Quantum circuit expectation values and real-time operator evolution via sparse Pauli dynamics

We present sparse Pauli dynamics, a method for simulating quantum circuit expectation values and real-time operator evolution. The method is benchmarked on the example of kicked Ising model dynamics on 127 qubits, which was proposed as evidence for quantum utility of modern quantum devices. Here, we show that sparse Pauli dynamics can simulate observables orders of magnitude faster than the quantum experiment and can also be systematically converged beyond the experimental accuracy.

Furthermore, we study real-time operator evolution. 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.