LINEAR-DEPTH QUANTUM SYSTEM FOR TOPOLOGICAL DATA ANALYSIS

A quantum computer-implemented system, method, and computer program product for quantum topological domain analysis (QTDA). The QTDA method achieves an improved exponential speedup and depth complexity of O(n log(1/(δ∈))) where n is the number of data points, ∈ is the error tolerance, δ is the small...

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Main Authors Clarkson, Kenneth Lee, Kalantzis, Vasileios, Horesh, Lior, Ubaru, Shashanka, Akhalwaya, Ismail Yunus, Squillante, Mark S
Format Patent
LanguageEnglish
Published 25.01.2024
Subjects
CALCULATING
COMPUTER SYSTEMS BASED ON SPECIFIC COMPUTATIONAL MODELS
COMPUTING
COUNTING
PHYSICS
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Summary:A quantum computer-implemented system, method, and computer program product for quantum topological domain analysis (QTDA). The QTDA method achieves an improved exponential speedup and depth complexity of O(n log(1/(δ∈))) where n is the number of data points, ∈ is the error tolerance, δ is the smallest nonzero eigenvalue of the restricted Laplacian, and achieves quantum advantage on general classical data. The QTDA system and method efficiently realizes a combinatorial Laplacian as a sum of Pauli operators; performs a quantum rejection sampling and projection approach to build the relevant simplicial complex repeatedly and restrict the superposition to the simplices of a desired order in the complex; and estimates Betti numbers using a stochastic trace/rank estimation method that does not require Quantum Phase Estimation. The quantum circuit and QTDA method exhibits computational time and depth complexities for Betti number estimation up to an error tolerance ∈.
Bibliography:Application Number: US202217863524