Approximate simulation of complex quantum circuits using sparse tensors

The study of quantum circuit simulation using classical computers is a key research topic that helps define the boundary of verifiable quantum advantage, solve quantum many-body problems, and inform development of quantum hardware and software. Tensor networks have become forefront mathematical tools for these tasks. Here we introduce a method to approximately simulate quantum circuits using sparsely-populated tensors. We describe a sparse tensor data structure that can represent quantum states with no underlying symmetry, and outline algorithms to efficiently contract and truncate these tensors. We show that the data structure and contraction algorithm are efficient, leading to expected runtime scalings versus qubit number and circuit depth. Our results motivate future research in optimization of sparse tensor networks for quantum simulation.

💡 Research Summary

The paper introduces a novel approach, termed Truncated Sparse Tensor Simulation (TruSTS), for approximately simulating quantum circuits on classical hardware using sparsely populated tensors. Traditional tensor‑network simulators rely heavily on symmetries, low‑dimensional structures, or matrix‑product‑state representations, which limits their applicability to highly random or highly entangled circuits. TruSTS overcomes this limitation by representing a quantum state |ψ⟩ with at most k non‑zero amplitudes, stored in two fixed‑size arrays: an integer array x