QART: A Quantum-Classical Hybrid Architecture for Long-Horizon Reasoning -- Exploring a Conditional Path toward Quantum Scaling

Lehao Lin; Yuheng Cheng; Guolong Liu; Yao Li; Xuning Tan; Xiyuan Zhou; Ruixi Zou; Shi Wang

cs.AISep 15, 2026

QART: A Quantum-Classical Hybrid Architecture for Long-Horizon Reasoning -- Exploring a Conditional Path toward Quantum Scaling

Authors: Lehao Lin, Yuheng Cheng, Guolong Liu, Yao Li, Xuning Tan, Xiyuan Zhou, Ruixi Zou, Shi Wang,

Organizations: QuantumMind · Shenzhen Institute of Artificial Intelligence and Robotics for Society · The Chinese University of Hong Kong, Shenzhen · Nanyang Technological University ·

Abstract

Long-horizon reasoning is vulnerable to early errors that compromise later decisions. We present QART, the Quantum-Augmented Reasoning Transformer, a quantum--classical hybrid architecture combining a backbone language model with quantum encoding, CIM-based QUBO optimization, and quantum decoding. Semantic information can come from hidden representations or model-generated text; detailed encoding and optimization procedures remain proprietary. Under explicit assumptions, we establish a conditional asymptotic reliability separation from single-trajectory autoregressive LLMs. For a common task family with aligned optimality and acceptance criteria, autoregressive acceptance probability tends to zero when cumulative conditional risk of irreversible errors diverges. QART's task-optimal-path recovery probability remains bounded away from zero if conditional probabilities for optimal-path coverage and semantic fidelity, spectral certification, dynamical reachability, and faithful readout remain uniformly positive under a specified resource schedule. The architecture alone does not imply these bounds. Paired measurements on six long-horizon benchmarks using DeepSeek V4 Flash, GLM-5.3, and GPT-5.5 xhigh in a Codex agent environment favor QART in 14 of 15 backbone--benchmark pairs. Relative gains reach 84.0% on SciCode, 47.6% on $τ^3$ -Bench, and 44.4% on Terminal-Bench 4.0; the DeepSeek V4 Flash configuration regresses by 7.8% on DeepSWE. These results do not directly validate the asymptotic separation. Potential quantum scaling laws are formulated as conditional hypotheses. A quantum-advantage interpretation requires a demonstrated CIM quantum advantage over strong classical solvers and its transfer to end-to-end reasoning after all system overheads.

Figures & tables

Figure 1: Architectural design of QART, combining a Transformer language model with an optimization component in a quantum–classical hybrid architecture. The diagram is a conceptual hidden-representation route; an alternative model-generated-content interface

y_{h}

is described in Section 6 . The solver returns a finite-budget candidate

\hat{z}=\operatorname{Solver}(Q;B)

, while

z^{*}\in\arg\min_{z}z^{\top}Qz

remains the theoretical reference optimum. The accompanying description focuses on functional roles rather than proprietary implementation details.

Benchmark	Backbone LLM	Classical baseline	QART hybrid	Absolute change	Relative gain
$\tau^{2}$ -Bench	GLM-5.3	84.11%	89.11%	+5.00 pp	+5.9%
	DeepSeek V4 Flash	85.52%	88.90%	+3.38 pp	+4.0%
	GPT-5.5 xhigh	88.23%	90.32%	+2.09 pp	+2.4%
$\tau^{3}$ -Bench	DeepSeek V4 Flash	21.65%	31.96%	+10.31 pp	+47.6%
	GLM-5.3	43.30%	45.36%	+2.06 pp	+4.8%
	GPT-5.5 xhigh	34.02%	39.18%	+5.15 pp	+15.2%

Table 1: Performance comparison between classical baselines and QART quantum–classical hybrid models across six benchmarks. Each row identifies a shared backbone LLM. “Classical baseline” reports the original classical model configuration, while “QART hybrid” reports the model incorporating quantum encoding, CIM-based QUBO optimization, and quantum decoding layers within the QART architecture. All scores are our measurements in the Codex agent environment and may differ from model-vendor or public leaderboard results. Absolute change and relative gain are measured against the corresponding classical baseline. Percentage-valued benchmarks use percentage points (pp) for absolute changes; LHTB retains native reward units. Within each benchmark group, the highest QART score and the largest absolute and relative gains are shown in bold.

