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Utilizing intermediate states in quantum annealing for multi-objective optimization

Keita Takahashi, Shu Tanaka

Abstract

We investigate obtaining intermediate quantum states during the quantum annealing process to address the limitation of the linear weighted sum method in multi-objective optimization, which inherently fails to reach non-convex regions of the Pareto front. We validate this approach through physical experiments utilizing quench-based readout and numerical simulations assuming ideal mid-anneal measurements. Both methods consistently demonstrate a clear trade-off where earlier timing enhances diversity of the solutions, whereas later timing ensures convergence to non-dominated solutions. Notably, a practical compromise timing balances both metrics. The qualitative agreement between practical quench and ideal simulation indicates the potential of accessing the intermediate states for comprehensive Pareto front exploration.

Utilizing intermediate states in quantum annealing for multi-objective optimization

Abstract

We investigate obtaining intermediate quantum states during the quantum annealing process to address the limitation of the linear weighted sum method in multi-objective optimization, which inherently fails to reach non-convex regions of the Pareto front. We validate this approach through physical experiments utilizing quench-based readout and numerical simulations assuming ideal mid-anneal measurements. Both methods consistently demonstrate a clear trade-off where earlier timing enhances diversity of the solutions, whereas later timing ensures convergence to non-dominated solutions. Notably, a practical compromise timing balances both metrics. The qualitative agreement between practical quench and ideal simulation indicates the potential of accessing the intermediate states for comprehensive Pareto front exploration.
Paper Structure (1 section, 4 equations, 5 figures)

This paper contains 1 section, 4 equations, 5 figures.

Table of Contents

  1. acknowledgement

Figures (5)

  • Figure 1: Annealing schedules for normal QA and QA with quench-based readout at $s=0.1$.
  • Figure 2: Dependence of evaluation metrics on the quench-based readout timing $s$ in physical quantum annealer experiments: (a) normalized HV, (b) normalized SP, and (c) RNI.
  • Figure 3: Sampling results using a physical quantum annealer. (a) QA with quench-based readout at $s=0.1$, (b) normal QA.
  • Figure 4: Dependence of evaluation metrics on mid-anneal measurement timing $s$ in closed-system simulations. Solid lines show average over 10 instances. (a) normalized HV, (b) normalized SP, and (c) RNI.
  • Figure 5: Simulation sampling results for a problem instance ($N=6$). Red squares indicate Pareto-optimal solutions identified by exhaustive enumeration of all $2^N$ configurations (minimization convention), while black circles denote non-Pareto solutions. The color bar represents the sampling frequency of each solution. (a) MAM-QA at $s=0.6$, (b) normal QA.