# Geometric pathway to scalable quantum sensing

## TL;DR

This paper introduces a scalable quantum sensing method using geometric phase gates that efficiently creates entangled states in spin ensembles, enhancing precision measurement capabilities while resisting decoherence.

## Contribution

It presents a novel control strategy employing nonlinear geometric phase gates and Grover's algorithm to prepare entangled states without requiring individual spin addressability or complex interactions.

## Key findings

- Achieves entangled state preparation with O(N^{5/4}) gates.
- Gates are insensitive to initial mode states and include dynamical decoupling.
- Method enhances robustness against dephasing errors.

## Abstract

Entangled resources enable quantum sensing that achieves Heisenberg scaling, a quadratic improvement on the standard quantum limit, but preparing large scale entangled states is challenging in the presence of decoherence. We present a quantum control strategy using highly nonlinear geometric phase gates for preparing entangled states on spin ensembles which can be used for practical precision metrology. The method uses a dispersive coupling of $N$ spins to a common bosonic mode and does not require addressability, special detunings, or interactions between the spins. Using a control sequence that executes Grover's algorithm on a subspace of permutationally symmetric states, a target entangled resource state can be prepared using $O(N^{5/4})$ geometric phase gates. The geometrically closed path of the control operations ensures the gates are insensitive to the initial state of the mode and the sequence has built-in dynamical decoupling providing resilience to dephasing errors.