Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty

• URL: http://arxiv.org/abs/2607.11273v1
• Date: Mon, 13 Jul 2026 08:57:23 GMT
• Title: Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty
• Abstract summary: Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold.<n>A prior estimate is already near-optimal, so high fidelity at few measurements'' can be family memorization rather than tomography.<n>We propose a emph-protocol amortized MPS estimator trained once with a gauge-invariant fidelity loss.
• Score: 31.082191748525137
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold. A $k{=}0$ prior-only control shows that on concentrated families a prior estimate is already near-optimal, so ``high fidelity at few measurements'' can be family memorization rather than tomography; genuine measurement-efficiency needs a model that conditions on the measurements and demonstrably uses them. On a shared matrix-product-state (MPS) core parameterization we study two routes. Approach~A learns a generative prior over MPS cores with measurement-guided posterior inference (gold-standard-validated, but whose few-measurement accuracy the control shows is largely the prior). Approach~B, our main proposal, is a \emph{fixed-protocol amortized} MPS estimator trained once with a gauge-invariant fidelity loss; we deliberately do not rest it on a permutation-invariant set encoder (a plain MLP matches it). The decisive lever is the measurement design: motivated by the fact that local reduced density matrices determine a $χ$-MPS, conditioning on an \emph{informative local} Pauli set rather than random strings turns a modest, memorization-prone estimator into a high-fidelity one ($\approx\!0.95$, up to $+0.59$ over prior-only, decisively passing a shuffled-measurement control). A dropout ensemble, conformally recalibrated, gives $\approx\!90\%$-coverage intervals -- including for observables never measured, where a shot-based interval does not exist. Quality holds as the system grows (fidelity $0.90$ at $n{=}10$, gain \emph{growing} in $n$; $0.88$ at bond dimension $χ{=}4$), the parameterization is polynomial (native contraction to $20$ qubits), and we close the loop on IBM hardware ($5$ states at $0.97$ from hardware-measured Paulis).

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