MIS/MWIS in Asymmetric Quantum Networks with Qubit Control
Quantum Computing Breakthrough: New Detuning Control Optimises 30-Qubit Processor
MIS, MWIS
On existing quantum technology, employing quantum computers to address combinatorial optimisation issues like finding the Maximum Independent Set (MIS) and Maximum Weighted Independent Set (MWIS) is difficult. Sem Saada Khelkhal and Louis Barcikowsky devised a new computational method to precisely regulate qubit “detuning.” This unique strategy aims to decrease unwanted interactions in complex, asymmetric networks.
Methods suitable for existing technology allowed the researchers to demonstrate reliable performance on quantum processors with up to 30 qubits. This effort advances quantum optimisation in real life.
Limits of Analogue Quantum Hardware
Combinatorial issues like MIS and MWIS are crucial to scheduling, resource allocation, and complicated networks, but classical computers struggle to tackle them, especially as graph sizes expand.
Ising model allows neutral-atom quantum processors like Pasqal's to natively represent independent graph topologies, encoding these problems. These systems are limited by a limited number of qubits (up to 30 were tested), control parameters like Rabi frequency and detuning, maximum sequence durations, confinement space, and most importantly, parasitic interactions between nearby, unconnected atoms. These unwanted interactions impair outcomes, especially in arbitrary asymmetric graphs.
Why Standard Detuning Failed
Traditional techniques to establishing the detuning parameter set a lower constraint based on the highest undesirable long-range interaction involving any atom. However, this traditional method has two major issues.
First, it often ignores the compounding effect of multiple powerful, unrelated interactions on a single atom. Even with a satisfied constraint, the cumulative intensity of these interactions can inhibit atom activation. Second, the conventional approach has no detuning limit. Too high a detuning value allows related atoms to be excited concurrently, violating the fundamental restriction of an independent set.
Better Detuning Calculation
To address these limits, the study team developed a new method for estimating each atom's detuning value. This new formulation guarantees that an atom's detuning is higher than the total of its unrelated interactions. It keeps the detuning below the lowest relevant interaction simultaneously. This delicate balancing act improves the method's accuracy in identifying Maximum Independent Sets across graph topologies.
Three Current and Future Hardware Strategies
The researchers offered three detuning methods for different hardware maturity levels:
Theoretical Local Detuning: This speculative method uses atom-specific detuning parameters to set a baseline performance based on pure theory. This requires local control capabilities that are currently unavailable.
DMM aims to balance theoretical precision and experimental viability. DMM closely matches the theoretical model by gradually biassing atoms towards their ideal values via a locally scaled global detuning function. The DMM approach yields results similar to the best local detuning procedure.
Global-Pulse Implementation: This technique deviates from theory yet works on quantum hardware under stricter operating conditions. Global pulses and frequency shifts are used.
Method Extension to Weighted Graphs
Extending the detuning algorithm solved the MWIS problem, which weighs each vertex. This extension uses linearly interpolating vertex weights to determine a weight-dependent scaling factor. This bias ensures that nodes with larger weights are activated first, maximising the overall weight.
Performance and Future
These strategies were tested on arbitrary asymmetric graphs with up to 30 qubits using Pasqal's emulators. Simulated performance was realistic and transferable within existing hardware restrictions and followed realistic physical constraints.
The strategies showed good odds of measuring an independent set, even though it's hard to get the maximum answer every time. Local Detuning and DMM consistently outperform the prior standard solution for MIS situations. The approaches had high optimality ratios and success probabilities for MWIS, demonstrating that even if the optimal solution is not found, the results are close.
The researchers conclude that these novel protocols must be implemented on real hardware to fully test their robustness and dependability. This will enable the use of analogue quantum computing units to solve difficult optimisation issues.
