Hybrid Quantum-Classical Lattice Problem Solver
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Solution Overview
Problem
Current methods for solving lattice problems, particularly in quantum computing, are inefficient and unable to effectively handle learning in feed-forward neural networks due to decoherence issues and the inability to efficiently apply quantum algorithms to nonlinear systems.
Innovation Solution
A hybrid approach combining classical and quantum computers, where classical computers handle light tasks and quantum computers handle heavy tasks, using quantum computation to transform the closest vector problem into a modified learning with errors problem, enabling efficient solution of lattice problems and learning in feed-forward neural networks.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Speed
If quantum algorithms are used to solve lattice problems, then computation speed is improved, but decoherence due to noise limits the execution time period
Solution Approach 1:
The patent segments the computation process into two distinct parts: classical computation for preparing input data and light tasks, and quantum computation for handling heavy computational tasks. This segmentation allows the quantum computer to operate only for the essential quantum operations, reducing the overall execution time period affected by decoherence while maintaining the speed advantages for critical computations.
Solution Approach 2:
The patent applies preliminary action by having the classical computer perform data preparation and preprocessing tasks before the quantum computation begins. This includes preparing input data, setting up problem parameters, and performing initial computations that do not require quantum resources, thereby reducing the time the quantum system must remain active and minimizing decoherence effects.
2Productivity
If quantum algorithms are applied to nonlinear systems like deep neural networks, then learning efficiency is improved, but the HHL algorithm is inapplicable to feed-forward neural networks
Solution Approach 1:
The patent develops a quantum algorithm framework that serves multiple functions: it can handle lattice problems, solve linear systems for Boltzmann machines, and learn feed-forward neural networks. The algorithm uses quantum phase estimation and amplitude amplification techniques that are universally applicable across different computational tasks, making the quantum system versatile while maintaining efficiency.
Solution Approach 2:
The patent changes the computational parameters and approach by using quantum phase estimation and amplitude amplification instead of the HHL algorithm's specific linear system solving approach. This parameter change allows the algorithm to adapt to nonlinear systems and feed-forward neural networks by transforming the learning problem into a form suitable for quantum computation, thereby expanding adaptability while preserving learning efficiency.
3Ease of manufacture
If classical lattice reduction algorithms are used, then implementation is simple, but the length of the shortest vector increases exponentially in the worst case
Solution Approach 1:
The patent substitutes the classical mechanical/computational lattice reduction process with a quantum computational approach. Instead of using classical algorithms that iteratively reduce the lattice basis, the patent employs quantum phase estimation and amplitude amplification to directly find short vectors in the lattice. This substitution replaces the step-by-step classical reduction process with a quantum parallel search that achieves better precision without the exponential worst-case behavior.
Data Source
AI summary
First, a dual basis B− of B of modulo N is obtained by classical computation. Next, quantum computation is performed using the periodicity of a point sequence included in a sum set of sets obtained by parallel translation of a lattice L(B) by integral multiples of t for a plurality of integers, and an n-dimensional rj=(rj1, . . . , rjn) and rj0 are obtained for j=1, . . . , m. Subsequently, by classical computation, the closest vector rj(c)=(rj1(c), . . . , rjn(c))∈L(B−) of the n-dimensional vector rj, and the difference vector rj(d)=rj−rj(c)=(rj1(d), . . . , rjn(d)) corresponding to rj(c) are obtained.