Randomized term grouping over physical law on digital quantum simulation

TL;DR

This paper presents physDrift, a randomized quantum algorithm based on qDrift for simulating Hamiltonian dynamics that respects physical conservation laws, demonstrating improved spectral accuracy and robustness on noisy quantum hardware.

Contribution

It introduces physDrift, a novel randomized algorithm for quantum simulation that maintains physical laws and performs well under noise, with empirical validation on hydrogen chains.

Findings

Better spectral error reduction compared to previous protocols

Effective noise modeling with circuit attenuation and depolarizing errors

Feasibility demonstrated on current noisy quantum hardware

Abstract

We introduce a randomized algorithm based on qDrift to compute Hamiltonian dynamics on digital quantum computers. We frame it as physDrift because conservation laws in physics are obeyed during evolution of arbitrary quantum states. Empirically we achieved better spectral error reduction with hydrogen chain model compared to previous protocols. Noisy model are investigated as well and we characterised them in the circuit with different schemes, i.e. an attenuation of the measured expectation value is fixed by keeping the circuit depth the same and depolarising error is simulated with randomly applied Pauli gates. This makes it our proposal particularly feasible for implementing and testing on present-day noisy hardware.