# Architectures for quantum simulation showing a quantum speedup

## TL;DR

This paper proposes feasible two-dimensional quantum simulation schemes that demonstrate quantum speedup, requiring minimal control and suitable for near-term experimental realization with platforms like cold atoms.

## Contribution

It introduces versatile, experimentally feasible schemes for quantum simulators that show quantum speedup using simple Hamiltonians and measurements, advancing towards practical demonstrations.

## Key findings

- Schemes show quantum speedup with minimal control
- Final states are efficiently certifiable
- Compatible with existing quantum platforms

## Abstract

One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy", referring to the experimental realization of a quantum device that computationally outperforms classical computers. In this work, we show that one can devise versatile and feasible schemes of two-dimensional dynamical quantum simulators showing such a quantum speedup, building on intermediate problems involving non-adaptive measurement-based quantum computation. In each of the schemes, an initial product state is prepared, potentially involving an element of randomness as in disordered models, followed by a short-time evolution under a basic translationally invariant Hamiltonian with simple nearest-neighbor interactions and a mere sampling measurement in a fixed basis. The correctness of the final state preparation in each scheme is fully efficiently certifiable. We discuss experimental necessities and possible physical architectures, inspired by platforms of cold atoms in optical lattices and a number of others, as well as specific assumptions that enter the complexity-theoretic arguments. This work shows that benchmark settings exhibiting a quantum speedup may require little control in contrast to universal quantum computing. Thus, our proposal puts a convincing experimental demonstration of a quantum speedup within reach in the near term.