arXiv subjects

Hetta Vappula

Publications and source records attributed to Hetta Vappula.

3 recordsLinked to original sources

arXiv2026

Exploiting overcompleteness of Platonic-solid POVMs for shadow estimation

Accurately estimating expectation values of observables from a finite number of measurement shots is a central challenge in quantum information science. Informationally overcomplete measurements provide a route to reduce estimation variance through optimized classical post-processing. However, the interplay between measurement geometry and dual-frame construction remains largely unexplored. In this work, we study Platonic solid POVMs ---highly symmetric, overcomplete single-qubit measurements whose effects correspond to the vertices of the five Platonic solids on the Bloch sphere--- for the estimation of molecular Hamiltonians. Using $k$-locally optimal dual frames, we show that the geometry of the POVM can have a non-trivial and non-monotonic effect on the estimation variance. We further propose a joint optimization of the POVM orientation and effect weights using a classical proxy state, either a product state or a Matrix Product State (MPS) approximation. We demonstrate that optimized Platonic solid POVMs can outperform standard randomized Pauli measurements, provided the MPS bond dimension is sufficient to faithfully represent the target state. These results reveal a trade-off between classical preprocessing and estimation accuracy, suggesting a practical route to improved observable estimation on near-term quantum hardware.

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arXiv2025

Improving shadow estimation with locally-optimal dual frames

Accurate estimation of observables in quantum systems is a central challenge in quantum information science, yet practical implementations are fundamentally constrained by the limited number of measurement shots. In this work we explore a variation of the classical shadows protocol in which the measurements are kept local while allowing the resulting classical shadows themselves to be correlated. By constructing locally optimal shadows, we obtain unbiased estimators that are competitive with state-of-the-art methods in terms of measurement overhead, while requiring only single-qubit measurements and allowing for the estimation of any observable in pure post-processing, reducing estimation errors by orders of magnitude over standard classical shadows. We validate our approach through numerical experiments on molecular Hamiltonians with up to 40 qubits consistently observing significant reductions in estimation errors, including for estimations of multiple chemically relevant observables simultaneously.

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arXiv2024

Practical techniques for high-precision measurements on near-term quantum hardware and applications in molecular energy estimation

Achieving high-precision measurements on near-term quantum devices is critical for advancing quantum computing applications. Quantum computers suffer from high readout errors, making quantum simulations with high accuracy requirements particularly challenging. This paper implements practical techniques to reach accuracies essential for quantum chemistry by addressing key overheads and noise sources. Specifically, we leverage locally biased random measurements for reducing shot overhead, repeated settings with parallel quantum detector tomography for reducing circuit overhead and mitigating readout errors, and blended scheduling for mitigating time-dependent noise. We demonstrate these techniques via molecular energy estimation of the BODIPY molecule on a Hartree-Fock state on an IBM Eagle r3, obtaining a reduction in measurement errors by an order of magnitude from 1-5% to 0.16%. These strategies pave the way for more reliable quantum computations, particularly for applications requiring precise molecular energy calculations.

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