Comparing Quantum Annealing and BF-DCQO

arXiv:2509.14358 · quant-ph · Submitted 2025-09-17 · Read on arXiv

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Introduction to the show: ident: Quantum Radio. Generated commentary on the latest quantum physics and condensed matter papers.

Kai: We're looking at the paper: "Comparing Quantum Annealing and BF-DCQO".

Mira: Here's the gist of the paper. The gist: D-Wave quantum annealers find solutions of far greater quality than claimed in Ref.

1: , while using far less computation time, and the quantum component of the hybrid approach makes minimal contributions to solution quality Quantum Computing Paradigms Quantum annealing (QA) is a computational paradigm where a quantum system stays near its instantaneous ground state while the Hamiltonian that governs its evolution is modified D-Wave’s quantum annealing processing units (QPU) implement the QA paradigm The native problem implemented on these platforms contains linear and quadratic terms and is known as the Ising model or quadratic unconstrained binary optimization (QUBO) Gate model (GM) quantum computers can implement a discretized approximation to QA called quantum approximate optimization algorithm (QAOA) This approach uses a quantum circuit subroutine that is iteratively optimized, as a pair of parameter vectors (⃗γ, β⃗) is varied Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO) Cadavid et al.

2: described the bias-field digitized counterdiabatic quantum optimization (BFDCQO) method This approach is similar to QAOA, with fixed (⃗γ, β⃗) and counterdiabatic terms

6: The approach also includes per-qubit bias fields (BF) These biases point toward the average value of the best solutions in the previous iteration In some implementations, the classical component adds a greedy-descent refinement step to those solutions

7–9: As a result, BF-DCQO poses a stark contrast to QAOA by letting the classical loop directly influence individual qubit values This makes it possible for the classical solution refinement, selection, and biasing mechanisms to become the primary drivers for the hybrid solver’s solution quality, possibly pushing the quantum computer to a secondary role in the hybrid approach in which it makes minimal contributions to solution quality Performance Comparison on Ising Problems In Section I, experimental results show that quantum annealing significantly outperforms BF-DCQO, returning far better-quality solutions than reported in Ref.

2: D-Wave Single and Parallel return ground-state probabilities that are significantly higher than BF-DCQO and DCQO, and the performance gap increases with problem size Figure 1 shows that D-Wave Single and Parallel return ground-state probabilities that are significantly higher than BF-DCQO and DCQO, and the performance gap increases with problem size The authors of two BF-DCQO studies

1, 7: that report comparisons to D-WaveTM quantum processors declined to share their data with us We therefore used the problem definitions in

1, 2: to build random generators for two input classes, called Ising and hising (i.e., higherorder Ising problem) in this paper, that we believe are accurate enough to support comparison of the reported performance of BF-DQCO with results from our tests using D-Wave quantum processors Performance Comparison on Hising Problems In Section II B, the D-Wave quantum annealer results come from a single programming per problem, 1000 reads and 350 µs anneals (see Section II) We see that the QA results are notably better than the results from BF-DCQO using far less resources (see Section II) Similarly to BF-DCQO, the BF-Null results come from the tenth iteration, with α = 0.02, γ = 2, and 1000 reads We see that the QA results are notably better than the results from BF-DCQO using far less resources (see Section II) The D-Wave quantum annealing results come from a single programming (35 ms) and 1000 anneals of 350 µs each, with 98 µs readout and 60 µs delay, totaling 543 ms of QPU access time The experiment from the paper takes an estimated time of ∼ 55 seconds, about 101× longer than D-Wave QPU access time Runtimes and Conclusion In Table I, the Runtime (seconds) for 1000 reads shows that BF-DCQO is significantly slower than D-Wave quantum annealing for both Ising and Hising problems These results show that D-Wave quantum annealers significantly outperform BF-DCQO in a variety of optimization problems by routinely finding better results in orders-of-magnitude shorter time This is consistent with current literature, where annealing quantum computers clearly outperform other quantum systems in optimization tasks We also emphasize the importance of both reporting computation times when evaluating optimization performance as well as disclosing sufficient details in test designs to allow independent replication The paper concludes that D-Wave quantum annealers significantly outperform BF-DCQO in a variety of optimization problems by routinely finding better results in orders-of-magnitude shorter time The bias-field null-hypothesis (BF-Null) method consists in replacing the quantum computer in BF-DCQO with a simple classical routine as a subsolver This type of sanity check to detect a quantum contribution can be found in previous performance studies of hybrid algorithms (e.g.

