Core Concepts
新しい量子制約ハミルトニアン最適化(Q-CHOP)アルゴリズムは、制約最適化問題における革新的なアプローチを提供する。
Abstract
I. Introduction to Constrained Optimization Problems:
Combinatorial optimization problems in science and industry involve constraints.
Quantum computers offer a new approach to tackle these challenges.
II. Quantum Algorithms for Constrained Optimization:
Various quantum algorithms proposed for constrained optimization.
Adiabatic quantum computation is a promising class of algorithms.
III. Adiabatic Quantum Algorithms:
Adiabatic quantum algorithms follow an adiabatic path from an easy-to-prepare ground state to the problem's ground state.
IV. Quantum Constrained Hamiltonian Optimization (Q-CHOP):
A. General Strategy:
Identify initial Hamiltonian and construct a ramp to trace a path to the objective Hamiltonian.
B. Odd Objectives and Bad Solutions:
Q-CHOP strategy when the objective is odd and worst feasible state is easy to prepare.
C. Arbitrary Objectives and Feasible States:
Relaxing requirements for worst feasible state preparation in Q-CHOP algorithm.
D. Inequality Constraints:
Treatment of inequality constraints in Q-CHOP and SAA, introducing slack variables.
E. Numerical Experiments:
1. Maximum Independent Set (MIS):
Q-CHOP outperforms SAA in finding high-quality solutions on average for MIS problems.
2. Directed Minimum Dominating Set (DMDS):
Similar performance trends observed for DMDS as with MIS using Q-CHOP and SAA.
3. Knapsack Problem:
Q-CHOP achieves higher approximation ratios and optimal-state probabilities compared to SAA for knapsack instances.
4. Combinatorial Auction (CA):
Performance evaluation of CA problem instances with Q-CHOP and SAA.
Stats
Adiabatic quantum computation is polynomially equivalent to standard gate-based quantum computation [17].
The spectral gap ∆con can typically be determined by inspection of the constraint Hamiltonian Hcon.