Figure 2: Classical baseline and QART hybrid model performance across six benchmarks. Each pair of bars compares two model configurations sharing the backbone LLM identified on the horizontal axis. The QART configuration incorporates quantum encoding, CIM-based QUBO optimization, and quantum decoding layers into the hybrid reasoning architecture. Scores are measured under the benchmark evaluation setup described in Section 6 . LHTB reward is multiplied by 100 for visualization only. All values are our measurements rather than model-vendor or public leaderboard scores.

Figure 3: Performance changes from classical baselines to QART hybrid models constructed with the same backbone LLM. The left panel shows absolute score changes, and the right panel shows relative gains over the corresponding classical baseline. Results are grouped by benchmark, with colors identifying the backbone LLM. Positive values favor the QART hybrid configuration; negative values indicate a regression. Missing bars denote combinations that were not evaluated. LHTB absolute changes are multiplied by 100 for bar length, while annotations retain native reward units.

Benchmark	Best QART backbone	Score	Closest QART model(s)
$\tau^{2}$ -Bench	GPT-5.5 xhigh	90.32%	GLM-5.3: 89.11% ( $-1.21$ pp); DeepSeek V4 Flash: 88.90% ( $-1.42$ pp)
$\tau^{3}$ -Bench	GLM-5.3	45.36%	GPT-5.5 xhigh: 39.18% ( $-6.18$ pp)
SciCode	GLM-5.3	34.38%	DeepSeek V4 Flash: 31.94% ( $-2.44$ pp)
LHTB	DeepSeek V4 Flash	0.3591	GLM-5.3: 0.3419 ( $-0.0172$ )
DeepSWE	GPT-5.5 xhigh	72.50%	GLM-5.3: 65.40% ( $-7.10$ pp)
Terminal-Bench 4.0	GLM-5.3 / DeepSeek V4 Flash	20.63%	Tie: both models score 20.63% (0.00 pp)

Table 2: Highest-scoring QART hybrid models on each benchmark and their closest evaluated QART counterparts. Models are identified by their classical backbone LLMs. All scores correspond to QART hybrid configurations incorporating the quantum encoding, CIM-based QUBO optimization, and quantum decoding layers. Parentheses report score differences from the highest-scoring QART model in the benchmark’s native units. Rankings are restricted to the configurations evaluated in this report.

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning and dimension
$h,\ m(h)$	Reasoning horizon and number of critical decisions; positive integers.
$q_{h},\ y_{h}$	Task specification and generated textual information; elements of task and text spaces.
$\mathcal{A}_{h},\ \Pi_{h},\ \Pi_{h}^{\star}$	Acceptable trajectories, declared admissible paths, and objective minimizers; finite sets in this formulation.
$C_{h,j},\ e_{h,j},\ E_{h}$	Prefix-survival event, scalar conditional exit probability, and scalar cumulative risk.
$Z_{h}$	Accessible hidden states; for a single layer, $Z_{h}\in\mathbb{R}^{\ell_{h}\times d}$ , with token count $\ell_{h}$ and hidden width $d$ .
$u_{h},\ \mathcal{U}_{h}$	Semantic information and its representation space; if vector-valued, $u_{h}\in\mathbb{R}^{d_{u}(h)}$ .

Appendix

Table 6

Long-Horizon LLM Reasoning

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Separating quantum circuits from classical LLMs

Srinivasan Arunachalam, Arkopal Dutt, Hari Krovi, Rik Sengupta

IBM Research

Decoder-Only Language Models Diffusion Language Models

Open paper AskPDF arXiv

Modern large language models - transformers and diffusion language models - are built around two canonical algorithmic tasks: prediction and generation. We prove unconditional separations between low-depth quantum computation and the corresponding bounded-resource classical language-model architectures in both regimes. Concretely, we exhibit the following: 1. Distributional separation. We give a distribution that is sampleable by

\textsf{QNC}^0

circuits (i.e., a family of constant-depth quantum circuits consisting of bounded fan-in gates) that no constant-round diffusion language model (

\textsf{DLM}

) with shallow scheduling and denoising can sample within constant distance, even when allowed sublinear chain-of-thought and output-token revision/remasking events, the very features modern

\textsf{DLM}

s rely on. 2. Functional separation. We exhibit a function computable in

\land \circ \textsf{QNC}^0[\log\log n]

(i.e., a family of O

(\log\log n)

-depth

\textsf{QNC}^0

circuits, where

n

is the input length, followed by a single classical

\mathsf{AND}

gate) such that any constant-depth decoder-only transformer computing the function must be large: it would have to have width

n^{Ω(1)}

. Together, our work initiates the study of quantum advantage in the era of large language models.

Abstract

Long-Horizon LLM Reasoning

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