Theoretical Bounds on Data Requirements for the Ray-Based Classification

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

doi:10.1007/s42979-021-00921-0

Cited by 4 publications

(4 citation statements)

References 35 publications

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“…This places our algorithm within a factor 10 of the minimum amount (G • T ) of measurements required to verify the learned polytope. This is in contrast to the bounds obtained for the number of line-search directions for uninformed sampling strategies (see Theorem 2 in [17]), which are exponential in the dimension of the number of dots and which assume perfect line-search accuracy.…”

Section: Discussioncontrasting

confidence: 70%

Learning Coulomb Diamonds in Large Quantum Dot Arrays

Krause,

Chatterjee,

Kuemmeth

et al. 2022

Preprint

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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 onedimensional 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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Section: Discussioncontrasting

confidence: 70%

Learning Coulomb Diamonds in Large Quantum Dot Arrays

Krause,

Chatterjee,

Kuemmeth

et al. 2022

Preprint

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show abstract

“…This places our algorithm within a factor 10 of the minimum amount (G• T ) of measurements required to verify the learned polytope. This is in contrast to the bounds obtained for the number of line-search directions for uninformed sampling strategies (see Theorem 2 in [17]), which are exponential in the dimension of the number of dots and which assume perfect line-search accuracy. The reason for our sample efficiency compared to the naive bound is our sampling procedure, as visualized in Figure 4.…”

Section: Discussioncontrasting

confidence: 70%

Learning Coulomb Diamonds in Large Quantum Dot Arrays

et al. 2022

View full text Add to dashboard Cite

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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“…Compared to random sampling, our sampling approach using active learning seems to be superior. For random sampling, the number of samples requires depends largely on the relative size of a facet compared to the overall surface area [15]. Thus, for the small size of facets on our polytope, an average of 1500 samples is significantly less than expected via random sampling.…”

Section: Discussionmentioning

confidence: 99%

“…However, obtaining a dataset with the required resolution in higher dimensions is very expensive. For the line-search based approaches mentioned above, it has been shown [15] that for a naive measurement design that does not have any knowledge of the position of transitions, the number of line-searches required to correctly identify all transitions of a state increases exponentially with the dimensionality. The key difficulty lies in obtaining a grid of measurements fine enough to obtain enough points on the smallest facets of the polytope to estimate the slopes.…”

mentioning

confidence: 99%

Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays

et al. 2022

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In spin based quantum dot arrays, material or fabrication imprecisions affect the behaviour of the device, which must be taken into account when controlling it. This requires measuring the shape of specific convex polytopes. We present an algorithm that automatically discovers count, shape and size of the facets of a convex polytope from measurements by alternating a phase of model-fitting with a phase of querying new measurements, based on the fitted model. We evaluate the algorithm on simulated polytopes and devices, as well as a real 2 × 2 spin qubit array. Results show that we can reliably find the facets of the convex polytopes, including small facets with sizes on the order of the measurement precision.

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Theoretical Bounds on Data Requirements for the Ray-Based Classification

Cited by 4 publications

References 35 publications

Learning Coulomb Diamonds in Large Quantum Dot Arrays

Learning Coulomb Diamonds in Large Quantum Dot Arrays

Learning Coulomb Diamonds in Large Quantum Dot Arrays

Estimation of Convex Polytopes for Automatic Discovery of Charge State Transitions in Quantum Dot Arrays

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