Quantum Image Cross-Correlation Using Amplitude Estimation
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Solution Overview
Problem
Current computing systems, including those using cross correlation techniques and expectation maximization maximum likelihood (EMML) algorithms, face significant computational challenges when processing large datasets, particularly in fields like image processing and charged particle systems, and are hindered by the inability to perform certain calculations within quantum computing systems.
Innovation Solution
The implementation of quantum computing systems that compute cross-correlations between images using qubits configured for quantum amplitude estimation, allowing for the determination of correlation values and generation of less noisy images through quantum EMML algorithms, thereby leveraging quantum computing's speedup capabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum computing systems are used to compute cross-correlations, then computational speedup is achieved, but the ability to perform certain calculations within quantum systems is currently limited
Solution Approach 1:
The patent uses quantum amplitude estimation as an intermediary mechanism to enable cross-correlation calculations in quantum systems. The quantum amplitude estimation algorithm acts as a mediator that translates classical cross-correlation operations into quantum-compatible operations, allowing the quantum system to perform calculations that were previously thought impossible while maintaining quadratic speedup over classical systems.
2Loss of time
If classical cross-correlation techniques are used, then computational complexity is reduced from O(N2) to O(N log N), but processing time remains hundreds of hours for large datasets
Solution Approach 1:
The patent replaces the classical mechanical computing system with a quantum computing system. By substituting quantum mechanics principles (superposition, entanglement, quantum amplitude estimation) for classical mechanical computation, the system achieves quadratic speedup, reducing processing time from hundreds of hours to a fraction of that time while maintaining computational efficiency.
3Measurement precision
If EMML algorithms are applied to noisy images, then image quality is improved, but large amounts of computing resources are required
Solution Approach 1:
The patent changes the fundamental parameters of the computation by moving from classical to quantum computing. This parameter change allows the EMML algorithm to process noisy images and improve image quality while consuming significantly fewer computing resources, as quantum systems can process information in superposition states, exponentially reducing the computational burden compared to classical iterative approaches.
Data Source
AI summary
Methods and systems for quantum computing based sample analysis include computing cross-correlations of two images using a quantum processing system, and computing less noisy image based of two or more images using a quantum processing system. Specifically, the disclosure includes methods and systems for utilizing a quantum computing system to compute and store cross correlation values for two sets of data, which was previously believed to be physically impossible. Additionally, the disclosure also includes methods and systems for utilizing a quantum computing system to generate less noisy data sets using a quantum expectation maximization maximum likelihood (EMML). Specifically, the disclosed systems and methods allow for the generation of less noisy data sets by utilizing the special traits of quantum computers, the systems and methods disclosed herein represent a drastic improvement in efficiency over current systems and methods that rely on traditional computing systems.