Quantum Branch-and-Bound Algorithms with Heuristics
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Solution Overview
Problem
Existing quantum algorithms for Mixed Integer Programming (MIP) lack incorporation of search heuristics, limiting their ability to leverage domain knowledge and are outperformed by classical algorithms despite superior worst-case guarantees, as they only search for exact optimal solutions and do not adapt well to practical problems.
Innovation Solution
Implementing quantum branch-and-bound algorithms with heuristic functions that utilize a classical computer to set up and guide a quantum computer in exploring a tree of relaxed problems, incorporating depth-based or cost-based heuristics to efficiently find approximate solutions by iteratively refining the search and estimating subtree sizes, thereby leveraging both classical and quantum computing capabilities.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If existing quantum algorithms are used to solve MIP problems, then worst-case runtime guarantee is improved (quadratic speedup), but practical performance deteriorates because they cannot incorporate search heuristics and domain knowledge
Solution Approach 1:
The patent merges classical and quantum computing resources into a hybrid system where the quantum computer performs subtree size estimation while the classical computer manages the branch-and-bound framework and heuristic functions. This combination allows the system to maintain quantum speedup advantages while incorporating classical search heuristics for practical problem solving.
Solution Approach 2:
The patent introduces a hybrid classical-quantum interface that acts as an intermediary between the quantum subtree size estimation algorithm and the classical branch-and-bound framework. This intermediary layer enables bidirectional communication and coordination, allowing heuristic information to guide quantum computations while quantum results feed back into the classical optimization process.
2Measurement precision
If quantum algorithms search for exact optimal solutions only, then solution accuracy is improved, but computation time deteriorates because they cannot use approximation margins to prune the search tree
Solution Approach 1:
The patent applies partial action by allowing the quantum algorithm to estimate subtree sizes with approximate precision rather than exact values. By using an approximation margin parameter, the system performs sufficiently accurate subtree size estimation to enable effective pruning, without requiring perfect precision. This partial accuracy is sufficient to achieve practical speedups while reducing computational overhead.
3Productivity
If classical branch-and-bound algorithms use search heuristics, then practical performance is improved by finding good approximate solutions faster, but worst-case runtime guarantee deteriorates because heuristics cannot prevent exploring the entire tree in worst cases
Solution Approach 1:
The patent implements feedback mechanisms where the quantum subtree size estimation results are fed back into the classical branch-and-bound algorithm to dynamically adjust the search strategy. The estimated subtree sizes provide feedback that guides which branches to explore first and when to prune branches, creating a closed-loop system that adapts to the problem structure while maintaining theoretical guarantees.
Data Source
AI summary
Quantum branch-and-bound algorithms with heuristics are disclosed. A method may include: receiving a branch and bound problem; setting an upper bound, a best bound, an incumbent, and a counter i; executing a subtree estimation procedure that returns branch_m that represents a tree of size m; determining branch_i and cost_i for branch_m; setting cost_feas to a value COST(N) for feasible nodes N, and to +∞ for unfeasible nodes; instructing a quantum computer to execute a QuantumMinimumLeaf procedure to get a node N and setting incumbent′ to COST(N); instructing the quantum computer to execute the QuantumMinimumLeaf procedure to get a node N′ and to setting best bound′ to equal COST(N′); and returning the node N when an absolute value of a difference between a minimum of incumbent and incumbent′ and a minimum of best bound and best bound′ is less than the approximation margin.