On the Representational Limits of Quantum-Inspired 1024-D Document Embeddings: An Experimental Evaluation Framework

Dario Maio

cs.IRApr 10, 2026

On the Representational Limits of Quantum-Inspired 1024-D Document Embeddings: An Experimental Evaluation Framework

Authors: Dario Maio

Organizations: Department of Computer Science and Engineering, University of Bologna, Italy

Abstract

Text embeddings are central to modern information retrieval and Retrieval-Augmented Generation (RAG). While dense models derived from Large Language Models (LLMs) dominate current practice, recent work has explored quantum-inspired alternatives motivated by the geometric properties of Hilbert-like spaces and their potential to encode richer semantic structure. This paper presents an experimental framework for constructing quantum-inspired 1024-dimensional document embeddings based on overlapping windows and multi-scale aggregation. The pipeline combines semantic projections (e.g., EigAngle), circuit-inspired feature mappings, and optional teacher-student distillation, together with a fingerprinting mechanism for reproducibility and controlled evaluation. We introduce a set of diagnostic tools for hybrid retrieval, including static and dynamic interpolation between BM25 and embedding-based scores, candidate union strategies, and a conceptual alpha-oracle that provides an upper bound for score-level fusion. Experiments on controlled corpora of Italian and English documents across technical, narrative, and legal domains, using synthetic queries, show that BM25 remains a strong baseline, teacher embeddings provide stable semantic structure, and standalone quantum-inspired embeddings exhibit weak and unstable ranking signals. Distillation yields mixed effects, improving alignment in some cases but not consistently enhancing retrieval performance, while hybrid retrieval can recover competitive results when lexical and embedding-based signals are combined. Overall, the results highlight structural limitations in the geometry of quantum-inspired embeddings, including distance compression and ranking instability, and clarify their role as auxiliary components rather than standalone retrieval representations.

Figures & tables

Space	Pearson	Spearman	MAE	Mean sim.
Teacher (E5)	0.97	0.95	0.44	0.88
QEMB (baseline)	-0.25	-0.44	0.54	0.87
QEMB (amplitude, exp.)	0.58	0.65	0.44	0.84

Table 1: Pairwise similarity evaluation across embedding spaces.

Space	Pearson	Spearman	MAE	Mean sim.
ZZ (raw)	0.04	-0.36	0.73	0.00
ZZ (teacher)	0.46	0.22	0.52	0.97
ZZ (window raw)	0.34	0.55	0.45	0.80

Table 2: Pairwise similarity evaluation for ZZ-based transformations.

Figure 1: Distribution of similarity scores for ZZ-based transformations compared with teacher embeddings. The distribution shows strong concentration in the high-similarity region, with limited separation between semantic classes.

Figure 2: Distribution of similarity scores for ZZ-based transformations compared with LLM-based similarity scores. The compression of similarity values reduces discriminative power across semantic classes.

Comparison	Pearson	Spearman
Teacher vs LLM	0.97	0.95
Quantum vs Teacher	0.25	0.18
Quantum vs LLM	0.16	0.24

Table 3: Quantum kernel similarity evaluation.

Panel of Figure 3 — Figure 3: Distribution of similarity scores for the quantum kernel compared with teacher embeddings (top) and LLM-based similarity scores (bottom). The similarity distribution collapses toward near-zero values, significantly reducing separability across semantic classes.

Figure 4: Distribution of similarity scores for the quantum kernel compared with teacher embeddings on a small set of legal-domain sentence pairs. Unlike the teacher model, which preserves a meaningful separation between semantic classes, the quantum kernel collapses most similarities toward zero, leading to near-orthogonal representations and loss of discriminative power.

Figure 5: QEMB encoding pipeline from raw text to 1024-dimensional sub-chunk embeddings. Documents are first segmented into logical chunks and sub-chunks. Each sub-chunk is processed through fixed windows whose features are obtained via angle projection and a quantum-inspired encoder implemented either with the Aer backend or a Torch surrogate.

