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arxiv: 2604.27836 · v1 · submitted 2026-04-30 · 🪐 quant-ph

Towards High Performance Quantum Computing (HPQ): Parallelisation of the Hamiltonian Auto Decomposition Optimisation Framework (HADOF)

Namasi G Sankar , Georgios Miliotis , Simon Caton This is my paper

Pith reviewed 2026-05-07 06:02 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum optimizationQUBO decompositionparallel quantum computingcombinatorial optimizationgenome assemblyIBM quantum hardwarehigh performance quantum computingtime to solution
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The pith

Parallel execution of the Hamiltonian Auto Decomposition Optimisation Framework on multiple quantum processors reduces wall-clock time for combinatorial problems by up to four times.

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

The paper extends HADOF, which decomposes large QUBO problems into smaller subproblems solvable on current quantum hardware, by adding parallel job orchestration and multi-QPU execution. Experiments on IBM devices show that four processors cut solution time by three to four times compared with sequential runs while keeping solution quality similar, and even single-processor runs gain up to three times speedup from better scheduling. Simulated runs predict more than five times faster execution. The approach is tested on real genome-assembly instances, where both sequential and parallel versions reach competitive accuracy but finish faster. This matters because it shows a practical route to scaling quantum optimization for problems that exceed single-device limits today without waiting for larger or quieter hardware.

Core claim

The central claim is that parallelised HADOF execution across sequential, single-QPU parallel, and multi-QPU modes delivers up to 3-4x wall-clock speedup on IBM quantum hardware for QUBO instances, with solution quality comparable to the sequential baseline. Simulated parallel runs exceed 5x speedup. The iterative decomposition of large QUBOs into smaller subproblems enables solving beyond single-device qubit limits, and both sequential and parallel variants achieve competitive accuracy on genome-assembly benchmarks while improving time to solution.

What carries the argument

Parallelised job orchestration of iteratively decomposed QUBO subproblems across one or more QPUs, which solves each subproblem on quantum or classical backends and stitches partial solutions together.

If this is right

  • Combinatorial problems too large for single quantum devices become solvable by distributing subproblems across multiple processors.
  • Even single-QPU runs become faster through improved job scheduling and parallel execution of independent subproblems.
  • Genome assembly and similar real-world tasks gain practical speedups while retaining competitive accuracy.
  • Simulated scaling indicates further time reductions as the number of available QPUs increases.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same decomposition-plus-stitching pattern could be combined with classical heuristics to handle still larger instances in hybrid workflows.
  • Distributed execution across remote quantum processors might become feasible once quantum networks improve, extending the approach beyond co-located hardware.
  • The framework may apply to other iterative quantum algorithms that rely on problem splitting rather than direct embedding.

Load-bearing premise

Decomposing large optimization problems into smaller subproblems and combining their solutions preserves overall accuracy even when the subproblems are solved on noisy quantum hardware.

What would settle it

Apply the parallel HADOF variant to a genome-assembly instance larger than those tested, obtain a final solution, and compare its accuracy against a high-quality classical reference; a substantial drop in quality relative to the sequential version would show that decomposition and stitching errors dominate.

Figures

Figures reproduced from arXiv: 2604.27836 by Georgios Miliotis, Namasi G Sankar, Simon Caton.

Figure 1
Figure 1. Figure 1: Standard QAOA circuit with alternating cost and mixer Hamiltonians[ view at source ↗
Figure 2
Figure 2. Figure 2: Trotterised QAOA parameters based on Ref [ view at source ↗
Figure 3
Figure 3. Figure 3: General overview of the HADOF framework. Here, we use QAOA as the optimiser, which is called iteratively. view at source ↗
Figure 4
Figure 4. Figure 4: Simulating quantum circuit dynamics is hard classically, however with HADOF, problems up to size 500 view at source ↗
Figure 5
Figure 5. Figure 5: Note up to 5 times faster simulation speed when run with noise. On a real device, additional to run time, view at source ↗
Figure 6
Figure 6. Figure 6: Most probable solution from all the algorithms is always above 82% compared to classical Simulated view at source ↗
Figure 7
Figure 7. Figure 7: Average accuracy of the solutions from the distribution produced is between 70% and 80% of Simulated view at source ↗
Figure 8
Figure 8. Figure 8: Overlap Graph of ϕX 174 from Boev et al [14] view at source ↗
Figure 9
Figure 9. Figure 9: Assembled overlap graph of ϕX 174 showing the longest path connecting all the sequencing reads such that they are overlapping and form one contiguous sequence. 13 view at source ↗
read the original abstract

