Ising Machine Solving L0 Sparse Modeling Combinatorial Explosion

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Solution Overview

Problem

Conventional algorithms for sparse modeling, such as L0 sparse modeling, are impractical due to their association with combinatorial explosion, making it difficult to optimize combinatorial optimization problems within a reasonable calculation time, especially when dealing with large scales and ensuring complete data restoration in applications like compressed sensing.

Innovation Solution

The proposed method employs an Ising machine to convert combinatorial optimization problems into an Ising model, leveraging quantum annealing to efficiently solve L0 sparse modeling and optimize observation variable dimension selection, thereby reducing calculation time and ensuring accurate sparse solution generation.

Engineering Contradictions & Design Principles

VSEngineering Contradiction Analysis

1Ease of manufacture

If conventional algorithms for sparse modeling are used, then the method is simple to implement, but the calculation time becomes excessively long due to combinatorial explosion

Engineering Contradiction:

ImproveEase of implementationVSAvoidCalculation time

Core Design Contradiction:

Ease of manufactureVSLoss of time

Solution Approach 1:

The patent replaces conventional computational algorithms with a quantum-inspired Ising machine that uses physical quantum annealing processes to solve combinatorial optimization problems. This substitution of mechanical/computational systems with quantum physical systems enables exponential speedup in solving sparse modeling problems without sacrificing implementation feasibility, as the Ising machine handles the combinatorial explosion through quantum tunneling and annealing rather than classical enumeration.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

2Measurement precision

If L0 sparse modeling is performed to ensure complete data restoration, then the accuracy of sparse solution is improved, but the computational complexity increases causing combinatorial explosion

Engineering Contradiction:

ImproveAccuracy of sparse solutionVSAvoidComputational complexity

Core Design Contradiction:

Measurement precisionVSDevice complexity

Solution Approach 1:

The patent replaces classical computational algorithms with a quantum-inspired Ising machine to solve L0 sparse modeling problems. The quantum annealing process naturally handles the combinatorial complexity of L0 norm minimization by mapping it to an Ising Hamiltonian, where the ground state corresponds to the optimal sparse solution. This physical system approach maintains high accuracy for complete data restoration while avoiding the combinatorial explosion that plagues classical algorithms.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Solution Approach 2:

The patent transforms the L0 sparse modeling problem by changing the parameter representation from classical computational variables to quantum spin variables in the Ising model. This parameter transformation allows the system to exploit quantum effects for solving the optimization problem efficiently, maintaining the accuracy required for complete data restoration in compressed sensing applications.

Inventive Principle:

Principle #35Parameter changes

3Measurement precision

If observation variable dimension selection is optimized for accurate sparse modeling, then the quality of sparse solution is improved, but the calculation time increases significantly

Engineering Contradiction:

ImproveQuality of sparse solutionVSAvoidCalculation time

Core Design Contradiction:

Measurement precisionVSLoss of time

Solution Approach 1:

The patent replaces classical optimization algorithms with a quantum-inspired Ising machine for observation variable dimension selection. The quantum annealing process efficiently searches the combinatorial space of possible dimension selections and identifies the optimal subset that maximizes sparse solution quality. This physical system approach dramatically reduces calculation time compared to exhaustive classical search methods while maintaining or improving the quality of sparse modeling results.

Inventive Principle:

Principle #28Mechanics substitution (Replace mechanical system)

Applied Scientific Principles

This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.

Function Achieved in This Case

This approach enables faster and more accurate sparse modeling by transforming combinatorial optimization problems into an Ising model, allowing for high-speed optimization and reliable dimension selection in compressed sensing, thus overcoming the limitations of traditional methods.

Implementation Method 1

leveraging quantum annealing to efficiently solve L0 sparse modeling and optimize observation variable dimension selection

Methodology Applied

Scientific EffectQuantum annealing: Annealing

Data Source

PatentUS20230342416A1Optimization problem solving method and optimization problem solving device

Publication Date: 2023.10.26 SONY GROUP CORP

AI summary

An optimization problem solving method according to the present disclosure includes: inputting first data from a sensor; generating an objective function for performing sparse modeling on the first data; generating a coefficient matrix related to a variable to be optimized in the objective function; transmitting the coefficient matrix to a first Ising machine that performs combinatorial optimization calculation; and generating an optimum solution of sparse modeling based on second data received from the first Ising machine.