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Grover’s search algorithm (GSA) offers quadratic speedup in searching unstructured databases but suffers from exponential circuit depth complexity. Here, we present two quantum circuits called HX and Ry layers for the searching problem. Remarkably, both circuits maintain a fixed circuit depth of two and one, respectively, irrespective of the number of qubits used. When the target element’s position index is known, we prove that either circuit, combined with a single multi-controlled X gate, effectively amplifies the target element’s probability to over 0.99 for any qubit number greater than seven. To search unknown databases, we use the depth-1 Ry layer as the ansatz in the Variational Quantum Search (VQS), whose efficacy is validated through numerical experiments on databases with up to 26 qubits. The VQS with the Ry layer exhibits an exponential advantage, in circuit depth, over the GSA for databases of up to 26 qubits.
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Symmetry-aware recursive image similarity exploration for materials microscopy
Abstract In pursuit of scientific discovery, vast collections of unstructured structural and functional images are acquired; however, only an infinitesimally small fraction of this data is rigorously analyzed, with an even smaller fraction ever being published. One method to accelerate scientific discovery is to extract more insight from costly scientific experiments already conducted. Unfortunately, data from scientific experiments tend only to be accessible by the originator who knows the experiments and directives. Moreover, there are no robust methods to search unstructured databases of images to deduce correlations and insight. Here, we develop a machine learning approach to create image similarity projections to search unstructured image databases. To improve these projections, we develop and train a model to include symmetry-aware features. As an exemplar, we use a set of 25,133 piezoresponse force microscopy images collected on diverse materials systems over five years. We demonstrate how this tool can be used for interactive recursive image searching and exploration, highlighting structural similarities at various length scales. This tool justifies continued investment in federated scientific databases with standardized metadata schemas where the combination of filtering and recursive interactive searching can uncover synthesis-structure-property relations. We provide a customizable open-source package ( https://github.com/m3-learning/Recursive_Symmetry_Aware_Materials_Microstructure_Explorer ) of this interactive tool for researchers to use with their data.
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- Award ID(s):
- 1839234
- PAR ID:
- 10309686
- Date Published:
- Journal Name:
- npj Computational Materials
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2057-3960
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1038/s41524-021-00637-y
