QTIS: A QAOA-Based Quantum Time Interval Scheduler

TL;DR

This work tackles time-interval task scheduling with limited resources by formulating the problem as a QUBO and embedding it in a QTIS-QAOA framework. It decomposes the problem Hamiltonian into $H_p$ (objective plus early penalties) and $H_c$ (overlap penalties), enabled by an ancilla-assisted conflict-detection circuit that provides dynamic constraint information to the variational form. Three minimization strategies—Standard QAOA, T-QAOA, and HT-QAOA—are evaluated, with results showing that separate angles for $H_p$ and $H_c$ ($\vec{\gamma} \neq \vec{\zeta}$) generally improve solution quality, and that T-QAOA achieves the lowest mean energy at depth 10, while HT-QAOA offers a favorable trade-off between performance and runtime. The approach demonstrates the potential of hybrid quantum–classical optimization in complex scheduling settings and lays groundwork for scalable, constraint-aware quantum scheduling on NISQ devices.

Abstract

Task scheduling with constrained time intervals and limited resources remains a fundamental challenge across domains such as manufacturing, logistics, cloud computing, and healthcare. This study presents a novel variant of the Quantum Approximate Optimization Algorithm (QAOA) designed to address the task scheduling problem formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. The proposed method, referred to as Quantum Time Interval Scheduler (QTIS), integrates an ancilla-assisted quantum circuit to dynamically detect and penalize overlapping tasks, enhancing the enforcement of scheduling constraints. Two complementary implementations are explored for overlap detection: a quantum approach based on RY rotations and CCNOT gates, and a classical alternative relying on preprocessed interval comparisons. QTIS decomposes the problem Hamiltonian, Hp, into two components, each parameterized by a distinct angle. The first component encodes the objective function, while the second captures penalty terms associated with overlapping intervals, which are controlled by the auxiliary circuit. Subsequently, three minimization strategies are evaluated: standard QAOA, T-QAOA, and HT-QAOA, showing that employing separate parameters for the different components of the problem Hamiltonian leads to lower energy values and improved solution quality. Results confirm the efficiency of QTIS in scheduling tasks with fixed temporal windows while minimizing conflicts, demonstrating its potential to advance hybrid quantum-classical optimization in complex scheduling environments.

Figures (13)

• Figure 1: Task scheduling problem with start time and duration restrictions. Schedule A with optimal planning for the eight tasks, Schedule B with no allocated T4 task
• Figure 2: QAOA Algorithm
• Figure 3: Example of Job Shop Scheduling Problem with 10 jobs and 2 Machines. The goal of the problem is minimizing the total processing time, in this case 9 time units.
• Figure 4: L layers QTIS-QAOA with the parametrized circuits associated to the Hamiltonians $H_p, H_c, H_B$ and the conflict detection circuit
• Figure 5: Circuit for time difference calculations