aiqbench analysis
This paper presents a method to reduce the computational cost of estimating partial-transpose moments from classical shadows, improving upon previous cubic-scaling limits in quantum state tomography. By exploiting the factorized structure of incoming snapshots and utilizing Pauli basis updates, the authors achieve subcubic time complexity per shot while maintaining fixed memory requirements. This optimization directly enhances the efficiency of entanglement certification and phase diagnostics protocols in practical quantum computing applications.
Online Estimation of Partial Transpose Moments via Fast Classical Updates
arXiv:2605.01433v2 Announce Type: replace Abstract: Partial-transpose (PT) moments are among the most practically relevant nonlinear quantities accessible from local Pauli classical shadows, because they directly underpin mixed-state entanglement certification and recent PT-moment-based phase diagnostics. The online framework of Marso \emph{et al.} rewrote the exact PT-moment statistic into a fixed-memory recurrence that updates a small collection of accumulated matrices after each new shadow snapshot. Its update cost is independent of the shot number, but each step treats the incoming partially transposed snapshot as a generic dense matrix. Therefore, the arithmetic cost scales cubically with the dimension of the Hilbert space. We show that the same estimator can be updated exactly in subcubic time per shot while retaining the same memory. The key point is that the accumulated matrices become dense, but the fresh partially transposed snapshot still factorizes into local factors. Right-multiplication by that factorized snapshot can therefore be executed by exact column-pair sweeps. For the second PT moment, we further optimize the process by utilizing a Pauli basis update.
Abstract:Partial-transpose (PT) moments are among the most practically relevant nonlinear quantities accessible from local Pauli classical shadows, because they directly underpin mixed-state entanglement certification and recent PT-moment-based phase diagnostics. The online framework of Marso \emph{et al.} rewrote the exact PT-moment statistic into a fixed-memory recurrence that updates a small collection of accumulated matrices after each new shadow snapshot. Its update cost is independent of the shot number, but each step treats the incoming partially transposed snapshot as a generic dense matrix. Therefore, the arithmetic cost scales cubically with the dimension of the Hilbert space. We show that the same estimator can be updated exactly in subcubic time per shot while retaining the same memory. The key point is that the accumulated matrices become dense, but the fresh partially transposed snapshot still factorizes into local factors. Right-multiplication by that factorized snapshot can therefore be executed by exact column-pair sweeps. For the second PT moment, we further optimize the process by utilizing a Pauli basis update.
arXiv:2605.01433 [quant-ph]
(or arXiv:2605.01433v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2605.01433 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 253 words
