Efficiently preparing Schr\"odinger's cat, fractons and non-Abelian topological order in quantum devices

TL;DR

This paper presents a scalable method to prepare various long-range entangled quantum states, including cat states, topological orders, and fractons, using existing quantum platforms like Rydberg atom arrays, with high fidelity.

Contribution

It introduces a two-step protocol leveraging intrinsic atomic interactions and measurements to efficiently generate complex entangled states on current quantum devices.

Findings

Fidelity per site exceeds 0.9999 for 1D GHZ and 2D toric code states.

Achieves fidelity approximately 0.998 for 3D fracton states.

Proposes methods for creating non-Abelian topological orders like S3 and D4.

Abstract

Long-range entangled quantum states -- like cat states and topological order -- are key for quantum metrology and information purposes, but they cannot be prepared by any scalable unitary process. Intriguingly, using measurements as an additional ingredient could circumvent such no-go theorems. However, efficient schemes are known for only a limited class of long-range entangled states, and their implementation on existing quantum devices via a sequence of gates and measurements is hampered by high overheads. Here we resolve these problems, proposing how to scalably prepare a broad range of long-range entangled states with the use of existing experimental platforms. Our two-step process finds an ideal implementation in Rydberg atom arrays, only requiring time-evolution under the intrinsic atomic interactions, followed by measuring a single sublattice (by using, e.g., two atom species). Remarkably, this protocol can prepare the 1D Greenberger-Horne-Zeilinger (GHZ) 'cat' state and 2D toric code with fidelity per site exceeding $0.9999$, and a 3D fracton state with fidelity $\gtrapprox 0.998$. In light of recent experiments showcasing 3D Rydberg atom arrays, this paves the way to the first experimental realization of fracton order. While the above examples are based on efficiently preparing and measuring cluster states, we also propose a multi-step procedure to create $S_3$ and $D_4$ non-Abelian topological order in Rydberg atom arrays and other quantum devices -- offering a route towards universal topological quantum computation.