arXiv:2602. 15202v2 Announce Type: replace-cross Abstract: We present an algebraic algorithm for quantum state tomography that leverages measurements of certain observables to estimate structured entries of the underlying density matrix.
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.
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.
arXiv:2608. 14941v1 Announce Type: new Abstract: Counting the global optima of a classical optimization problem is a #P-hard task.
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.
arXiv:2607. 11273v1 Announce Type: cross Abstract: Quantum state tomography is sample-starved, and the states one prepares live on a narrow, learnable manifold.
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.
arXiv:2412. 09557v3 Announce Type: replace-cross Abstract: Quantum kernel learning (QKL) promises efficient machine learning by encoding feature maps onto exponentially large Hilbert spaces inherent in quantum systems.
arXiv:2505.16305v3 Announce Type: replace Abstract: While CANDECOMP/PARAFAC (CP) decomposition (CPD) is fundamental for tensor reconstruction, Bayesian CPD often scales poorly because variational upd...
arXiv:2508. 12413v4 Announce Type: replace-cross Abstract: The flow matching has rapidly become a dominant paradigm in classical generative modeling, offering an efficient way to interpolate between two complex distributions.
arXiv:2503. 17020v2 Announce Type: replace-cross Abstract: Kernel methods compare inputs through feature maps.