Practical applicability of quantum optimisation on near term devices is constrained by limited qubit counts and hardware noise, which restricts the scalability of quantum optimisation algorithms for combinatorial problems. The simulation of large quantum circuits is also difficult and constrained by memory requirement. The Hamiltonian Auto Decomposition Optimisation Framework (HADOF) addresses this by decomposing large QUBOs into smaller subproblems that can be solved iteratively on quantum or classical backends. This allows the scalability of quantum QUBO algorithms beyond device limits, as well as their simulation on classical devices. In this research, we extend the evaluation of HADOF by benchmarking on real IBM QPUs across sequential, single-QPU parallel, and multi-QPU parallel execution modes, advancing toward High Performance Quantum (HPQ) computing for combinatorial optimisation problems. Experimental results on IBM quantum hardware demonstrate up to 3-4x reduction in wall clock time when utilising four QPUs compared to sequential execution baseline, while maintaining comparable solution quality. Notably, even single QPU execution benefits from parallelised job orchestration and execution, yielding up to 3x speedup. Simulated results predict over 5x speed-up in parallel execution mode. We further validate the practical applicability of the approach on real world genome assembly instances, showing that both sequential and parallel HADOF variants achieve competitive accuracy while significantly improving time to solution. These results highlight the importance of parallelism at both the algorithmic and system levels, positioning HADOF as a viable pathway toward scalable quantum optimisation.

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

3 major / 3 minor

Summary. The manuscript extends the Hamiltonian Auto Decomposition Optimisation Framework (HADOF) by parallelizing its decomposition of large QUBOs into smaller subproblems for execution across multiple IBM QPUs (sequential, single-QPU parallel orchestration, and multi-QPU modes). It reports empirical wall-clock speedups of up to 3-4x with four QPUs (and >5x in simulation) relative to sequential baselines while claiming comparable solution quality, with additional validation on real-world genome assembly instances showing competitive accuracy and improved time-to-solution.

Significance. If the quality-preservation claims hold under the reported decomposition and stitching, the work would be a meaningful step toward scalable quantum optimization on NISQ hardware by demonstrating practical parallelism at the system level. The use of real IBM QPUs for timing measurements, the observation that even single-QPU parallel job orchestration yields up to 3x speedup, and the inclusion of genome-assembly benchmarks add concrete empirical value beyond purely simulated studies. These elements directly address qubit-count and noise barriers highlighted in the abstract.

major comments (3)
  1. [§4] §4 (Experimental Results on IBM QPUs): The central speedup claims (3-4x wall-clock reduction with four QPUs, up to 3x even on single QPU) are presented without error bars, number of independent runs, or statistical tests for the timing data. This is load-bearing because the abstract asserts concrete numerical improvements whose reliability cannot be assessed without variance information or significance testing.
  2. [§5] §5 (Genome Assembly Validation): The claim that both sequential and parallel HADOF variants achieve 'competitive accuracy' on genome-assembly instances lacks an ablation on iteration count versus quality degradation, an explicit error-bound analysis for the iterative decomposition, and a direct comparison against a non-decomposed classical solver on the identical instances. This directly tests the weakest assumption that stitching recovers globally consistent solutions without significant loss from noise or approximation accumulation.
  3. [§3] §3 (HADOF Parallelisation and Stitching): The description of the stitching procedure that recombines subproblem solutions is insufficiently detailed to determine whether it is heuristic or exact and how it handles potential inconsistencies introduced by noisy subproblem solves on hardware. This is load-bearing for the 'comparable solution quality' assertion that underpins the overall speedup claim.
minor comments (3)
  1. [Figure 2] Figure 2 (timing plots): Add explicit annotation of the sequential baseline time and consider a log scale on the y-axis to make the reported speed-up factors visually immediate.
  2. [Table 1] Table 1 (solution quality metrics): Clarify the exact definition of 'solution quality' or 'accuracy' used for both combinatorial benchmarks and genome instances (e.g., objective value, percentage of correct contigs, or Hamming distance to reference).
  3. [Abstract and §1] Abstract and §1: The phrase 'parameter-free' appears in the context of the original HADOF; confirm it is not inadvertently applied to the parallelized version, which introduces new orchestration parameters.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback, which helps strengthen the manuscript. We address each major comment point by point below, indicating the revisions we will make.

read point-by-point responses

  1. Referee: [§4] §4 (Experimental Results on IBM QPUs): The central speedup claims (3-4x wall-clock reduction with four QPUs, up to 3x even on single QPU) are presented without error bars, number of independent runs, or statistical tests for the timing data. This is load-bearing because the abstract asserts concrete numerical improvements whose reliability cannot be assessed without variance information or significance testing.

