Multi-tasking through quantum annealing

TL;DR

MTQA enables efficient multitasking in quantum annealing, optimizing hardware utilization and improving throughput for concurrent tasks and demonstrating performance for problems up to 100 nodes in real-world applications.

Abstract

Quantum annealing approximately solves combinatorial optimization problems by leveraging the principles of adiabatic quantum systems. In this approach, the system's Hamiltonian evolves from an initial general state to a problem-specific state. This study introduces multi-tasking quantum annealing (MTQA), a method that enables the parallel processing of multiple optimization problems by embedding them into spatially distinct regions on quantum hardware. MTQA is evaluated using two NP-hard problems: the minimum vertex cover problem (MVCP) and the graph partitioning problem (GPP). This parallel approach optimizes quantum resource utilization by concurrently utilizing idle qubits. The findings demonstrate that MTQA achieves a solution quality comparable to single-problem quantum annealing and classical simulated annealing (SA), while notably reducing the time-to-solution (TTS) metrics. Eigenspectrum analysis further theoretically supports the hypothesis that parallel embedding preserves quantum coherence and does not increase computational complexity by efficiently utilizing available quantum hardware (e.g., qubits and couplers). MTQA enables efficient multitasking in quantum annealing, optimizing hardware utilization and improving throughput for concurrent tasks and demonstrating performance for problems up to 100 nodes in real-world applications.

Figures (9)

• Figure 1: Parallel embedding in D-Wave Advantage 6.4 hardware (Pegasus topology). (a) Dense parallel embedding without isolation, where problems are tightly embedded on hardware. MVCP (eight instances, shown in red) and GPP (eight instances, shown in blue) problems embedded into hardware, demonstrating maximum hardware utilization. (b) Magnified view of the region from (a), highlighting congested qubit environment where adjacent qubits support different tasks. (c) Parallel embedding with neighbor isolation strategy (gray regions represent isolation layers), which separates different problem instances on hardware. We embedded MVCP (six instances, shown in red) and GPP (five instances, shown in blue) with this method.
• Figure 2: Number of parallel embeddings with log scale as a function of graph size. Plot demonstrates how embedding capacity decreases with increasing problem size, with both isolated (solid lines) and non-isolated (dashed lines) strategies shown for MVCP (red) and GPP (blue). Both strategies show exponential decrease in embedding capacity as problem size increases, with convergence for larger problems.
• Figure 3: Chain length variations as a function of graph size. (a) MVCP chain length comparison showing average chain lengths (bars) and standard deviations (error bars) from 100 parallel embeddings for both isolated (red) and non-isolated (blue) strategies. (b) Similar analysis for GPP, demonstrating consistently longer chains and larger standard deviations, particularly for problems with more than 70 nodes.
• Figure 4: Ground-state probability (GSP) analysis comparing quantum and classical approaches. Plot demonstrates GSP values as problem size increases from 10 to 100 nodes. MTQA isolated (blue) and non-isolated (red) implementations compared to PQA (pink), traditional QA (green), and the classical Simulated Annealing (SA) heuristic (gray). MTQA, QA, and SA maintain high GSP ($>0.9$) across most problem sizes. In contrast, PQA fails for heterogeneous MVCP instances, with GSP dropping to near zero for $n \ge 30$.
• Figure 5: Time-to-solution (TTS) comparison across different approaches as a function of graph size. Plot shows TTS (log scale) for problems ranging from 10 to 100 nodes. MTQA approaches (both isolated and non-isolated) achieve lower TTS compared to standard QA and significantly outperform exact solvers in solution generation time (though exact solvers provide optimality guarantees). Simulated Annealing (SA) serves as a classical heuristic benchmark. Note that the PQA line for MVCP terminates at $n = 30$ because its success probability drops to zero, rendering TTS undefined.