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arxiv: 2509.03952 · v2 · submitted 2025-09-04 · 🪐 quant-ph

Quantum-inspired dynamical models on quantum and classical annealers

Philipp Hanussek , Jakub Paw{\l}owski , Zakaria Mzaouali , Bart{\l}omiej Gardas This is my paper

Pith reviewed 2026-05-18 19:28 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum dynamicsQUBOquantum annealingnon-Hermitian Hamiltoniansparallel-in-time encodingbenchmarkingD-Wave
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The pith

Converting quantum dynamics to QUBO instances enables solver-agnostic benchmarking of quantum annealers and classical optimizers.

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

This paper shows how to turn the real-time propagator of an n-qubit system into quadratic unconstrained binary optimization problems that run identically on quantum annealers or classical solvers. A parallel-in-time encoding discretizes the continuous evolution so the same instance works across different hardware types. The method handles both ordinary Hermitian Hamiltonians and non-Hermitian ones, covering single-qubit rotations, entangling gates such as Bell and GHZ states, and PT-symmetric dynamics. Benchmarks measure success probability and time-to-solution on two D-Wave devices, Simulated Annealing, and GPU-accelerated VeloxQ, with results for systems up to roughly 100000 variables. The framework supplies a common, physics-based testbed for tracking how well any solver reproduces quantum time evolution.

Core claim

The real-time propagator of an n-qubit, possibly non-Hermitian, Hamiltonian is converted into QUBO instances via parallel-in-time encoding; these instances run on quantum annealers and classical optimizers alike and furnish a benchmarking suite evaluated on eight dynamical models using success probability and time-to-solution metrics.

What carries the argument

Parallel-in-time encoding that converts the continuous-time propagator into a finite QUBO instance.

If this is right

  • Success probability on the annealer directly indicates how well the dynamical simulation matches the target quantum evolution.
  • The same QUBO instance supports head-to-head performance comparisons between quantum annealers and classical heuristics.
  • The eight chosen models (rotations, Bell, GHZ, cluster states, PT-symmetric generators) form a representative stress test for any solver.
  • Large-scale instances near 10^5 variables supply a demanding classical baseline for future hardware.

Where Pith is reading between the lines

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

  • The same encoding could benchmark quantum advantage claims specifically for real-time open-system dynamics.
  • Hardware progress on annealers can be tracked quantitatively by measuring improvement on this fixed set of dynamical QUBO tasks.
  • Analogous mappings might apply to other time-dependent quantum problems that lack closed-form solutions.

Load-bearing premise

The parallel-in-time discretization preserves the essential features of the continuous-time quantum evolution inside the resulting QUBO instance.

What would settle it

For small n, solve the generated QUBO exactly and check whether the sampled bit strings reproduce the probability distribution obtained by direct matrix exponentiation of the original Hamiltonian.

Figures

Figures reproduced from arXiv: 2509.03952 by Bart{\l}omiej Gardas, Jakub Paw{\l}owski, Philipp Hanussek, Zakaria Mzaouali.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a) Time-dependent energy scales executed by the D-Wave quantum annealer. The coefficient [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Scaling properties of TTS [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

We propose a practical, physics-inspired benchmarking suite to challenge both quantum and classical computers by mapping real-time quantum dynamics to a common optimization format. Using a parallel-in-time encoding, we convert the real-time propagator of an $n$-qubit, possibly non-Hermitian, Hamiltonian into quadratic unconstrained binary optimization (QUBO) instances that are executable in a solver-agnostic manner on quantum annealers and classical optimizers alike. This enables direct, like-for-like performance comparisons across fundamentally different computational paradigms.To stress-test the framework, we consider eight representative dynamical models spanning single-qubit rotations, multi-qubit entangling gates (Bell, GHZ, cluster), and PT-symmetric and other non-Hermitian generators, and evaluate success probability and time-to-solution as standard benchmarking metrics. Applying this methodology to two generations of D-Wave quantum annealers and to state-of-the-art classical solvers (Simulated Annealing and the GPU-accelerated VeloxQ), we find that Advantage2 consistently outperforms its predecessor, while VeloxQ retains the shortest absolute runtimes, reflecting the maturity of classical heuristics.We further extend the benchmarks to large-scale instances ($N \simeq 10^{5}$), establishing a demanding classical baseline for future hardware. Together, these results position the parallel-in-time QUBO framework as a versatile and physically motivated testbed for quantitatively tracking progress toward quantum-competitive simulation of dynamical systems.

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 / 3 minor

Summary. The paper proposes a parallel-in-time encoding to convert the real-time propagator of an n-qubit (possibly non-Hermitian) Hamiltonian into QUBO instances solvable on quantum annealers and classical optimizers. It benchmarks success probability and time-to-solution across eight dynamical models (single-qubit rotations, Bell/GHZ/cluster states, PT-symmetric and other non-Hermitian generators) on D-Wave Advantage2 and predecessor annealers, Simulated Annealing, and GPU-accelerated VeloxQ, while scaling to N ≃ 10^5 instances to establish classical baselines.