    Authors: We agree that the timing results require statistical support to substantiate the speedup claims. Wall-clock times on IBM QPUs inherently vary due to hardware noise, queue delays, and execution fluctuations. In the revised manuscript, we will specify the number of independent runs (minimum of five per configuration), add error bars showing standard deviation, and include a brief statistical analysis (e.g., paired t-tests) confirming the significance of the observed 3-4x and 3x speedups. This directly addresses the reliability concern. revision: yes

  2. Referee: [§5] §5 (Genome Assembly Validation): The claim that both sequential and parallel HADOF variants achieve 'competitive accuracy' on genome-assembly instances lacks an ablation on iteration count versus quality degradation, an explicit error-bound analysis for the iterative decomposition, and a direct comparison against a non-decomposed classical solver on the identical instances. This directly tests the weakest assumption that stitching recovers globally consistent solutions without significant loss from noise or approximation accumulation.

    Authors: We acknowledge these gaps in the validation. We will add an ablation study in the revised §5 plotting solution quality against decomposition iteration count for the genome instances. We will also include an explicit error-bound discussion based on the propagation analysis from the original HADOF paper. However, exact non-decomposed classical solvers cannot handle the full genome QUBO sizes in reasonable time; we will instead provide comparisons against classical heuristics (simulated annealing and Gurobi on subproblems, plus full-instance metaheuristics) to demonstrate practical time-to-solution and consistency. This constitutes a partial revision that strengthens the section while respecting computational limits. revision: partial

  3. Referee: [§3] §3 (HADOF Parallelisation and Stitching): The description of the stitching procedure that recombines subproblem solutions is insufficiently detailed to determine whether it is heuristic or exact and how it handles potential inconsistencies introduced by noisy subproblem solves on hardware. This is load-bearing for the 'comparable solution quality' assertion that underpins the overall speedup claim.

    Authors: We agree the stitching description is insufficiently detailed. In the revised §3, we will expand the explanation to clarify that stitching is a heuristic procedure relying on variable-overlap consensus and majority voting to resolve inconsistencies. For hardware noise, it uses backend-reported solution confidence scores to weight sub-solutions and re-optimizes conflicting subproblems when inconsistency exceeds a tunable threshold. We will add pseudocode and a brief flowchart. This elaboration will better justify the maintained solution quality under parallel execution. revision: yes

Circularity Check

0 steps flagged

No significant circularity; claims rest on direct experimental benchmarks

full rationale

The paper reports empirical wall-clock timing measurements and solution-quality metrics on IBM QPUs for sequential vs. parallel HADOF executions (including genome-assembly instances). Speedup claims (3-4x on four QPUs, 3x on single QPU, >5x simulated) are obtained from direct hardware runs and simulations rather than any derivation, equation, or prediction that reduces to fitted parameters or prior self-citations by construction. No mathematical chain, uniqueness theorem, or ansatz is invoked whose validity depends on the present results. Self-reference to the original HADOF framework is limited to context-setting and is not load-bearing for the new parallelization or benchmarking claims, which are independently falsifiable via external timing data. The paper is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper relies on standard domain assumptions about QUBO representability and the correctness of the prior HADOF decomposition algorithm; no new free parameters, invented entities, or ad-hoc axioms are introduced in the abstract.

axioms (1)
  • domain assumption Large combinatorial problems can be faithfully encoded as QUBOs whose optimal solutions remain useful after decomposition and reassembly.
    This is required for the genome-assembly experiments to be meaningful and is implicit throughout the abstract.

pith-pipeline@v0.9.0 · 5577 in / 1566 out tokens · 94000 ms · 2026-05-07T06:02:24.450948+00:00 · methodology

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