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arxiv: 2605.22980 · v1 · pith:7PWRUCMYnew · submitted 2026-05-21 · 🪐 quant-ph · cs.ET

Automatic De-Quantization of Quantum Programs Using Constant Propagation

Lian Remme , Alexander Weinert , Andre Waschk , Lukas Burgholzer , Robert Wille This is my paper

Pith reviewed 2026-05-25 05:31 UTC · model grok-4.3

classification 🪐 quant-ph cs.ET
keywords quantum computingconstant propagationde-quantizationhybrid optimizationquantum circuitscompiler passesnear-term devices
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The pith

Hybrid constant propagation replaces some quantum gates with classical instructions by tracking constants across domains.

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

The paper presents hybrid quantum-classical constant propagation to cut down on expensive quantum operations in near-term algorithms. It does this by following constants through both quantum and classical parts of a program so that gates whose results are already known classically can be removed. A hybrid state model formalizes the tracking and elimination steps, and the method is tested on benchmark circuits after implementation in a compiler tool. Readers would care because every avoided multi-qubit gate reduces error accumulation and runtime on current hardware.

Core claim

We formalize a hybrid state model for quantum-classical constant propagation, implement the optimizations in the MQT Core tool, and evaluate them on benchmark circuits. The results show that the approach reduces costly multi-qubit operations by trading them for fast classical instructions whenever constants can be tracked between domains.

What carries the argument

The hybrid state model that tracks constants between quantum and classical domains to identify and eliminate unnecessary quantum gates and controls.

If this is right

  • Circuits contain fewer multi-qubit gates after the pass runs.
  • Programs become more practical to run on noisy near-term hardware.
  • Hybrid compiler passes can now systematically move work from quantum to classical when constants allow.
  • Existing toolchains can incorporate the technique to improve resource use without manual rewriting.

Where Pith is reading between the lines

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

  • The same tracking idea could be extended to decide entire subroutines should stay classical.
  • Combining this pass with entanglement analysis might further shrink quantum resource needs.
  • Larger benchmarks would reveal how often real algorithms contain propagatable constants.
  • Formal verification of the hybrid model could become a separate research target.

Load-bearing premise

The hybrid state model can correctly spot when a quantum gate is redundant and replace it with a classical step without changing the program's output behavior.

What would settle it

Apply the optimization to a small circuit with known constants, then compare measurement statistics of the original and optimized versions on identical inputs; any statistically significant difference would falsify the claim that semantics are preserved.

Figures

Figures reproduced from arXiv: 2605.22980 by Alexander Weinert, Andre Waschk, Lian Remme, Lukas Burgholzer, Robert Wille.

Figure 1
Figure 1. Figure 1: An example for a dynamic circuit. The left and right [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Hadamard lifting: By commuting Pauli and Hadamard [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A circuit for which constant propagation is useful: [PITH_FULL_IMAGE:figures/full_fig_p003_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: We can commute a controlled Pauli-Z gate with a [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: If we have a CNOT target followed by a Hadamard [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: An example of a hybrid quantum circuit. We show the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The union table that results from the circuit in Figure 7. [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: The amount of quantum resources reduced on average in circuits implementing different algorithms by quantum-classical [PITH_FULL_IMAGE:figures/full_fig_p009_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: The duration in ms needed to apply the optimization techniques quantum-classical constant propagation (CP), quantum [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
read the original abstract

Quantum computing promises to solve problems beyond the reach of classical computers, but today's quantum hardware is error-prone and much slower than classical hardware. Every quantum operation is costly, making it crucial to minimize quantum resource usage in near-term algorithms. Quantum resources should only be used when they are truly essential for quantum advantage, and not wasted on operations that can be efficiently handled by classical computation. In this work, we focus on de-quantizing quantum operations to classical computation whenever possible. The approach we propose for this is hybrid quantum-classical constant propagation, an optimization which reduces quantum operations by trading them for fast, reliable classical instructions. This is done by tracking between quantum and classical states to identify and eliminate unnecessary quantum gates and controls. We formalize a hybrid state model for quantum-classical constant propagation, implement our optimizations in the open-source MQT Core tool, and evaluate them on benchmark circuits. The obtained results show that quantum-classical constant propagation can reduce costly multi-qubit operations, making quantum programs more practical and robust for near-term devices. This opens the door to new hybrid compiler strategies that leverage the best of both quantum and classical worlds.