Panel of Figure 6 — Figure 6: Embedding construction and hybrid retrieval pipeline. Top: embedding assembly. Bottom: hybrid retrieval pipeline. The upper diagram shows the assembly of the final 1024-dimensional sub-chunk embedding. The lower diagram illustrates the hybrid retrieval architecture combining vector similarity search over QEMB embeddings with lexical BM25 retrieval and optional cross-encoder re-ranking.

Method	H@1	H@3	H@5	H@10	nDCG	MRR	MAP
Teacher	0.90	1.00	1.00	1.00	0.963	0.95	0.95
BM25	0.80	0.90	1.00	1.00	0.893	0.858	0.858
QEMB (raw)	0.30	0.30	0.50	1.00	0.542	0.41	0.41
QEMB (dist.)	0.00	0.40	0.40	1.00	0.409	0.24	0.24
Hybrid (raw)	0.90	1.00	1.00	1.00	0.963	0.95	0.95
Hybrid (dist.)	0.70	1.00	1.00	1.00	0.889	0.85	0.85

Table 4: Retrieval results on the technical corpus (10 descriptive queries). Hybrid configurations use score-level interpolation with

\alpha=0.7

Method	H@1	H@3	H@5	H@10	nDCG	MRR	MAP
Teacher	0.62	0.75	0.88	1.00	0.787	0.721	0.721
BM25	0.53	0.75	0.85	1.00	0.748	0.669	0.669
QEMB (raw)	0.08	0.35	0.55	1.00	0.455	0.292	0.292
QEMB (dist.)	0.20	0.38	0.63	1.00	0.516	0.372	0.372
Hybrid (raw)	0.63	0.75	0.85	1.00	0.795	0.732	0.732
Hybrid (dist.)	0.50	0.67	0.78	1.00	0.714	0.627	0.627

Table 5: Retrieval results on the technical corpus (60 mixed queries). Hybrid configurations use score-level interpolation with

\alpha=0.7

Method	H@1	H@3	H@5	H@10	nDCG	MRR	MAP
Teacher	0.37	0.58	0.75	1.00	0.650	0.542	0.542
BM25	0.50	0.65	0.78	1.00	0.714	0.627	0.627
QEMB (raw)	0.12	0.35	0.58	1.00	0.480	0.324	0.324
QEMB (dist.)	0.20	0.33	0.45	1.00	0.502	0.358	0.358
Hybrid (raw)	0.42	0.62	0.75	1.00	0.674	0.574	0.574
Hybrid (dist.)	0.43	0.60	0.72	1.00	0.672	0.573	0.573

Table 6: Retrieval results on the narrative corpus (60 mixed queries). All methods use top-

k=10

retrieval followed by cross-encoder re-ranking.

Method	H@1	H@3	H@5	H@10	nDCG	MRR	MAP
Teacher	0.96	0.99	1.00	1.00	0.984	0.979	0.979
BM25	1.00	1.00	1.00	1.00	1.000	1.000	1.000
QEMB (raw)	0.11	0.37	0.61	1.00	0.474	0.315	0.315
QEMB (dist.)	0.19	0.42	0.67	1.00	0.524	0.380	0.380
Hybrid (raw)	0.99	1.00	1.00	1.00	0.996	0.994	0.994
Hybrid (dist.)	0.92	0.99	0.99	1.00	0.966	0.954	0.954

Table 7: Retrieval results on the legal corpus (84 mixed queries). Hybrid configurations use score-level interpolation with

\alpha=0.7

Method	H@1	H@3	H@5	H@10	nDCG	MRR	MAP
Teacher	0.03	0.30	0.43	0.67	0.251	0.206	0.192
QEMB (raw)	0.00	0.00	0.03	0.07	0.026	0.014	0.014

Table 8: Sub-chunk-level retrieval results on the technical corpus (30 queries).

Quantum-Inspired ML

Quantum-inspired machine learning adapts quantum concepts such as phases, measurements and tensor networks to classical and hybrid learning.

