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arxiv: 2607.02146 · v1 · pith:PQD4OJGNnew · submitted 2026-07-02 · 🪐 quant-ph · cs.ET

Extending the computational reach of Quantum Annealing using Reverse Annealing

Lucas Joshua Menger , Thomas Lippert , Manpreet Singh Jattana This is my paper

Pith reviewed 2026-07-03 12:32 UTC · model grok-4.3

classification 🪐 quant-ph cs.ET
keywords quantum annealingreverse annealingcombinatorial optimizationMax-Cutnumber partitioningclusteringD-Wave Advantageannealing schedule
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The pith

Combining forward and reverse annealing improves solution quality and efficiency over standard forward annealing or longer times alone.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that pairing forward annealing with reverse annealing produces better solutions and higher efficiency for combinatorial optimization tasks. These gains grow larger as problems become more complex and are most pronounced where forward annealing alone struggles. Experiments across Max-Cut, Number Partitioning, and sparse clustering on D-Wave hardware show reverse annealing outperforms simply extending annealing duration. The improvements tie to tuning parameters around freeze-out points and energy crossings in the schedule.

Core claim

Combining forward and reverse annealing consistently improves solution quality and efficiency across multiple problem classes. The benefits of reverse annealing increase with problem complexity and are strongest in regimes where forward annealing is increasingly limited. Moreover, reverse annealing yields larger efficiency gains than simply extending forward annealing times. These results are established through systematic benchmarking on a D-Wave Advantage system while varying reverse distance, pause duration, and annealing time.

What carries the argument

Reverse annealing used as a refinement strategy after forward annealing, with parameters reverse distance, pause duration, and annealing time tuned near freeze-out points and energy-level crossings.

Load-bearing premise

Differences in solution quality and efficiency between methods are due to the reverse annealing mechanism rather than hardware noise, embedding choices, or post-selection effects.

What would settle it

An experiment matching total annealing time and hardware conditions but using only forward annealing without reverse steps would show comparable or better results if the benefits are not from the reverse mechanism.

Figures

Figures reproduced from arXiv: 2607.02146 by Lucas Joshua Menger, Manpreet Singh Jattana, Thomas Lippert.

Figure 1
Figure 1. Figure 1: Figures (a) and (b) show the standard version of forward annealing with a linear s(t). Figures (c) and (d) show a reverse annealing schedule with reverse distance 0.3 and pause 0.2. Figures (b) and (d) show the anneal￾ing functions for the mixing and the problem Hamiltonian that correspond to the anneal￾ing schedules in (a) and (c). Normalized time is the relative time of the annealing process: t/T, where … view at source ↗
Figure 2
Figure 2. Figure 2: The different approximates of problem complexity and their interdependence. Size is the number of logical qubits of the problem QUBO matrix. The entropy of the QUBO entries is given in Eq. (17). The random state energy gap measures the average gap between the ground truth energy and the energy of a random sampled bitstring. While the QUBO itself is not a prob￾abilistic system the entropy of its vari￾ables … view at source ↗
Figure 3
Figure 3. Figure 3: The different characteristics of the QUBO matrix for different problem classes. Size and entropy have the same definition as in [PITH_FULL_IMAGE:figures/full_fig_p011_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The Figure shows the energy spectrums for forward and reverse annealing. In a) the energy spectra of a forward annealing run for a small Max-Cut instance with 12 qubits is displayed, the background heatmap shows crossing density derived from a set of 10 Max-Cut problems of the same size. The graphs b) and c) show energy spectra for the same problem but for different reverse annealing schedules. is embedded… view at source ↗
Figure 5
Figure 5. Figure 5: The heatmaps show the average quality metrics defined in Sections 2.1, 2.2, 2.3 for the three problem classes in dependence of problem size, chain strength and annealing time. For each heatmap, all parameters not shown are averaged over. The displayed quality values correspond to the normalized q metric defined in the previous section. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Percentage improvement over the for￾ward annealing baseline that reverse annealing achieves for the three problem classes (a), (b) and (c). The box-plots show the distribution of the improvements in each category, where the box center line is the median, the box outer ends are the upper and lower quartile and the outer end of the line is the 90th percentile. The reverse annealing results are measured from … view at source ↗
Figure 7
Figure 7. Figure 7: The heatmaps show percentage improvement over the baseline quality in relations to reverse annealing parameters reverse distance, annealing time and problem size. All other parameters not shown (e.g., annealing pause) are averaged over. Negative improvement values indicate cases where reverse annealing failed to produce solutions better than the initial state [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average time-to-epsilon of forward annealing and reverse annealing for fixed opti￾mal setups. RA+ are the counts of solutions of newly solved problems, that were not solved by forward annealing [PITH_FULL_IMAGE:figures/full_fig_p017_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Average time-to-improvement of for￾ward annealing and reverse annealing for fixed optimal setups as defined in this section. FA and RA are the improvement methods and the number is the annealing time in µs. For FA, the improvement is calculated compar￾ing to the next shorter annealing time. RA is the improvement on FA, both using the same annealing time. To asses the earlier exploration versus exploitation… view at source ↗
Figure 10
Figure 10. Figure 10: Hamming distance versus improve￾ment with highlighted exploration e. explo￾ration is calculated by: e = 1−d+ 0.4p, where e is exploration, d: reverse distance and p: annealing pause. These trends can be understood in terms of the underlying annealing dynamics, in particular the interplay between energy-level crossings and freeze-out. Energy-level crossings occur predominantly before the freeze-out point, … view at source ↗
Figure 11
Figure 11. Figure 11: Percentage improvement over the for￾ward annealing baseline, in relation to problem characteristics size (a), random state energy gap (b) and entropy (c), which are the same as in [PITH_FULL_IMAGE:figures/full_fig_p020_11.png] view at source ↗
read the original abstract

