A Quantum Constraint Generation Framework for Binary Linear Programs

Abstract

We propose a new approach to utilize quantum computers for binary linear programming (BLP), which can be extended to general integer linear programs (ILP). Quantum optimization algorithms, hybrid or quantum-only, are currently general purpose, standalone solvers for ILP. However, to consider them practically useful, we expect them to overperform the current state of the art classical solvers. That expectation is unfair to quantum algorithms: in classical ILP solvers, after many decades of evolution, many different algorithms work together as a robust machine to get the best result. This is the approach we would like to follow now with our quantum 'solver' solutions. In this study we wrap any suitable quantum optimization algorithm into a quantum informed classical constraint generation framework. First we relax our problem by dropping all constraints and encode it into an Ising Hamiltonian for the quantum optimization subroutine. Then, by sampling from the solution state of the subroutine, we obtain information about constraint violations in the initial problem, from which we decide which coupling terms we need to introduce to the Hamiltonian. The coupling terms correspond to the constraints of the initial binary linear program. Then we optimize over the new Hamiltonian again, until we reach a feasible solution, or other stopping conditions hold. Since one can decide how many constraints they add to the Hamiltonian in a single step, our algorithm is at least as efficient as the (hybrid) quantum optimization algorithm it wraps. We support our claim with results on small scale minimum cost exact cover problem instances.

References in corpus (19)

• A variational eigenvalue solver on a quantum processor
• Ising formulations of many NP problems
• Quantum Annealing in the Transverse Ising Model
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Variational ansatz-based quantum simulation of imaginary time evolution
• Obstacles to State Preparation and Variational Optimization from Symmetry Protection
• Challenges and Opportunities in Quantum Optimization
• Quantum speedup of branch-and-bound algorithms
• Digitized-Counterdiabatic Quantum Optimization
• Quantum-Informed Recursive Optimization Algorithms
• Variational Quantum Time Evolution without the Quantum Geometric Tensor
• Reachability Deficits in Quantum Approximate Optimization of Graph Problems
• Iterative Power Algorithm for Global Optimization with Quantics Tensor Trains
• Opening the Black Box Inside Grover's Algorithm
• Variational quantum iterative power algorithms for global optimization
• Mixed Integer Linear Programming Solver Using Benders Decomposition Assisted by Neutral Atom Quantum Processor
• Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end
• Practical limitations of quantum data propagation on noisy quantum processors