Real-time operator evolution in two and three dimensions via sparse Pauli dynamics

Abstract

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.

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• Simulating quantum circuits with arbitrary local noise using Pauli Propagation
• Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements
• Hardware-efficient quantum phase estimation via local control
• Simulating dynamics of the two-dimensional transverse-field Ising model: a comparative study of large-scale classical numerics
• Utility-Scale Quantum State Preparation: Classical Training using Pauli Path Simulation
• Majorana string simulation of nonequilibrium dynamics in two-dimensional lattice fermion systems
• paces: Parallelized Application of Co-Evolving Subspaces, a method for computing quantum dynamics on GPUs
• A Heuristic for Matrix Product State Simulation of Out-of-Equilibrium Dynamics of Two-Dimensional Quantum Spin Systems
• Scalable Simulation of Quantum Many-Body Dynamics with Or-Represented Quantum Algebra