Paper summary: Kai: So, to wrap up this paper, we’re talking about "Comparing Quantum Annealing and BF-DCQO." The authors found that D-Wave quantum annealers find solutions of far greater quality than claimed in Ref. one, while using far less computation time <ref:2509.14358#pg1,1 , while using far less computation time>.

Mira: The main point is that the quantum component of the hybrid approach makes minimal contributions to solution quality, and the performance gap increases with problem size when comparing D-Wave Single and Parallel against BF-DCQO and DCQO.

Lev: In simple terms, what this means for someone listening is that you should probably focus on running a direct quantum anneal for these optimization tasks if your goal is getting the best result in the shortest time possible based on these tests.

Kai: It suggests that the complex hybrid algorithm they were testing, BF-DCQO, isn't adding significant value to the quality of the answer when compared against a standard quantum annealer setup.

Mira: The paper concludes that D-Wave quantum annealers significantly outperform BF-DCQO in a variety of optimization problems by routinely finding better results in orders of magnitude shorter time.

Lev: We have to remember that this whole comparison is based on these specific problem definitions, like the Ising and hising problems they used, so applying those exact comparisons to totally different types of optimization might need more work.

Kai: So, the main implication is that for now, D-Wave quantum annealers are showing a clear advantage over this particular hybrid method in terms of practical performance metrics like solution quality and time taken.

Conclusion: Kai: So, we’re wrapping up this look at "Comparing Quantum Annealing and BF-DCQO" by Cadavid and their team.

Mira: Basically, they set up a head-to-head test between D-Wave's quantum annealing and this hybrid method called BF-DCQO.

Lev: The core finding is that the D-Wave annealers find solutions of much higher quality than what those in the first paper claimed, and they do it using significantly less computation time.

Kai: That means we have to be careful about how much time we budget for these optimization problems if we want a good answer.

Mira: They also showed that the quantum part of this hybrid approach actually makes very little difference to the final solution quality when you look at their null hypothesis test.

Lev: From an engineering standpoint, it confirms that for these types of problems, the overhead of adding that complex classical refinement loop doesn't pay off in terms of precision.

Kai: So what does this mean for a scientist trying to decide which tool to use—the raw annealer or this hybrid thing?

Mira: It suggests that for now, if your main goal is just getting a high-quality result quickly, the direct quantum annealer setup is still performing better.

Lev: If you were building actual hardware today, this comparison tells us where the real computational savings are hiding.

Kai: It’s interesting because it challenges the idea that adding more classical control loops always boosts quantum performance in these specific scenarios.

Mira: And it makes you think about what kind of problems would actually need that extra hybrid structure to be useful.

Pau Farré, • Erika Ordog, Kevin Chern, Catherine C. McGeoch

1D-Wave Quantum · 2D-Wave Quantum (Retired)

quant-ph

Submitted: 2025-09-17

Updated: 2026-10-16

Comments: 6 pages, 4 figures

Code: https://github.com/dwavesystems/dwave-ocean-sdk

License: http://creativecommons.org/licenses/by/4.0/

Importance score: 76/100

The gist: The gist: D-Wave quantum annealers find solutions of far greater quality than claimed in Ref.

Key concepts

Quantum Annealing (QA): A computational method where a quantum system evolves near its lowest energy state by slowly changing its governing rules (Hamiltonian). D-Wave's hardware implements this by solving problems represented as Ising models or QUBOs, aiming to find the best solution among many possibilities.
Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO): A hybrid algorithm similar to QAOA that uses both quantum and classical elements. It incorporates fixed parameters and per-qubit bias fields that guide the process toward better solutions through a classical refinement loop, potentially making the quantum part secondary.
Ising Model / QUBO: These are the mathematical forms used to represent optimization problems on quantum annealers. They consist of linear and quadratic terms involving binary variables, which is how D-Wave's processors natively process and solve these types of problems.
BF-Null Method: A sanity check used to test the quantum contribution in hybrid algorithms. It replaces the quantum computer with a simple classical routine that performs a single zero-temperature sweep to see if any improvement is made, helping to detect minimal quantum impact.

