Detuning Choice Solves Quantum MIS and MWIS Problems on Graphs up to 30 Qubits

The challenge of solving complex optimisation problems, such as finding the Maximum Weighted Independent Set and its quantum counterpart, frequently encounters limitations when implemented on current quantum hardware. Sem Saada Khelkhal and Louis Barcikowsky tackle this issue by introducing a novel computational method based on carefully controlling the ‘detuning’ of qubits, effectively minimising unwanted interactions in complex networks. This approach allows for more reliable calculations on asymmetric graphs, even with the constraints of limited qubit numbers and other hardware restrictions present in systems like those developed by Pasqal. By proposing three distinct variants, ranging from theoretical models to implementations suitable for today’s technology, the researchers demonstrate a pathway towards achieving realistic and transferable performance on quantum processors with up to thirty qubits, representing a significant step towards practical quantum optimisation.

The research focuses on mapping these problems onto quantum hardware and employing quantum computation to find approximate solutions, comparing methods such as local detuning, diagonal modulation, and global detuning. Results demonstrate high probabilities of measuring an independent set, suggesting these methods effectively identify large sets, though not always the absolute maximum. For MWIS, the team assessed both success probability and optimality ratio, showing that even when an exact solution isn’t found, the results often closely approximate the optimum.

While high MIS probabilities indicate reliable identification of large independent sets, achieving the absolute maximum remains a challenge. Local detuning and diagonal modulation consistently perform well, often achieving the highest probabilities and ratios, though performance is heavily dependent on the specific graph instance, a common characteristic of combinatorial optimization. This work directly confronts limitations imposed by current hardware, including qubit number, control parameter bounds, sequence durations, confinement space, minimum interatomic distances, and unwanted interactions between atoms. To achieve results compatible with existing technology, the team focused on asymmetric graphs, scaling their methods to systems of up to 30 qubits, and engineered three distinct approaches to detuning calculation, each tailored to different levels of hardware maturity. The first approach, a theoretical local-detuning method, treats each atom individually to establish a baseline for performance.

Building on this foundation, scientists introduced Detuning Map Modulation (DMM), which closely approximates the theoretical model while considering near-term feasibility. Finally, the team developed a global-pulse implementation, utilizing frequency shifts to create a method directly applicable to current hardware, even under stricter conditions. The research team developed a new detuning computation method that mitigates unwanted interactions in asymmetric graphs, achieving results directly compatible with current hardware. Three distinct approaches were introduced, each tailored to different levels of hardware maturity, and thoroughly evaluated on Pasqal’s emulators for graphs containing up to 30 qubits. The team’s innovative detuning method addresses the issue of unwanted interactions, which typically distort outcomes in asymmetric graphs, by proposing three complementary strategies.

A speculative local-detuning approach demonstrated the application of pure theory, while Detuning Map Modulation (DMM) closely approximated the theoretical framework with a view toward future implementation. Crucially, a global-pulse implementation, directly applicable with current technology, delivered good results under stricter conditions. The team addressed the practical limitations of current hardware, including qubit number, operational constraints, and unwanted interactions between qubits, by developing a new detuning computation technique. This approach balances theoretical accuracy with the demands of experimental implementation, offering a pathway towards solving complex combinatorial problems using analog quantum processing units, and introduced three variations of this detuning method, tailored to different stages of technological development. Simulations, performed on hardware emulators with asymmetric graphs of up to 30 qubits, demonstrated the relevance of their approach while adhering to realistic instrumental limitations, suggesting a viable path for utilizing near-term quantum devices to tackle challenging optimization problems.