20240028939. LINEAR-DEPTH QUANTUM SYSTEM FOR TOPOLOGICAL DATA ANALYSIS simplified abstract (INTERNATIONAL BUSINESS MACHINES CORPORATION)
Contents
LINEAR-DEPTH QUANTUM SYSTEM FOR TOPOLOGICAL DATA ANALYSIS
Organization Name
INTERNATIONAL BUSINESS MACHINES CORPORATION
Inventor(s)
Ismail Yunus Akhalwaya of Emmarentia (ZA)
Shashanka Ubaru of Ossining NY (US)
Kenneth Lee Clarkson of Madison NJ (US)
Mark S. Squillante of Greenwich CT (US)
Vasileios Kalantzis of White Plains NY (US)
Lior Horesh of North Salem NY (US)
LINEAR-DEPTH QUANTUM SYSTEM FOR TOPOLOGICAL DATA ANALYSIS - A simplified explanation of the abstract
This abstract first appeared for US patent application 20240028939 titled 'LINEAR-DEPTH QUANTUM SYSTEM FOR TOPOLOGICAL DATA ANALYSIS
Simplified Explanation
The abstract describes 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/(ε^2))) where n is the number of data points, ε is the error tolerance, and ε^2 is the smallest nonzero eigenvalue of the restricted Laplacian. It also achieves quantum advantage on general classical data.
The QTDA system and method efficiently realize a combinatorial Laplacian as a sum of Pauli operators. It performs a quantum rejection sampling and projection approach to repeatedly build the relevant simplicial complex and restrict the superposition to the simplices of a desired order in the complex. It estimates Betti numbers using a stochastic trace/rank estimation method that does not require quantum phase estimation. The quantum circuit and QTDA method exhibit computational time and depth complexities for Betti number estimation up to an error tolerance ε.
- Quantum computer-implemented system, method, and computer program product for quantum topological domain analysis (QTDA)
- Achieves improved exponential speedup and depth complexity
- Efficiently realizes a combinatorial Laplacian as a sum of Pauli operators
- Performs quantum rejection sampling and projection approach to build relevant simplicial complex repeatedly
- Restricts superposition to simplices of desired order in the complex
- Estimates Betti numbers using stochastic trace/rank estimation method
- Does not require quantum phase estimation
- Computational time and depth complexities for Betti number estimation up to an error tolerance ε
Potential applications of this technology:
- Topological data analysis in various fields such as biology, chemistry, physics, and finance
- Optimization problems in logistics, transportation, and supply chain management
- Machine learning and pattern recognition tasks
- Network analysis and graph theory
Problems solved by this technology:
- Efficient analysis of large-scale datasets
- Improved computational speed and complexity for topological domain analysis
- Overcoming limitations of classical computing in handling complex data structures
Benefits of this technology:
- Exponential speedup and depth complexity compared to classical methods
- Quantum advantage on general classical data
- Accurate estimation of Betti numbers without requiring quantum phase estimation
- Potential for breakthroughs in various scientific and industrial applications
Original Abstract Submitted
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/(�∈))) where n is the number of data points, ∈ is the error tolerance, � 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 ∈.