Terminology

Hybrid Approach — 1× in this paper · explained in 4 episodes
Quantum Annealing — 1× in this paper · explained in 2 episodes

Summary

The gist: D-Wave quantum annealers find solutions of far greater quality than claimed in Ref. [1], while using far less computation time, and the quantum component of the hybrid approach makes minimal contributions to solution quality

Quantum Computing Paradigms

Quantum annealing (QA) is a computational paradigm where a quantum system stays near its instantaneous ground state while the Hamiltonian that governs its evolution is modified D-Wave’s quantum annealing processing units (QPU) implement the QA paradigm The native problem implemented on these platforms contains linear and quadratic terms and is known as the Ising model or quadratic unconstrained binary optimization (QUBO) Gate model (GM) quantum computers can implement a discretized approximation to QA called quantum approximate optimization algorithm (QAOA) This approach uses a quantum circuit subroutine that is iteratively optimized, as a pair of parameter vectors (⃗γ, β⃗) is varied

Bias-Field Digitized Counterdiabatic Quantum Optimization (BF-DCQO)

Cadavid et al. [2] described the bias-field digitized counterdiabatic quantum optimization (BFDCQO) method This approach is similar to QAOA, with fixed (⃗γ, β⃗) and counterdiabatic terms [6] The approach also includes per-qubit bias fields (BF) These biases point toward the average value of the best solutions in the previous iteration In some implementations, the classical component adds a greedy-descent refinement step to those solutions [7–9] As a result, BF-DCQO poses a stark contrast to QAOA by letting the classical loop directly influence individual qubit values This makes it possible for the classical solution refinement, selection, and biasing mechanisms to become the primary drivers for the hybrid solver’s solution quality, possibly pushing the quantum computer to a secondary role in the hybrid approach in which it makes minimal contributions to solution quality

Performance Comparison on Ising Problems

In Section I, experimental results show that quantum annealing significantly outperforms BF-DCQO, returning far better-quality solutions than reported in Ref. [2] D-Wave Single and Parallel return ground-state probabilities that are significantly higher than BF-DCQO and DCQO, and the performance gap increases with problem size Figure 1 shows that D-Wave Single and Parallel return ground-state probabilities that are significantly higher than BF-DCQO and DCQO, and the performance gap increases with problem size The authors of two BF-DCQO studies [1, 7] that report comparisons to D-WaveTM quantum processors declined to share their data with us We therefore used the problem definitions in [1, 2] to build random generators for two input classes, called Ising and hising (i.e., higherorder Ising problem) in this paper, that we believe are accurate enough to support comparison of the reported performance of BF-DQCO with results from our tests using D-Wave quantum processors

Performance Comparison on Hising Problems

In Section II B, the D-Wave quantum annealer results come from a single programming per problem, 1000 reads and 350 µs anneals (see Section II) We see that the QA results are notably better than the results from BF-DCQO using far less resources (see Section II) Similarly to BF-DCQO, the BF-Null results come from the tenth iteration, with α = 0.02, γ = 2, and 1000 reads We see that the QA results are notably better than the results from BF-DCQO using far less resources (see Section II) The D-Wave quantum annealing results come from a single programming (35 ms) and 1000 anneals of 350 µs each, with 98 µs readout and 60 µs delay, totaling 543 ms of QPU access time The experiment from the paper takes an estimated time of ∼ 55 seconds, about 101× longer than D-Wave QPU access time

Runtimes and Conclusion

In Table I, the Runtime (seconds) for 1000 reads shows that BF-DCQO is significantly slower than D-Wave quantum annealing for both Ising and Hising problems These results show that D-Wave quantum annealers significantly outperform BF-DCQO in a variety of optimization problems by routinely finding better results in orders-of-magnitude shorter time This is consistent with current literature, where annealing quantum computers clearly outperform other quantum systems in optimization tasks We also emphasize the importance of both reporting computation times when evaluating optimization performance as well as disclosing sufficient details in test designs to allow independent replication The paper concludes that D-Wave quantum annealers significantly outperform BF-DCQO in a variety of optimization problems by routinely finding better results in orders-of-magnitude shorter time

