The paper investigates online learning of quantum states using logarithmic loss, a quantum analogue of online portfolio selection. It establishes a regret lower bound, proving that existing algorithms like Exponential Weights and Tseng et al. (2025) achieve optimal polynomial dependence on dimension. Leveraging this lower bound, the authors present a sample‑optimal quantum state tomography algorithm (up to polylogarithmic factors) and introduce a method for constructing confidence sequences for matrix‑valued random variables, with numerical results indicating competitive performance.
By Yen-Huan Li, Wei-Fu Tseng
We determine the optimal sample complexity of low-rank quantum state tomography when each measurement may act jointly on at most $t$ samples. For sufficiently small $\varepsilon$, estimating an unknow...
The paper studies how to reconstruct a quantum channel from classical data by formulating the fidelity optimization as a semidefinite program (SDP). When the fidelity can be expressed as a ratio of two quadratic forms—such as in mapping mixed to pure states, projective operators, or unitary learning—the SDP approach yields a convex optimization that can be efficiently solved with commercial solvers. Experiments show that the resulting channels often have a Kraus rank far below the maximum, indicating that a small Kraus rank suffices to capture the observed data, and the method is also applied to reconstruct projective operators and a classical computational model based on quantum channel transformation.
By Mikhail Gennadievich Belov, Victor Victorovich Dubov, Vadim Konstantinovich Ivanov, Alexander Yurievich Maslov, Olga Vladimirovna Proshina, Vladislav Gennadievich Malyshkin
QuanVI is a quantum-inspired algorithm for score-based variational inference that reformulates the optimization as a density-operator problem and uses a quantum tensor network parameterization with matrix product operators. By representing degenerate low-energy subspaces with maximally mixed states, it avoids the non-uniqueness of individual eigenvectors and compresses the density operator to prevent exponential parameter growth. Experiments demonstrate that QuanVI matches exact solutions in low dimensions and scales to high-dimensional synthetic and Bayesian posterior-approximation benchmarks, including challenging non‑Gaussian targets.
By Yuchen Cong, Zerui Tao, Chao Li, Zhe Sun, Qibin Zhao
The paper introduces a classical algorithm that dequantizes a quantum sampler used for learning with optimized random features. By sampling heavy indices and reducing the transformation to a small principal block, the method produces a sparse classical representation with operator‑norm guarantees. This approach enables a classical sampler with specified accuracy and polynomial runtime, demonstrating that quantum block‑encoding factorizations can provide sufficient classical structure even when direct sampling access to the composite matrix is unavailable.
By Natsuto Isogai, Mio Murao, Hayata Yamasaki
arXiv:2608. 14941v1 Announce Type: new Abstract: Counting the global optima of a classical optimization problem is a #P-hard task.
By Malay Marut Das, Mark A. Novotny, Yaroslav Koshka
In quantum image processing, a fundamental step is encoding classical image data into quantum states. This can be achieved using methods such as Flexible Representation of Quantum Images (FRQI), Quantum Probability Image Encoding (QPIE), and Novel Enhanced Quantum Representation (NEQR).
arXiv:2609. 17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.
By Jian-Feng Cai, Xiliang Lu, Juntao You
arXiv:2607. 11273v1 Announce Type: cross Abstract: Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold.
By Jian Xu, Delu Zeng, John Paisley, Qibin Zhao
Tensor Completion using Subspace Information (TCSI) is an algorithm that leverages side information by estimating a subspace and reformulating tensor completion as a matrix regression problem. Theoretical analysis shows that accurate subspace information reduces sample complexity to nearly linear in the uncoupled ambient dimensions and relaxes signal-to-noise ratio requirements compared to existing guarantees. Numerical simulations and an application to reconstructing global Total Electron Content (TEC) maps demonstrate lower reconstruction errors than competing methods.
By Jingyang Li, Michael K. Ng
arXiv:2608. 02049v1 Announce Type: cross 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.
By Vasilisa Usova, Phila Rembold, Ian Yang, Marco Rossignolo, Simone Montangero, Samuele Tosatto, Gerhard Kirchmair
arXiv:2512.00751v4 Announce Type: replace-cross
Abstract: In certain classes of physical quantum systems, the exponentially large state space "fragments" into many low-dimensional, dynamically discon...
By Mikhail Mints, Eric R. Anschuetz