Quantum Distance Computation via Amplitude Estimation
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Solution Overview
Problem
Conventional quantum computing methods for classification and distance measurements are inefficient, particularly when dealing with irregular or complex data distributions, often resulting in success probabilities no better than random guessing due to reliance on mean data values.
Innovation Solution
The development of quantum computation methods that use amplitude estimation and coherent majority voting to determine Euclidean distances and inner products between data vectors, allowing for accurate nearest neighbor classification and cluster assignment without explicit dependence on the number of features in a feature vector.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of manufacture
If mean value based quantum computing methods are used for classification, then the computation can be performed with simple algorithms, but the success probability is only about 50% which is no better than random guessing
Solution Approach 1:
The patent replaces mean value based quantum computing methods with amplitude estimation based quantum computing methods. This substitution transforms the underlying computational mechanism from one that computes average values to one that directly estimates amplitudes, thereby achieving both improved success probability (close to 100%) and maintained algorithmic simplicity through the use of quantum amplitude estimation techniques.
2Adaptability or versatility
If conventional quantum computing methods are used for distance measurements with irregular or complex data distributions, then the computation can be performed with existing algorithms, but the success probability is no better than random guessing
Solution Approach 1:
The patent changes the fundamental parameter being estimated from mean values to amplitudes. By using amplitude estimation instead of mean value computation, the method achieves high success probability (close to 100%) for irregular or complex data distributions while maintaining compatibility with existing quantum computing frameworks through standardized amplitude estimation procedures.
3Productivity
If quantum computing methods are used to achieve exponential speed-up over classical algorithms, then the computation time is reduced to logarithmic scale, but the reliability of classification results is compromised with only 50% success probability
Solution Approach 1:
The patent substitutes mean value based quantum computation with amplitude estimation based quantum computation. This replacement maintains the exponential speed-up advantage (logarithmic computation time) while simultaneously achieving high reliability (success probability close to 100%) by leveraging the precise amplitude measurement capabilities of quantum computers.
Data Source
Figure 1
Figure 2~3B
Figure 3A
AI summary
Nearest neighbor distances are obtained by coherent majority voting based on a plurality of available distance estimates produced using amplitude estimation without measurement in a quantum computer. In some examples, distances are Euclidean distances or are based on inner products of a target vector with vectors from a training set of vectors. Distances such as mean square distances and distances from a data centroid can also be obtained.