Fault-Tolerant One-Shot Entanglement Generation with Constant-Sized Quantum Devices in the Plane

TL;DR

This paper presents a protocol for robust, one-shot entanglement generation between distant qubits in a 2D grid, achieving constant-fidelity Bell pairs with minimal resource scaling under noise.

Contribution

It introduces the first single-shot, constant-time protocol for long-range entanglement in 2D quantum systems with constant-sized devices, robust to local stochastic noise.

Findings

Generates Bell pairs at arbitrary distances with constant fidelity under noise below a threshold.

Requires only a rectangular grid of size proportional to the distance, with constant time operations.

Establishes long-range localizable entanglement in 2D states robust to stochastic Pauli noise.

Abstract

Consider a rectangular grid of qubits in 2D with single-qubit and nearest-neighbor two-qubit operations subject to local stochastic Pauli noise. At different length scales, this setup describes both a single quantum computing device with geometrically limited connectivity between qubits arranged on a disc, and planar networks composed of quantum repeater stations of constant size. We give a protocol which robustly generates entanglement between distant qubits in this setup. For noise below a constant threshold error strength, it generates a constant-fidelity Bell pair between qubits separated by an arbitrarily large distance $R$. To generate distance-$R$ entanglement, a rectangular grid of qubits of dimensions $\Theta(R)\times \Theta(\mathsf{poly}(\log R))$ suffices. Our protocol applies quantum operations in one shot, establishing a Bell state in a constant time up to a known Pauli correction. In contrast, existing entanglement generation protocols either require local quantum devices controlling a number of qubits growing with the targeted distance, or are not single-shot, i.e., have a distance-dependent execution time. The protocol leverages many-body entanglement in networks and provides the first example of a short-range entangled state in 2D with long-range localizable entanglement robust to local stochastic Pauli noise. As an immediate corollary, we construct a 2D-local stabilizer Hamiltonian whose Gibbs states possess long-range localizable entanglement at constant positive temperature.