Simulations of the adiabatic quantum optimization for the Set Partition Problem

Abstract

We analyze the complexity of the quantum optimization algorithm based on adiabatic evolution for the set partition problem. We introduce a cost function defined on a logarithmic scale of the partition residues so that the total number of values of the cost function is of the order of the problem size. We simulate the behavior of the algorithm by numerical solution of the time-dependent Schroedinger equation as well as the stationary equation for the adiabatic eigenvalues. The numerical results for the time-dependent quantum evolution indicate that the complexity of the algorithm scales exponentially with the problem size.This result appears to contradict the recent numerical results for complexity of quantum adiabatic algorithm applied to a different NP-complete problem (Farhi et al, Science 292, p.472 (2001)).

13 pages, 5 figures Added simulation results for n=17 bits

References in corpus (6)

• Quantum Mechanics helps in searching for a needle in a haystack
• A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
• Quantum Search by Local Adiabatic Evolution
• Phase Transition in the Number Partitioning Problem
• Random Costs in Combinatorial Optimization
• A Numerical Study of the Performance of a Quantum Adiabatic Evolution Algorithm for Satisfiability

Cited by in corpus (6)

• Adiabatic Quantum Computing
• Prospects for Quantum Enhancement with Diabatic Quantum Annealing
• Adiabatic Quantum Computing for Random Satisfiability Problems
• Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability
• Experimental demonstration of perturbative anticrossing mitigation using non-uniform driver Hamiltonians
• Towards Large-Scale Quantum Computation