Variational Quantum Sensing for Structured Linear Function Estimation

TL;DR

The paper develops a variational quantum sensing framework to estimate a structured linear function of local phases by encoding $\phi_i = \alpha_i\theta$ and optimizing a dipolar-interacting circuit to maximize the Classical Fisher Information for a fixed readout. The authors introduce a layered ansatz on a polygon-centered qubit layout, implement directional phase encoding, and use CMA-ES to train the circuit parameters without gradients. Across uniform and weighted-central encodings, the learned probes approach the encoding-specific entanglement-enhanced (EE) precision bounds and show high GHZ-like fidelity at modest depths, highlighting the adaptability of variational methods to task geometry. These results offer a hardware-efficient route to tailor metrological entanglement for sensor networks and point toward noise-robust extensions and multiparameter generalizations with practical deployment significance.

Abstract

We study the variational optimization of entangled probe states for quantum sensing tasks involving the estimation of a structured linear function of local phase parameters. Specifically, we consider scenarios where each qubit in a spin-1/2 array accumulates a phase phi_i = alpha_i * theta, with a known weight vector alpha, reducing the task to single-parameter estimation of theta. Using parameterized quantum circuits composed of dipolar-interacting gates and global rotations, we optimize probe states with respect to the Classical Fisher Information (CFI) using a gradient-free evolutionary strategy. We benchmark the optimized circuits for two relevant cases: (i) uniform encoding, where all qubits contribute equally to the phase function, and (ii) a custom encoding where a central qubit dominates the weight vector. In both cases, the optimized probe states approach the respective entanglement-enhanced (EE) limits dictated by the encoding structure. Our results demonstrate the power of variational approaches for tailoring metrologically useful entanglement to specific estimation tasks in quantum sensor networks.

Figures (7)

• Figure 1: Overview of the variational quantum sensing protocol. (Task) A structured phase profile, defined by a weight vector $\vec{\alpha}$, is imprinted across the qubits. (Variational design) A hardware-efficient ansatz with dipolar interactions and collective rotations is optimized to minimize a metrological cost function, here based on the Classical Fisher Information (CFI). (Deployment) The optimized probe can then be implemented on an experimental platform for enhanced parameter estimation.
• Figure 2: Polygon-centered lattice geometries considered in this work. Central qubits (red) are surrounded by $(N{-}1)$ peripherals (blue); grey lines indicate dipolar couplings used in the ansatz.
• Figure 3: Schematic of the variational quantum circuit for metrology. The circuit consists of repeated state preparation layers (green dashed box) composed of global rotations and parameterized entangling gates, followed by phase encoding and projective measurement.
• Figure 4: CFI versus qubit number $N$ under uniform encoding, for circuit depths $L=1$–$4$.
• Figure 5: CFI versus qubit number $N$ under weighted-central encoding, for circuit depths $L=1$–$4$.