quant-phAug 3, 2026

Adaptive Reconstruction of Bosonic Quantum States

Authors: Vasilisa Usova, Phila Rembold, Ian Yang, Marco Rossignolo, Simone Montangero, Samuele Tosatto, Gerhard Kirchmair

Abstract

Bosonic quantum systems provide a hardware-efficient platform for quantum information processing but remain challenging to characterise due to their large Hilbert space and the high measurement cost of state tomography. Existing approaches estimate the fidelity with respect to a single target state, making them unsuitable for applications in which physically equivalent states differ by phase space translations, rotations, or other transformations. Here, we introduce an adaptive reconstruction technique that estimates the fidelity with respect to a family of bosonic states while reconstructing the underlying Wigner function from a small number of measurements. The method combines a physics-informed parametric model with Bayesian inference, bootstrap, and active learning to iteratively select the most informative phase space sampling points. We implement the approach on a circuit quantum electrodynamics platform and benchmark it on Schrödinger cat states with amplitudes α∈[1,3]α\in[1,3]. The reconstruction yields reproducible fidelity estimates within a few minutes, remains robust to substantial displacements and rotations in phase space despite using a mismatched prior, and is sensitive to subtle state imperfections. We further compare the adaptive strategy with existing Wigner function sampling protocols experimentally, demonstrating the advantage of adaptive sampling for measurement-efficient fidelity estimation with respect to a family of cat states. Finally, we incorporate the reconstructed fidelity into the figure of merit used in a proof-of-principle closed-loop quantum optimal control experiment, demonstrating the applicability of the method to autonomous optimisation of bosonic quantum states.

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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
N$-Qubit Stabilizer StatesDistributional FidelityTomographyPosteriorConformal Prediction
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Sep 9, 2026quant-ph

Optimal Low-Rank Quantum State Tomography with Bounded-Sample Joint Measurements

We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most tt samples. For sufficiently small ε\varepsilon, estimating an unknown state on Cd\mathbb{C}^d of rank at most rr to trace norm error ε\varepsilon with constant success probability requires, and is achievable with, Θ(drε2max⁡{1,rt}) Θ\left( \frac{dr}{\varepsilon^2} \max\left\{1,\frac r{\sqrt t}\right\} \right) samples. The lower bound allows the protocol to choose each joint measurement adaptively using all previous classical outcomes; the matching upper bound is nonadaptive. Thus joint measurements on at most tt samples improve the complexity of algorithms making single-sample measurements by at most a factor t\sqrt t. Further, measuring order r2r^2 samples jointly is necessary and sufficient to attain the unrestricted collective rate. For the lower bound, we vary the support of a state with fixed uniform spectrum and bound the Fisher information trace of every joint measurement on tt samples. The adaptive Fisher chain rule and the van Trees inequality then give the trace norm lower bound. For the upper bound, we construct and analyze a nonadaptive tomography protocol based on a Gaussian joint measurement. An explicit second moment identity and a conditional Gaussian law outside the state's support give a rank-dependent error analysis, yielding the matching rate.
Ashwin Nayak, Xingyu Zhou
N$-Qubit Stabilizer StatesOptimal Sample ComplexitySpectral NormMutual InformationTomography
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Oct 7, 2025quant-ph

Efficient learning of bosonic Gaussian unitaries

Bosonic Gaussian unitaries are fundamental building blocks of central continuous-variable quantum technologies such as quantum-optic interferometry and bosonic error-correction schemes. In this work, we present the first time-efficient algorithm for learning bosonic Gaussian unitaries with a rigorous analysis. Our algorithm produces an estimate of the unknown unitary that is accurate to small worst-case error, measured by the physically motivated energy-constrained diamond distance. Its runtime and query complexity scale polynomially with the number of modes, the inverse target accuracy, and natural energy parameters quantifying the allowed input energy and the unitary's output-energy growth. The protocol uses only experimentally friendly photonic resources: coherent and squeezed probes, passive linear optics, and heterodyne/homodyne detection. We then employ an efficient classical post-processing routine that leverages a symplectic regularization step to project matrix estimates onto the symplectic group. In the limit of unbounded input energy, our procedure attains arbitrarily high precision using only 2m+22m+2 queries, where mm is the number of modes. To our knowledge, this is the first provably efficient learning algorithm for a multiparameter family of continuous-variable unitaries.
Marco Fanizza, Vishnu Iyer, Junseo Lee +2
N$-Qubit Stabilizer StatesResource-Constrained Edge Devices
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