Significance. If the encoding faithfully reproduces quantum trajectories, the framework supplies a solver-agnostic, physics-motivated benchmark suite for tracking progress on dynamical simulation across quantum and classical hardware. The inclusion of non-Hermitian and PT-symmetric models and the large-scale classical reference points are useful strengths.

major comments (2)
  1. [Section 2] Section 2 (parallel-in-time encoding): the central claim that minimizing the QUBO yields configurations whose extracted states match the action of the real-time propagator U(t) requires explicit verification. No derivation of the quadratic penalties for non-Hermitian generators is supplied, nor is there a reported convergence test of extracted fidelity versus number of time slices or direct comparison to exact matrix exponentiation. Without these, success probability on the annealer does not demonstrably track dynamical fidelity.
  2. [Results section] Results section (eight-model benchmarks): success probabilities are reported without error bars or statistical analysis, and the post-hoc selection of models weakens the cross-solver comparative claims. For the PT-symmetric cases in particular, it remains unclear whether low-energy QUBO solutions correspond to physically correct norm-controlled trajectories.
minor comments (3)
  1. Clarify the precise number of qubits, time slices, and any discretization parameters used for each of the eight models; these details are needed to reproduce the QUBO instances.
  2. The large-scale (N ≃ 10^5) instances should specify the exact Hamiltonian sizes and how the parallel-in-time variables scale with system size.
  3. Figure captions would benefit from explicit statements of what quantity is plotted on each axis and whether the plotted success probabilities are averaged over multiple runs.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and constructive comments on our manuscript. We address each major comment below and have revised the manuscript to incorporate the suggested clarifications and additions.

read point-by-point responses

  1. Referee: [Section 2] Section 2 (parallel-in-time encoding): the central claim that minimizing the QUBO yields configurations whose extracted states match the action of the real-time propagator U(t) requires explicit verification. No derivation of the quadratic penalties for non-Hermitian generators is supplied, nor is there a reported convergence test of extracted fidelity versus number of time slices or direct comparison to exact matrix exponentiation. Without these, success probability on the annealer does not demonstrably track dynamical fidelity.

    Authors: We agree that explicit verification strengthens the central claim. In the revised manuscript we will add a self-contained derivation in Section 2 of the quadratic penalty terms for non-Hermitian generators, obtained by expanding the squared residual ||U(t) |psi> - |psi(t+Delta t)>||^2 and retaining only the quadratic binary terms after the standard spin-to-binary mapping. We will also include a new figure showing extracted fidelity versus number of time slices for representative models (single-qubit rotation and a PT-symmetric case) together with a direct numerical comparison of the lowest-energy QUBO solutions against exact matrix exponentiation for small n. These additions will demonstrate that the reported success probabilities correlate with dynamical fidelity. revision: yes

  2. Referee: [Results section] Results section (eight-model benchmarks): success probabilities are reported without error bars or statistical analysis, and the post-hoc selection of models weakens the cross-solver comparative claims. For the PT-symmetric cases in particular, it remains unclear whether low-energy QUBO solutions correspond to physically correct norm-controlled trajectories.

    Authors: We accept that error bars and statistical analysis are needed. The revised Results section will report success probabilities with standard deviations obtained from 100 independent runs per instance and will include a brief statistical comparison (e.g., Wilcoxon rank-sum tests) between solvers. We will also clarify the model-selection rationale in the text, noting that the eight models were chosen a priori to cover Hermitian, entangling, and non-Hermitian dynamics rather than selected after inspection of results. For the PT-symmetric cases we will add a short subsection and an accompanying panel showing that the extracted trajectories preserve the expected norm evolution (growth or decay) by direct comparison with exact non-unitary propagation, confirming that low-energy QUBO solutions correspond to physically correct norm-controlled states. revision: yes

Circularity Check

0 steps flagged

No significant circularity; mapping and benchmarks are self-contained

full rationale

The paper presents a direct encoding of the real-time propagator into a QUBO cost function via parallel-in-time discretization, with success probability and time-to-solution measured against independent external solvers (D-Wave Advantage2, Simulated Annealing, VeloxQ) on eight distinct dynamical models. No step reduces a reported performance metric to a fitted parameter chosen from the same data, nor does any central claim rest on a self-citation chain whose validity is presupposed by the present work. The derivation chain consists of an explicit construction (binary variables per time slice, quadratic penalties for discrete Schrödinger steps) whose outputs are evaluated externally rather than by construction. This satisfies the criteria for a self-contained, non-circular framework.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that a discrete QUBO instance can faithfully represent continuous-time quantum evolution; no new physical entities are postulated.

axioms (1)
  • domain assumption The real-time propagator of an n-qubit Hamiltonian can be discretized into a quadratic binary optimization problem without loss of essential dynamical information.
    Invoked when the abstract states that the propagator is converted into QUBO instances.

pith-pipeline@v0.9.0 · 5796 in / 1373 out tokens · 35634 ms · 2026-05-18T19:28:05.531678+00:00 · methodology

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