of-the-art tensor network methods. We further demonstrate the flexibility of the approach by studying quench dynamics in the 3D transverse-field Ising model which is highly challenging for tensor network methods. For the simulation of expectation value dynamics starting in a computational basis state, we introduce an extension of sparse Pauli dynamics that truncates the growing sum of Pauli operators by discarding terms with a large number of X and Y matrices. This is validated by our 2D and 3D simulations. Finally, we argue that sparse Pauli dynamics is not only capable of converging challenging observables to high accuracy, but can also serve as a reliable approximate approach even when given only limited computational resources.
Forward citations
Cited by 4 Pith papers
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A one-layer UCJ quantum chemistry circuit can have its energy computed classically in O(N^7) time, so single-layer UCJ circuits cannot provide quantum advantage for energy estimation.
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Second-order out-of-time-order correlators measured on 65-qubit random circuits remain sensitive to dynamics and are estimated to be beyond the reach of current classical tensor-network simulation.
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Efficient computation of real-time correlators using Pauli Propagation
Short-time truncated Pauli propagation combined with low-rank positive semi-definite time extension recovers dynamical structure factors for 1D/2D Heisenberg models beyond the direct Pauli window.
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Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra
ORQA, a Pauli-string based simulation framework, is parallelized to run on Fugaku with up to 2^17 processes, tracking over a trillion Pauli strings and reproducing kicked Ising results.
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