Quantum Warm-Start Optimisation for Faster Classical Convergence
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Solution Overview
Problem
Existing classical optimisation algorithms face challenges in efficiently solving hard problems due to the limitations of NISQ quantum computers, which require excessive accuracy and fail to leverage the valuable information encoded in approximate quantum solutions.
Innovation Solution
Utilize approximate quantum solutions as 'warm starts' for classical algorithms, leveraging the quantum process's ability to probe solution spaces and cluster around better solutions, thereby improving the efficiency of classical algorithms by providing high-quality initial inputs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Extent of automation
If quantum computers in the NISQ era are used to solve optimisation problems directly, then quantum computational capability is utilized, but the limited hardware capabilities and high error rates prevent achieving sufficient solution accuracy
Solution Approach 1:
The solution process is segmented into two distinct phases: (1) quantum phase that generates approximate solutions and explores solution space, and (2) classical phase that refines these solutions to optimality. This segmentation allows each phase to operate within its strengths while avoiding its weaknesses.
Solution Approach 2:
The quantum computer performs preliminary action by generating approximate solutions and identifying promising regions of the solution space before the classical refinement phase begins. This preliminary exploration provides a head start that accelerates the overall solution process.
2Measurement precision
If bespoke classical algorithms are used to correct quantum output errors, then solution accuracy is improved, but the algorithms become highly specific and fail to leverage general classical optimisation capabilities
Solution Approach 1:
The classical refinement phase uses universal classical optimisation algorithms that can handle various types of optimisation problems, rather than problem-specific bespoke algorithms. This allows the same classical algorithms to work with outputs from different quantum algorithms and for different optimisation problem types.
Solution Approach 2:
The approximate quantum solution acts as an intermediary that bridges quantum computation and classical optimisation. Instead of directly correcting quantum errors, the classical algorithm receives the quantum output as a starting point and guides it toward the optimal solution using general optimisation principles.
3Measurement precision
If quantum computers are required to provide highly accurate solutions directly, then solution quality is maintained, but the computational resources and time required become excessive for NISQ hardware
Solution Approach 1:
The quantum computer performs partial action by generating only approximate solutions rather than requiring complete and accurate solutions. This partial computation is sufficient to provide a good starting point that dramatically reduces the workload for the classical refinement phase.
Solution Approach 2:
The quantum phase performs preliminary exploration of the solution space to identify promising regions before the classical algorithm begins its systematic refinement. This preliminary action avoids the need for the quantum computer to perform the computationally expensive task of finding the exact optimal solution.
4Device complexity
If classical algorithms start with random initial solutions, then algorithm simplicity is maintained, but convergence time and resource usage increase significantly
Solution Approach 1:
The quantum computer performs preliminary action by generating informed initial solutions that are already close to optimal, rather than using completely random starting points. This preliminary generation of quality initial solutions dramatically reduces the number of iterations needed for classical convergence.
Solution Approach 2:
The initial solutions generated by the quantum computer have different statistical properties compared to random solutions. They exhibit clustering around optimal regions and have lower objective function values on average, which fundamentally changes the convergence characteristics of the classical refinement algorithm.
Data Source
AI summary
The invention relates to methods and apparatuses for improving the efficiency of solving optimisation problems. The invention includes the use of a quantum computer to provide a warm start to a known optimisation algorithm, thereby resulting in the known algorithm starting from a better (more promising) location in the solution space. This better starting point allows the known algorithm to converge on a good (i.e. toward an optimum) solution quicker, e.g. in fewer steps, and to reach better solutions sooner than known methods involving cold starts.