FIXED-PROTOCOL AMORTIZED MPS TOMOGRAPHY WITH CONFORMALIZED PREDICTIVE UNCERTAINTY

Quantum state tomography (QST) is notoriously sample-inefficient, requiring an exponential number of measurements as the number of qubits increases. The authors address this by leveraging the fact that experimentally prepared quantum states often occupy a narrow, structured manifold rather than the entire Hilbert space. They propose a fixed-protocol amortized estimator that maps noisy, local Pauli measurement data directly to the cores of a matrix-product-state (MPS) representation. By training this model with a gauge-invariant fidelity loss, they avoid the pitfalls of coordinate-dependent regression and ensure the model learns the underlying state structure rather than just memorizing the training distribution.

The study introduces two primary routes for reconstruction: a generative prior-based approach (Approach A) and a measurement-conditioned amortized estimator (Approach B). Through rigorous integrity controls—specifically a k=0 prior-only baseline and a shuffled-measurement test—the authors demonstrate that Approach A often relies too heavily on the prior. In contrast, Approach B, when provided with informative local Pauli measurements (e.g., weight-1 and nearest-neighbor weight-2 Paulis), achieves high-fidelity reconstruction (approx. 0.95) that demonstrably utilizes the measurement data. The model scales polynomially, maintaining high fidelity as the system size grows to 20 qubits, and successfully reconstructs states on IBM quantum hardware.

Beyond point estimation, the authors provide a method for quantifying predictive uncertainty. By using a dropout ensemble and applying conformal recalibration, they generate distribution-free, marginal 90%-coverage intervals for observables. This allows the model to provide meaningful uncertainty estimates even for observables that were not directly measured, offering a practical tool for benchmarking quantum hardware.