Variational Joint Magnetometry and Gradiometry on Dipolar Spin Chains

TL;DR

This paper develops a variational framework for joint magnetometry and gradiometry on dipolar spin chains, achieving near-optimal quantum Fisher information performance for two-parameter sensing.

Contribution

It introduces a variational approach with a diagonal circuit ansatz to optimize joint magnetic field and gradient estimation, surpassing classical limits.

Findings

Achieves 0.92 of the best benchmark det(F) at N=5, a 4.2x SQL advantage.

Variational probes at L=3 reach near-optimal performance, outperforming fixed decoders.

The optimal measurement structure follows from Dicke-sector decomposition, focusing on specific quantum states.

Abstract

Estimating a uniform magnetic field B0 and its spatial gradient g on a dipolar-coupled spin chain calls for a multiparameter figure of merit. The GHZ state, optimal for single-parameter Heisenberg-limited sensing, has a rank-one quantum Fisher information matrix with det(Q^GHZ) = 0 at every chain length N, ruling it out for the two-parameter problem. We present a variational framework that takes det(F) as the objective and a hardware-motivated layered dipolar circuit as the ansatz. Both encoding generators are diagonal in the computational basis, which reduces the search for the quantum Fisher information benchmark to a probability-simplex optimization and yields a tractable best-found benchmark det(Q*) against which variational performance is compared. The same diagonal structure makes the classical Fisher information depend only on basis-state probabilities under any single-qubit decoder, so encoder and decoder parameters are co-trained with CMA-ES in a single run. Decoder optimization past fixed Ramsey adds at most a few percentage points across the grid, in contrast to the persistent decoder gains seen in our prior single-parameter work. Variational probes at L = 3 reach 0.92 of the best-found benchmark at N = 5, a 4.2x SQL advantage in det(F), and concentrate on a four-string motif of the two GHZ extrema and two half-chain-flip strings whose structure follows from the Dicke-sector decomposition of the two generators.