Methodology for Null Hypothesis Testing

The bias-field null-hypothesis (BF-Null) method consists in replacing the quantum computer in BF-DCQO with a simple classical routine as a subsolver This type of sanity check to detect a quantum contribution can be found in previous performance studies of hybrid algorithms (e.g. [19]) Here we use a simple single zero-temperature sweep subsolver: starting from a random solution, pass once through all variables in fixed order and flip their state if total solution energy is improved The complete procedure consists of performing b biasfield iterations with the subsolver (Alg.1)

Relative Error Measurement

Since different random instances have different egs, we compare solution qualities across instances based on relative error: the normalized distance between optimal e and egs In Figures 2A and 3A, adapted from Ref. [2], the lowest energy on the left corresponds to the ground state egss, with RE = 0 We note that the reported ground-state energies of the Ising instance shown in Figures 2A, 3A and hising instance shown in Figure 4A are both statistically consistent with the ground states of our generated ensemble of instances (used in Figures 2B, 3B and 4B, respectively)

Problem Reduction Techniques

The reduction of a hising problem to Ising requires representing products of variables with auxiliary variables In the experiments of Section I B, we reduced the three-body hising terms to pairwise Ising terms by introducing up to two auxiliary variables per cubic term, with a penalty equal to 5, using the dimod.higherorder.make quadratic tool available in the DWave Ocean SDK [20] The parallel embeddings in Table II were found by an iterative method that consists of embedding one copy of the problem at a time onto the unused qubits of the QPU until minorminer.find embedding fails to fit more embeddings The reduction of a hising problem to Ising requires representing products of variables with auxiliary variables, and then setting penalties to ensure that the value of the product variable is consistent with the values of the original variables The paper concludes that D-Wave quantum annealers significantly outperform BF-DCQO in a variety of optimization problems by routinely finding better results in orders-of-magnitude shorter time.

Data Availability

Supporting problem instances, solver solutions and ground-state energies are publicly available at the Zenodo repository https://doi.org/10.

Improvements for AI systems

textbfImprove Hybrid Solver Efficiency via Quantum Component De-emphasis: The BF-DCQO mechanism suggests that the quantum component of the hybrid approach makes minimal contributions to solution quality. This implies that AI systems utilizing this framework can achieve superior results by shifting computational focus toward classical refinement mechanisms, as demonstrated by showing substituting a poor classical solver for the quantum solver in the BF-DCQO workflow yields equal or better results than those reported in [1, 2].
textbfEnhance Solution Quality on Complex Optimization Problems: The paper demonstrates that D-Wave quantum annealers find solutions of far greater quality than claimed in Ref. [1], while using far less computation time, suggesting that AI systems can leverage QA for finding better ground states in Ising and hising problems compared to other methods. This is particularly evident when comparing D-Wave Single and Parallel return ground-state probabilities that are significantly higher than BF-DCQO and DCQO.
textbfProvide Robust Performance Benchmarking: Implement a rigorous benchmarking protocol requiring the disclosure of runtimes, as suggested by the paper's caution: Don’t claim superior performance without mentioning runtimes. This allows AI researchers to accurately assess how much time is needed to obtain a target solution quality, preventing misleading claims about computational advantage.
textbfEnable Scalable Problem Solving for Higher-Order Interactions: The method of reducing hising problems to Ising by introducing up to two auxiliary variables per cubic term, with a penalty equal to 5 allows AI systems to tackle higher-order unconstrained binary optimization (HUBO) problems effectively on QPUs, enabling them to solve more complex structures like the cubic hising Hamiltonian.
textbfDetect Quantum Contribution via Null Hypothesis Testing: AI systems can employ the bias-field null-hypothesis algorithm (BF-Null) as a sanity check to determine if a quantum component is performing any nontrivial work. This involves comparing BF-DCQO results against this classical counterpart to confirm that the quantum computation is not providing a significant advantage over simpler classical heuristics.

Abstract

Recent work [1] has claimed that a gate-model quantum-classical hybrid algorithm called bias-field digitized counterdiabatic quantum optimization (BF-DCQO) [2] outperforms D-Wave's annealing quantum computers in optimization tasks. We find the opposite to be true, and demonstrate that D-Wave's quantum annealers find solutions of far greater quality than claimed in Ref. [1], while using far less computation time. We also present evidence that suggests the quantum component of the hybrid approach makes minimal contributions to solution quality.