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Quantum Simulation

On the Computational Complexity of Schrödinger Operators

arXiv
Authors: Yufan Zheng, Jiaqi Leng, Yizhou Liu, Xiaodi Wu

Year

2024

Paper ID

37018

Status

Preprint

Abstract Read

~2 min

Abstract Words

135

Citations

N/A

Abstract

We study computational problems related to the Schrödinger operator H = -Δ+ V in the real space under the condition that (i) the potential function V is smooth and has its value and derivative bounded within some polynomial of n and (ii) V only consists of O(1)-body interactions. We prove that (i) simulating the dynamics generated by the Schrödinger operator implements universal quantum computation, i.e., it is BQP-hard, and (ii) estimating the ground energy of the Schrödinger operator is as hard as estimating that of local Hamiltonians with no sign problem (a.k.a. stoquastic Hamiltonians), i.e., it is StoqMA-complete. This result is particularly intriguing because the ground energy problem for general bosonic Hamiltonians is known to be QMA-hard and it is widely believed that texttt{StoqMA}varsubsetneq texttt{QMA}.

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  • We study computational problems related to the Schrödinger operator H = -Δ+ V in the real space under the condition that (i) the potential function V is smooth and has its...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2411.05120 [2] arXiv https://arxiv.org/abs/2411.05120 [3] Publisher https://arxiv.org/abs/2411.05120

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