Quantum annealers have been assessed primarily by their ability to find low-energy configurations; however, reaching a degenerate ground state and uniformly sampling it are distinct capabilities. Optimisation success does not guarantee fair sampling.

Reaching optimal solutions and exploring all possibilities are distinct capabilities within quantum computing; even with successful identification of many correct answers, systems can favour some over others. Improvements in *finding* these ideal states do not automatically equate to better overall exploration of those options. By comparing D-Wave hardware against classical simulations, researchers have established a new benchmark for evaluating performance beyond basic optimisation tasks.

Researchers from Tohoku University demonstrated that finding optimal solutions and fairly exploring all possibilities are distinct capabilities within quantum computing; identifying ideal states doesn’t guarantee equal consideration for each one. To quantify this difference, they used an Ising ring, a network of interconnected magnets preferring opposing alignments made more complex by additional connections like adjusting springs in a mechanical system, with known properties.

They embedded instances containing up to 162 logical spins onto a D-Wave Advantage processor and compared its performance against classical simulations. For N=160 spins, the processor achieved a higher probability of reaching a ground state (0.869 versus 0.519) but exhibited greater deviation from uniform sampling, like rolling two different dice that both land on numbers 1, 6, yet some are more likely than others (total variation distance: 0.317 vs 0.136).

D-Wave achieves record ground state solutions but reveals tradeoffs between speed

More importantly, with N=160 logical spins, the machine showed an impressive leap in performance: a ground state hit probability of 0.869 compared to just 0.519 using classical simulated annealing. This represents the first time such high probabilities have been consistently achieved on a quantum annealer while simultaneously highlighting that optimisation success and uniform exploration are not inherently linked, previously impossible without sacrificing fair sampling.

Experiments conducted on a D-Wave Advantage processor demonstrated that achieving high probabilities for any valid solution does not guarantee unbiased sampling; it recorded a ground state hit probability of 0.869, compared to only 0.519 with classical simulated annealing, for an N=160 instance. Introducing a pause during the anneal process, where the system settles into its lowest energy configuration, increased this hit probability from 0.42 to 0.86 without improving how evenly those solutions were distributed across different possibilities. The team also classified these ground states based on spin arrangements into “defect sectors,” finding that even with improved accuracy, biases remained in favouring specific defect structures.

Benchmarking Quantum Annealers Using Precisely Characterised Ising Ring Instances

The technique centred on constructing precisely defined instances of an *Ising ring*, a network of interconnected magnets favouring opposing alignments complicated by additional connections akin to adjusting springs within a mechanical system, and carefully analysing their properties; this allowed the creation of problems with known ground states for benchmarking purposes. They derived the exact energy, degeneracy (multiple equally stable lowest points like a plateau landscape), and defect structure for these rings up to 162 logical spins, categorising solutions based on remainders after division by four. These *Ising rings*, networks of interacting magnets with adjustable connections, served as benchmark problems for a D-Wave Advantage quantum annealer built up to 162 logical spins and categorised by remainders after division by four.

Frustrated magnetism reveals subtle limits of quantum annealing performance

Establishing an exactly defined problem, a frustrated magnetic network known as the Ising ring, offers valuable new tools for benchmarking quantum annealers against classical methods; however, it simultaneously stresses a critical point often glossed over in discussions of ‘quantum advantage’. While D-Wave’s Advantage processor demonstrably excels at *finding* ground states, the lowest energy solutions to complex problems, this success doesn’t automatically translate into exploring all possible solutions equally.

This detailed analysis matters profoundly despite revealing limitations in how well the machine explores potential solutions because it establishes a rigorous standard against which future devices can be measured. This exacting ‘Ising ring’ problem defines a new standard for evaluating quantum annealers and highlights that finding solutions isn’t equivalent to exploring them all equally.

The researchers established a clear distinction between successfully locating ground states, the lowest energy solutions to complex problems, and uniformly sampling across them; achieving one does not guarantee the other. By carefully constructing frustrated Ising rings with known properties, they created an exacting benchmark against which to evaluate performance on both classical simulators and D-Wave’s Advantage processor. Results showed that while the quantum annealer excelled at identifying many correct answers (reaching a hit probability of 0.869 for N=160), it did so without distributing its exploration evenly amongst those options.

Future work will focus on refining benchmarks to truly assess progress toward useful quantum computation.

Researchers demonstrated that finding ground states in a complex system is distinct from uniformly sampling all possible solutions using antiferromagnetic Ising rings with up to 162 logical spins, tested on a D-Wave Advantage processor. This distinction matters because it establishes a rigorous benchmark for evaluating open-system quantum annealing and clarifies that optimization success does not inherently guarantee uniform exploration of solution space; future work aims to refine such benchmarks further.

👉 More information
🗞 Optimization versus fair sampling in quantum annealing: An exactly characterized frustrated Ising benchmark
✍️ Masaru Hitomi and Masayuki Ohzeki (Tohoku University)
🧠 ArXiv: https://arxiv.org/abs/2610.29035

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