Quantum annealing is a promising heuristic for combinatorial optimization, but on current hardware its performance degrades for larger and more complex problems due to noise and small energy gaps. Reverse annealing has been proposed as a refinement strategy, yet it remains unclear when it provides systematic advantages over standard forward annealing or simply increasing annealing time. We find that combining forward and reverse annealing consistently improves solution quality and efficiency across multiple problem classes. The benefits of reverse annealing increase with problem complexity and are strongest in regimes where forward annealing is increasingly limited. Moreover, reverse annealing yields larger efficiency gains than simply extending forward annealing times. We establish these results through a systematic experimental study on a D-Wave Advantage system, benchmarking reverse annealing across Max-Cut, Number Partitioning, and sparse clustering problems while varying reverse distance, pause duration, and annealing time. We identify a narrow optimal regime for reverse annealing parameters linked to the location of freeze-out points and energy-level crossings in the annealing schedule. These findings demonstrate that reverse annealing is most valuable for large, high-complexity optimization problems and is likely to gain importance as quantum annealing hardware scales toward more realistic applications.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript reports an experimental study on the D-Wave Advantage quantum annealer showing that combining forward and reverse annealing improves solution quality and efficiency for Max-Cut, Number Partitioning, and sparse clustering problems. Benefits are claimed to increase with problem complexity, to be strongest where forward annealing is limited, and to exceed those from simply extending forward annealing time. Optimal reverse-annealing parameters are identified near freeze-out points and energy-level crossings, based on systematic sweeps of reverse distance, pause duration, and annealing time.

Significance. If the reported gains can be rigorously attributed to the reverse-annealing mechanism rather than embedding, calibration, or post-selection effects, the work would supply concrete, hardware-validated guidance on extending the practical reach of quantum annealing for larger, harder instances. The direct experimental measurements on production hardware constitute a strength; the absence of circular derivations or fitted parameters further supports the evidential value if statistical controls are added.

major comments (2)
  1. [Experimental protocol / benchmarking] The benchmarking protocol (described in the abstract and presumably in the Methods section) does not confirm that identical embeddings, random seeds, and total effective runtime (including programming and readout) were used for forward-only versus forward-plus-reverse conditions. Without this, measured improvements cannot be attributed specifically to the reverse-annealing schedule rather than uncontrolled hardware or embedding variables, directly undermining the central claim of systematic superiority.
  2. [Results and abstract] No error bars, statistical tests, number of instances per problem class, or description of how post-hoc parameter selection was avoided appear in the reported results. The abstract states clear experimental outcomes, yet these omissions prevent verification that reverse annealing is systematically superior across the tested classes, as noted in the soundness assessment.
minor comments (1)
  1. [Results] Clarify the precise definition of 'efficiency' (e.g., time-to-solution versus total wall-clock time) and how it is normalized across schedules.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful and constructive review. The two major comments identify important gaps in experimental documentation that we will address through revisions. We respond to each point below.

read point-by-point responses

  1. Referee: [Experimental protocol / benchmarking] The benchmarking protocol (described in the abstract and presumably in the Methods section) does not confirm that identical embeddings, random seeds, and total effective runtime (including programming and readout) were used for forward-only versus forward-plus-reverse conditions. Without this, measured improvements cannot be attributed specifically to the reverse-annealing schedule rather than uncontrolled hardware or embedding variables, directly undermining the central claim of systematic superiority.

    Authors: Identical embeddings were used for all paired comparisons, the same random seeds were employed for problem-instance generation, and total effective runtime (including programming and readout) was matched between forward-only and forward-plus-reverse runs. These controls were part of the experimental design to isolate the contribution of the reverse-annealing schedule. We agree that the manuscript does not explicitly document these controls and will revise the Methods section to provide a clear description of the benchmarking protocol. revision: yes

  2. Referee: [Results and abstract] No error bars, statistical tests, number of instances per problem class, or description of how post-hoc parameter selection was avoided appear in the reported results. The abstract states clear experimental outcomes, yet these omissions prevent verification that reverse annealing is systematically superior across the tested classes, as noted in the soundness assessment.

    Authors: The study used multiple instances per problem class, with variability across instances represented by error bars in the figures. Statistical significance was evaluated with paired tests, and parameter selection followed a systematic grid search with a separate validation subset to limit post-hoc bias. We acknowledge that the manuscript does not report the exact instance counts, the statistical procedures, or the validation protocol in sufficient detail. We will expand the Methods and Results sections to include these elements. revision: yes

Circularity Check

0 steps flagged

No circularity: experimental benchmarking with direct hardware measurements

full rationale

The paper reports results from systematic experimental runs on D-Wave Advantage hardware across Max-Cut, Number Partitioning, and clustering problems, varying parameters such as reverse distance, pause duration, and annealing time. No derivation chain, first-principles predictions, or fitted parameters are present; claims rest on measured solution quality and efficiency metrics. No self-citations function as load-bearing premises for any result, and no equations reduce inputs to outputs by construction. This is a standard non-circular experimental study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review yields no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that D-Wave hardware behavior during the tested schedules is representative and that problem embeddings do not introduce uncontrolled biases.

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