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 / 2 minor

Summary. The paper introduces hybrid quantum-classical constant propagation as a technique to automatically de-quantize parts of quantum programs by replacing quantum operations with classical computation when constants can be tracked across domains. It formalizes a hybrid state model, implements the optimization pass in the open-source MQT Core framework, and evaluates the approach on benchmark circuits, claiming reductions in the number of costly multi-qubit operations.

Significance. If the formal model preserves semantics and the reported reductions hold under realistic conditions, the work could improve resource efficiency for near-term quantum devices by systematically exploiting classical pre-computation. The open-source implementation and benchmark evaluation provide concrete reproducibility value.

major comments (2)
  1. [Formalization of the hybrid state model] The central claim rests on the hybrid state model correctly identifying eliminable gates without semantic change. The formalization section should explicitly state and prove the key invariant (e.g., that constant propagation commutes with the quantum semantics) or provide a machine-checked reference if one exists.
  2. [Evaluation on benchmark circuits] Benchmark results are cited as showing reduction in multi-qubit operations, but the evaluation section must include the raw counts or percentages before/after optimization, the set of benchmarks used, and a comparison against at least one baseline (e.g., standard constant propagation or no optimization) to substantiate the claim.
minor comments (2)
  1. The abstract would benefit from one or two quantitative summary statistics (e.g., average percentage reduction) rather than a purely qualitative statement.
  2. Notation for the hybrid state (quantum vs. classical components) should be introduced once with a clear table or diagram to avoid ambiguity in later sections.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We address each major comment below and will incorporate revisions to strengthen the paper as indicated.

read point-by-point responses

  1. Referee: [Formalization of the hybrid state model] The central claim rests on the hybrid state model correctly identifying eliminable gates without semantic change. The formalization section should explicitly state and prove the key invariant (e.g., that constant propagation commutes with the quantum semantics) or provide a machine-checked reference if one exists.

    Authors: We agree that explicitly stating and proving the key invariant is essential for rigor. In the revised manuscript, we will expand the formalization section to include an explicit statement of the invariant (that hybrid constant propagation commutes with quantum semantics and preserves the overall state evolution) along with a proof sketch. We will also search for and cite any relevant machine-checked references if they exist. revision: yes

  2. Referee: [Evaluation on benchmark circuits] Benchmark results are cited as showing reduction in multi-qubit operations, but the evaluation section must include the raw counts or percentages before/after optimization, the set of benchmarks used, and a comparison against at least one baseline (e.g., standard constant propagation or no optimization) to substantiate the claim.

    Authors: We acknowledge that the current evaluation would be strengthened by additional detail. In the revision, we will add explicit tables listing the raw counts and percentages of multi-qubit operations before and after optimization for each benchmark, enumerate the full set of benchmarks used, and include comparisons against a no-optimization baseline (and standard constant propagation where feasible). revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The manuscript formalizes a hybrid quantum-classical state model for constant propagation, implements the optimization pass in MQT Core, and evaluates it on benchmark circuits. No equations, fitted parameters, or 'predictions' appear that could reduce to inputs by construction. No load-bearing self-citations, uniqueness theorems, or ansatzes imported from prior author work are described. The central claim (correct de-quantization without semantic change) rests on the explicit formal model plus external benchmark evaluation, which is independent of the result itself. This is a standard self-contained compiler-optimization paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review; no free parameters, axioms, or invented entities are described.

pith-pipeline@v0.9.0 · 5737 in / 1018 out tokens · 22034 ms · 2026-05-25T05:31:04.056038+00:00 · methodology

discussion (0)

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