Quantum Supremacy for Simulating A Translation-Invariant Ising Spin Model

TL;DR

This paper presents a translation-invariant Ising spin model demonstrating quantum supremacy, showing it cannot be efficiently simulated classically, and proposes an experimental implementation with certification methods.

Contribution

Introduces a non-universal, translation-invariant Ising model with single-instance-hardness, enabling quantum supremacy demonstration and feasible experimental realization.

Findings

Classical intractability unless polynomial hierarchy collapses

Single fixed unitary evolution suffices for intractable results

Feasible experimental scheme with certification using local measurements

Abstract

We introduce an intermediate quantum computing model built from translation-invariant Ising-interacting spins. Despite being non-universal, the model cannot be classically efficiently simulated unless the polynomial hierarchy collapses. Equipped with the intrinsic single-instance-hardness property, a single fixed unitary evolution in our model is sufficient to produce classically intractable results, compared to several other models that rely on implementation of an ensemble of different unitaries (instances). We propose a feasible experimental scheme to implement our Hamiltonian model using cold atoms trapped in a square optical lattice. We formulate a procedure to certify the correct functioning of this quantum machine. The certification requires only a polynomial number of local measurements assuming measurement imperfections are sufficiently small.