We study low-rank quantum state tomography from finite-bit Pauli batch responses. To avoid bias introduced by generic quantization, we propose HyperQuant, a mean-preserving hyperbolic quantizer adapted to the second-moment scale of Pauli responses. We establish minimax distortion guarantees and show that exact mean preservation enables direct rank-constrained least-squares recovery without altering the population target. We derive nonasymptotic recovery guarantees and an explicit bit--shot tradeoff under which finite-bit responses retain the error order of unquantized batch averages using fewer response bits. For efficient computation, we develop QuantRGD, a Riemannian gradient method with provable linear convergence to the corresponding statistical neighborhood under explicit resource conditions. Numerical experiments validate the predicted quantization, recovery, and convergence behavior.
Approximate Message Passing (AMP) algorithms are attractive as they are computationally efficient and simultaneously admit a precise characterization in terms of the low-dimensional"state-evolution"recursion. In this work, we establish quantitative universality for AMP with centered rank-one sensing matrices $Z_i=(x_ix...
Sample-based quantum linear solvers measure quantum Krylov states $e^{-iAT}|b\rangle$ and reconstruct the solution of $Ax=b$ classically on the observed basis states. We develop this approach for positive-definite systems that arise from elliptic partial differential equations. We show that the sampling guarantees hold...
DoyeolDavidAhn, Byeongyong Park Center for Quantum Information Processing, University of Seoul et al.· 0 citations
Quantum state tomography provides a foundation for characterizing state preparation and predicting measurement outcomes. We characterize the minimax expected trace norm risk of quantum state tomography over classes with polynomial spectral decay under randomized nonadaptive single copy measurements. Under an explicit s...
We prove a local amplitude-ratio bound for positive ground states and an explicit reverse comparison for fidelity under finite-region erasure. An exact lattice calculation for a connected critical Ising chain gives amplitude exponent $1/8$, preserved by arbitrary optimal control on any fixed spin set and, at the level...
This work proposes PRISM-ZO, a projection-robust framework that samples low-dimensional random tangent subspaces and combines symmetric finite differences with median-of-means or Huber aggregation and establishes the unbiasedness of the correctly rescaled projected direction in expectation over the random subspace.
Yin-Pu Ma, Cunlin Li, Shiyue Zhang· Journal of King Saud Univers...· 0 citations
QCGD is introduced, a quantum-compatible implementation of Riemannian conjugate gradient that combines the steepest descent direction with information retained from previous search directions and may offer practical advantages, particularly in the early fault-tolerant regime.
Andres Arcia-Lopez, M. Gluza, Yudai Suzuki et al.· 0 citations
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