Variational Joint Magnetometry and Gradiometry on Dipolar Spin Chains

• URL: http://arxiv.org/abs/2605.03906v1
• Date: Tue, 05 May 2026 15:59:22 GMT
• Title: Variational Joint Magnetometry and Gradiometry on Dipolar Spin Chains
• Abstract summary: We present a variational framework that takes det(F) as the objective and a hardware-motivated layered dipolar circuit as the ansatz.<n>Both encoding generators are diagonal in the computational basis, which reduces the search for the quantum Fisher information benchmark to a probability-simplex optimization.
• Score: 14.720429715932829
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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