{"ID":6537630,"CreatedAt":"2026-07-14T02:54:43.516908796Z","UpdatedAt":"2026-07-15T03:28:55.185153975Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2607.11273","arxiv_id":"2607.11273","title":"Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty","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).","short_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 mea...","url_abs":"https://arxiv.org/abs/2607.11273","url_pdf":"https://arxiv.org/pdf/2607.11273v1","authors":"[\"Jian Xu\",\"Delu Zeng\",\"John Paisley\",\"Qibin Zhao\"]","published":"2026-07-13T08:57:23Z","proceeding":"quant-ph","tasks":"[\"quant-ph\",\"cs.LG\"]","methods":"[]","has_code":false}