Ray-based classification framework for high-dimensional data

Zwolak, Justyna P.; Kalantre, Sandesh S.; McJunkin, Thomas; Weber, Brian; Taylor, J. Madison

doi:10.48550/arxiv.2010.00500

Cited by 6 publications

(19 citation statements)

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“…We close this section with two remarks. The first is that the RBC framework has already seen considerable experimental success [1]. The second remark concerns a subordinate problem that is beyond the scope of this work: boundary identification.…”

Section: Problem Formulationmentioning

confidence: 94%

“…The second remark concerns a subordinate problem that is beyond the scope of this work: boundary identification. In the quantum computing application for which RBC was originally designed [1] boundaries are identified by measuring discrete tunneling events, and there is little ambiguity in determining when a boundary was crossed. Since the fingerprinting method relies on identifying boundary crossings, in other circumstances boundary detection might require some other resolution.…”

Section: Problem Formulationmentioning

confidence: 99%

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Theoretical bounds on data requirements for the ray-based classification

Weber,

Kalantre,

McJunkin

et al. 2021

Preprint

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The problem of classifying high-dimensional shapes in real-world data grows in complexity as the dimension of the space increases. For the case of identifying convex shapes of different geometries, a new classification framework has recently been proposed in which the intersections of a set of one-dimensional representations, called rays, with the boundaries of the shape are used to identify the specific geometry. This ray-based classification (RBC) has been empirically verified using a synthetic dataset of two-and threedimensional shapes [1] and, more recently, has also been validated experimentally [2]. Here, we establish a bound on the number of rays necessary for shape classification, defined by key angular metrics, for arbitrary convex shapes. For two dimensions, we derive a lower bound on the number of rays in terms of the shape's length, diameter, and exterior angles. For convex polytopes in R N , we generalize this result to a similar bound given as a function of the dihedral angle and the geometrical parameters of polygonal faces. This result enables a different approach for estimating high-dimensional shapes using substantially fewer data elements than volumetric or surface-based approaches.

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Section: Problem Formulationmentioning

confidence: 94%

Section: Problem Formulationmentioning

confidence: 99%

Theoretical bounds on data requirements for the ray-based classification

Weber,

Kalantre,

McJunkin

et al. 2021

Preprint

Self Cite

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“…4) learns to "ignore" all of the points measured between transition lines (Ziegler et al, 2021). One way to reduce the number of unnecessary data points collected during measurement is to employ the ray-based classification (RBC) framework developed for classifying simple high-dimensional geometrical structures (Zwolak et al, 2020a).…”

Section: Setting Topology With Raysmentioning

confidence: 99%

“…The RBC framework has been tested using simulated data for the case of two and three QDs (Zwolak et al, 2020a). It has also been implemented experimentally (both off-line and in situ) (Zwolak et al, 2021) and shown performance on par with the moredata-demanding CNN-based classification (Zwolak et al, 2020b) while requiring up to 70 % fewer measurement points.…”

Section: Setting Topology With Raysmentioning

confidence: 99%

“…III.B), the total number of parameters defining the ML model used for state assessment was reduced by two orders of magnitude compared to a CNN model (1.2 × 10 4 vs. 2.2 × 10 6 parameters, see Zwolak et al (2020b)). While this number is still fairly high, it has been noted that the size and complexity of the DNN can be further reduced by at least an order of magnitude (Zwolak et al, 2020a). Importantly, the RBC does not require any significant data processing, which further improves the computational efficiency of this approach and makes it an appealing candidate for the "on-chip" implementation on miniaturized hardware with low power consumption (Sebastian et al, 2020).…”

Section: B Toward "On-chip" Implementationsmentioning

confidence: 99%

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Colloquium: Advances in automation of quantum dot devices control

Zwolak¹

2021

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Learning Coulomb Diamonds in Large Quantum Dot Arrays

et al. 2022

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We introduce an algorithm that is able to find the facets of Coulomb diamonds in quantum dot arrays. We simulate these arrays using the constant-interaction model, and rely only on one-dimensional raster scans (rays) to learn a model of the device using regularized maximum likelihood estimation. This allows us to determine, for a given charge state of the device, which transitions exist and what the compensated gate voltages for these are. For smaller devices the simulator can also be used to compute the exact boundaries of the Coulomb diamonds, which we use to assess that our algorithm correctly finds the vast majority of transitions with high precision.

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Ray-based classification framework for high-dimensional data

Cited by 6 publications

References 0 publications

Theoretical bounds on data requirements for the ray-based classification

Theoretical bounds on data requirements for the ray-based classification

Colloquium: Advances in automation of quantum dot devices control

Learning Coulomb Diamonds in Large Quantum Dot Arrays

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