Quantum-Assisted MIP Solving with BQM Sampling Heuristics
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Solution Overview
Problem
Classical solvers for mixed integer problems (MIPs) are inefficient due to high computational time and cannot certify optimality, while quantum processors alone are not suited for representing continuous variables, necessitating a hybrid classical and quantum MIP solver.
Innovation Solution
A method involving a digital processor augmented with quantum-assisted heuristics, such as crossover or mutation heuristics, to reduce the search space of MIPs by generating sample solutions using a quantum processor, embedding Binary Quadratic Models (BQMs), and updating incumbent solutions based on quantum-generated samples.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If classical solvers are used to solve mixed integer problems, then solution accuracy can be maintained, but computational time becomes excessively long
Solution Approach 1:
The patent segments the MIP solving process into distinct phases: classical preprocessing to generate initial feasible solutions and identify integer variables, quantum processing to generate diverse candidate solutions by sampling from probability distributions, and classical post-processing to evaluate and refine solutions. This segmentation allows each component to operate in its optimal domain, reducing overall computational time while maintaining solution accuracy.
Solution Approach 2:
The patent introduces quantum processors as an intermediary between classical solvers and the MIP problem. The quantum processor acts as a mediator that generates candidate solutions through quantum sampling, which are then evaluated by classical solvers. This intermediary approach leverages quantum parallelism to explore the solution space more efficiently than classical methods alone, thereby reducing computational time without sacrificing solution quality.
2Loss of time
If quantum processors are used to solve MIPs, then computational time can be reduced, but the ability to represent continuous variables is lost
Solution Approach 1:
The patent segments variables into two categories: continuous variables are handled by classical solvers during preprocessing and post-processing, while only integer variables are processed by the quantum processor. This segmentation allows the system to leverage quantum computing's speed advantages for discrete optimization while maintaining full capability for continuous variable representation through classical methods.
Solution Approach 2:
The classical solver acts as an intermediary that bridges the quantum processor's limited representation capability with the full requirements of MIPs. It performs preprocessing to identify integer variables for quantum processing, and post-processing to evaluate candidate solutions and handle continuous variables, thereby enabling the hybrid system to solve complete MIPs despite the quantum processor's limitations.
3Measurement precision
If quantum-assisted heuristics are implemented, then solution quality improves, but system complexity increases
Solution Approach 1:
The patent segments the hybrid system into modular components with clearly defined interfaces: a classical preprocessing module that prepares the MIP by identifying integer variables and generating initial solutions, a quantum processing module that generates candidate solutions, and a classical post-processing module that evaluates and refines solutions. This modular segmentation manages system complexity by allowing each component to be developed, tested, and optimized independently while maintaining overall integration.
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 significantly reduces computational time and cost by leveraging quantum-assisted heuristics to improve the solution quality and efficiency of MIP solvers.
Implementation Method 1
A quantum computer is a system that makes direct use of at least one quantum-mechanical phenomenon, such as, superposition, tunneling, and entanglement, to perform operations on data.
Implementation Method 2
A quantum computer is a system that makes direct use of at least one quantum-mechanical phenomenon, such as, superposition, tunneling, and entanglement, to perform operations on data.
Implementation Method 3
A quantum computer is a system that makes direct use of at least one quantum-mechanical phenomenon, such as, superposition, tunneling, and entanglement, to perform operations on data.
Implementation Method 4
Operation of superconducting qubits is based on the underlying principles of magnetic flux quantization, and Josephson tunneling.
Implementation Method 5
Operation of superconducting qubits is based on the underlying principles of magnetic flux quantization, and Josephson tunneling.
Implementation Method 6
Adiabatic quantum computation can include evolving a system from an initial Hamiltonian to a final Hamiltonian by a gradual change.
Implementation Method 7
While classical annealing uses classical thermal fluctuations to guide a system to a low-energy state, quantum annealing may use quantum effects, such as quantum tunneling, as a source of delocalization to reach an energy minimum more accurately and/or more quickly than classical annealing.
Data Source
AI summary
There is provided a system and methods to determine an improved solution to a Mixed Integer Problem (MIP) using a quantum-assisted MIP solver. The methods are performed by a digital processor in communication with a quantum processor. Methods include: selecting at least one feasible solution determined by an MIP solver, determining a first sub-problem of the MIP based on the at least one feasible solution; casting the first sub-problem as Binary Quadratic Models (BQMs); solving the BQMs using the quantum processor to generate sample solutions; determining a second sub-problem based on at least the sample solutions, and obtaining a current solution to the MIP by evaluating the second sub-problem; and updating an incumbent solution if the current solution improves over the current incumbent solution. The quantum-assisted MIP solver uses hybrid crossover and mutation heuristics to improve the convergence time and accuracy of solutions obtained using Branch-and-Cut solvers.