quant-phJun 10, 2026

Sparsified Kolmogorov-Arnold Networks for Interpretable Quantum State Tomography

Authors: Xinge Wu, Huaxin Wang, Jiajun Liu, Ruiqing He, Jiandong Shang, Hengliang Guo, Qiang Chen

Abstract

Machine-learning approaches to quantum state tomography can achieve high reconstruction fidelity, but the physical structure used by the trained model often remains implicit. Here we ask whether a sparsified Kolmogorov-Arnold Network (KAN) can be used not only as a regressor, but also as an inspectable reconstruction rule whose internal organization can be checked against known Pauli structure. We study a controlled three-qubit GHZ-family benchmark in which all 63 non-identity Pauli expectation values are used to reconstruct three GHZ-subspace variables: the population imbalance zz, the real off-diagonal component cc, and the imaginary off-diagonal component ss. Under finite-shot sampling and depolarizing noise, external ablation identifies the extended 12-channel GHZ-relevant Pauli set from the 63 measurements, with exact top-12 recovery across the tested shot counts and depolarizing-noise strengths. These support patterns remain stable across multi-seed random-initialization and noise-level analyses, and collapse under random-label controls. The dominant pruned input-hidden-output pathways organize Z-type population observables and X/Y off-diagonal observables in a pattern consistent with the analytic GHZ Pauli grouping, and sparse formula recovery recovers the canonical signed Pauli relations. The contribution of the KAN is therefore pathway-level structural interpretability within a neural reconstruction model, rather than superior sparse regression. Together with negative controls, these probes provide a consistency chain for auditing learned reconstruction rules against known physical structure.

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Jul 13, 2026quant-ph

Fixed-Protocol Amortized MPS Tomography with Conformalized Predictive Uncertainty

Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold. A k=0k{=}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. ApproachA 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). ApproachB, 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 χχ-MPS, conditioning on an \emph{informative local} Pauli set rather than random strings turns a modest, memorization-prone estimator into a high-fidelity one (≈ ⁣0.95\approx\!0.95, up to +0.59+0.59 over prior-only, decisively passing a shuffled-measurement control). A dropout ensemble, conformally recalibrated, gives ≈ ⁣90%\approx\!90\%-coverage intervals -- including for observables never measured, where a shot-based interval does not exist. Quality holds as the system grows (fidelity 0.900.90 at n=10n{=}10, gain \emph{growing} in nn; 0.880.88 at bond dimension χ=4χ{=}4), the parameterization is polynomial (native contraction to 2020 qubits), and we close the loop on IBM hardware (55 states at 0.970.97 from hardware-measured Paulis).
Jian Xu, Delu Zeng, John Paisley +1
Structural FidelityPosteriorConformal Prediction
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Jul 1, 2026quant-ph

Mechanistic Interpretability and Causal Feature Steering of Neural Quantum States via Sparse Autoencoders

Neural Quantum States (NQS) are a remarkably expressive class of variational ansätze for quantum many-body wavefunctions, yet little is understood about their internal mechanisms: trained on variational objectives alone, how do NQS accurately capture physical observables that they have never been explicitly optimized for? In this work, we present a systematic approach to analyze the internal activations of NQS using sparse autoencoders. We extract features from the residual stream and demonstrate that these features strongly correlate with physical observables such as order parameters, staggered magnetization, and half-chain correlators, across both ground state representation and real-time dynamics. Remarkably, the discovery of these features is entirely unsupervised, with no physical labels provided. We further establish that such features causally affect the corresponding observables predicted by NQS, by showing that targeted, post-training intervention on a \textit{single} feature smoothly and monotonically steers the corresponding observable, while leaving the variational energy nearly unchanged. These results demonstrate that NQS are not merely functional approximators, but encode rich, interpretable internal representations of physical information. Our approach provides both a diagnostic and an intervention tool for NQS, and serves as a foundation for using mechanistic interpretability towards more reliable, transparent NQS.
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May 9, 2026quant-ph

Learning Pure Quantum States in Any Dimension (Almost) Without Regret

We extend quantum state tomography with minimal cumulative disturbance, first investigated in [arXiv:2406.18370], to arbitrary finite-dimensional pure states. A learner sequentially receives fresh copies of an unknown pure state, chooses a rank-one projector for each copy using the previous outcomes, and performs the corresponding two-outcome projective measurement. The goal is to learn the state while keeping the chosen projectors close to the unknown state in order to minimize disturbance. The qubit solution relies on the special geometry of the Bloch sphere and does not extend directly to qudits, where pure states form a curved manifold. We show that this obstruction can be overcome by working locally on the pure-state manifold. The algorithm proceeds in epochs. In each epoch, it fixes a current estimate, measures pairs of nearby rank-one projectors obtained by moving in opposite tangent directions, and takes differences of the corresponding outcomes. This gives an exact linear observation of the tangent component of the error. The resulting local linear models are combined with a robust variance-adaptive estimator and a hot-start regularization that transfers precision across epochs. For every unknown pure state in dimension dd, after TT measured copies, our protocol achieves cumulative regret O(d3log⁡2T)\mathcal{O}(d^3\log^2 T), and at each intermediate time t≤Tt\leq T its current estimate has online infidelity O(d3log⁡(T)/t)\mathcal{O}(d^3\log(T)/t). Hence, pure-state tomography with essentially no cumulative disturbance is not a peculiarity of qubits but a geometric phenomenon that persists for qudits.
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