Classical Thermometry of Quantum Annealers Quantifies Residual Non-Thermal Effects across Three Orders of Magnitude

Quantum annealers represent a promising new avenue for investigating complex magnetic systems, but a fundamental question regarding their operation has remained unanswered: do they truly sample from the expected thermal distribution? George Grattan, Pratik Sathe, and Cristiano Nisoli, from Los Alamos National Laboratory and D-Wave Quantum Inc., now present a comprehensive experimental investigation into this critical issue, rigorously testing the assumption that these machines produce results governed by standard thermal statistics. Their work spans a vast range of system sizes and operating conditions, revealing a consistent, previously unrecognised offset in the effective temperature of the annealer, and a discrepancy between the measured output and the device’s physical temperature. This research not only establishes a more accurate understanding of how quantum annealers function, but also provides a crucial thermometry framework, enabling researchers to confidently utilise these machines as experimental platforms for exploring challenging problems in physics and materials science.

Quantum annealers are emerging as programmable platforms for investigating complex systems, but a fundamental question remains: do these machines accurately mimic the behaviour of classical thermal systems? Researchers have now rigorously tested this assumption, examining whether quantum annealers produce samples consistent with a Gibbs distribution, which describes the probability of different states in a thermal ensemble.

Effective Temperature Characterization of Quantum Annealers

This work focuses on characterizing the effective temperature of D-Wave quantum annealers using principles from classical statistical mechanics. Understanding the effective temperature is crucial for assessing how well the annealer explores the energy landscape of a problem, calibrating its performance, and bridging the gap between quantum behaviour and classical understanding. The research team employed a measure called Total Variation Distance (TVD) to compare the distribution of samples from the annealer to the ideal Boltzmann distribution expected from a perfectly thermal system. The study systematically varied key parameters, including the strength of interactions between qubits, the number of qubits used, and the duration of the annealing process.

By analyzing the resulting data, scientists aimed to determine whether the annealer’s behaviour aligns with the predictions of classical thermal sampling. The investigation revealed that the effective temperature generally decreases as interactions become stronger and the system size increases, suggesting a cooling effect. The TVD plots demonstrated that D-Wave annealers do not perfectly sample according to a Boltzmann distribution, especially for strong interactions and small system sizes. In summary, this research provides a detailed analysis of the effective temperature and sampling behaviour of D-Wave quantum annealers. The findings demonstrate that the annealers do not perfectly sample according to a Boltzmann distribution and that their behaviour varies depending on the problem being solved and the machine being used. This information is crucial for understanding the limitations of quantum annealers and optimizing their performance.

Quantum Annealers Exhibit Residual Non-Thermal Effects

Researchers have now assessed the fidelity of quantum annealers as experimental platforms, testing whether these machines produce classical Gibbs ensembles at large qubit scales. Experiments were conducted on four different D-Wave quantum processing units, ranging in size from 21 to 4000 qubits, and explored a range of coupling constants and annealing times. Scientists extracted an effective, dimensionless sampling temperature from the data and correlated it with annealing parameters and machine temperature. The team discovered that the assumed scaling law for effective temperature requires a correction, demonstrating residual non-thermal effects that still conform to an effective Gibbs description.

Measurements revealed a systematic discrepancy between the physical temperature inferred from the sampled ensemble and the nominal cryogenic temperature of the devices, which is approximately 15 mK. The study quantified this offset, showing it is robust across different machines and parameter regimes. The research focused on a one-dimensional Hamiltonian programmed into the annealers, with interactions reaching values of approximately 0. 407 K for the Advantage system. Data analysis revealed that the effective temperature decreases with longer annealing times and is influenced by system size. Researchers proposed a model for effective temperature, incorporating a machine-dependent factor that appears to depend weakly on system size but strongly on annealing time. These findings provide a physically grounded framework for benchmarking quantum annealers and assessing their viability for probing classical thermodynamics.

Annealer Temperature Scales with Time and Coupling

This research presents a comprehensive assessment of how well quantum annealers approximate the behaviour of classical thermal systems, specifically verifying the assumption of a Gibbs distribution in their output. Across a wide range of machine parameters and system sizes, spanning over three orders of magnitude, the team confirmed that the effective temperature generally decreases with annealing time and scales inversely with the encoded coupling strength, aligning with existing assumptions. Importantly, the study demonstrates that the effective temperature remains largely independent of system size, supporting the use of these devices for finite-size scaling analyses commonly used in classical statistical physics. However, the findings also reveal systematic deviations from ideal thermal behaviour.

The widely held assumption that effective temperature is solely determined by the encoded coupling strength breaks down due to a consistent, coupling-independent offset, likely originating from machine noise. Newer generation quantum processing units exhibited larger deviations from Gibbs distributions, potentially linked to increased quantum coherence and reduced thermalization efficiency. This work establishes the first scalable, physically grounded method for benchmarking the thermometric properties of quantum annealers, providing a crucial foundation for future experimental investigations.