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Quanta: A Self-Contained Python Library for Hybrid Retrieval over Quantised Embeddings, Lexical Indexes, and Knowledge Graphs

An advanced retrieval-augmented generation pipeline is typically assembled from three or four independently operated systems: an approximate nearest-neighbour index, a full-text search engine, a graph database, and a relational document store. Each contributes its own deployment surface, configuration model, and failure modes, and the integration logic that binds them is written anew in every project. In this work, we present Quanta, an open-source Python library, which unifies dense vector search over 4-bit quantised embeddings, BM25 full-text retrieval, and knowledge-graph traversal behind a single retrieval API. Quanta makes two design commitments, which distinguish it from existing hybrid retrieval stacks. First, signals are combined by weighted reciprocal rank fusion rather than by normalising heterogeneous scores onto a shared range, which we argue is ill-posed because such normalisations are query-dependent. Second, the graph is a candidate expander and not a relevance scorer: traversal widens the candidate pool, and the newly admitted documents are re-scored by the dense indexes under an identifier allowlist, so structural adjacency determines what is considered while content evidence determines how it ranks.

Ioannis E. Livieris

Novelcore, Athens, GR 10436 · Department of Business Administration & Organization Administration, University of Peloponnese, Kalamata, GR 24100

Graph-Based Retrieval Hybrid Retrieval

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Aug 18, 2026

DEPT: Document Embedding Preservation Tuning for Unified Query Expansion and Retrieval

Large language models (LLMs) can both expand underspecified queries and encode text as dense representations, suggesting a unified model for query expansion and retrieval. Existing systems usually rely on prompted expansions, independently trained modules, or staged optimization, leaving generated expansions only indirectly aligned with the retrieval loss that judges them. We train a single decoder-only LLM end to end, where the same model generates the expansion and encodes both the expanded query and candidate documents. This unified setting creates a moving-target problem: retrieval supervision should improve query-side expansion, but the same update also shifts the document embeddings that serve as retrieval targets. We introduce Document Embedding Preservation Tuning (DEPT), which keeps tuned document embeddings close to cached initial embeddings while allowing retrieval gradients to pass through straight-through decoding into the generator. DEPT converts joint query--document movement into query-side adaptation against approximately stable, whitened document embeddings that support index reuse and online hard-negative mining. Experiments with Qwen3-4B-Instruct-2507 and LLaMA-3.2-3B-Instruct on five datasets in BEIR benchmark show that DEPT improves average retrieval quality over training-free, independently trained, and staged unified baselines, while ablations isolate the effects of preservation, whitening, end-to-end expansion training, and online negatives. Code is available at https://github.com/ILSparkle/DEPT.

Jingyuan Wang, Richong Zhang, Zhijie Nie +2

Beihang University, China

Dense Retrieval Query Expansion LLM Fine-Tuning Text Embedding Models

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Oct 6, 2026

Learning to Retrieve via Reinforcement Learning in Embedding Space

Dense retrieval models are typically trained with contrastive objectives that learn effective representations but do not directly optimize retrieval metrics or downstream task performance. To address this problem, we introduce RELER (REinforcement LEarning for Retrieval), a reinforcement learning framework that enables existing embedding models to learn to retrieve directly in embedding space and align to task-specific rewards. We train RELER by sampling unit-length query and document embedding actions from von Mises-Fisher (vMF) distributions centered on normalized encoder outputs, scoring the resulting retrieval or downstream outcomes as rewards, and updating the encoder with REINFORCE using a leave-one-out baseline (RLOO). As exploration in the high-dimensional embedding space is prone to sampling noise, we further propose conditional-mean projection (CMP), which projects each sampled embedding onto the low-dimensional subspace spanned by its encoder output and the candidate embeddings it is compared against, reducing noise in the policy gradient while preserving its expectation. We evaluate RELER on BRIGHT, a benchmark with reasoning-intensive queries that remain challenging for existing embedding models. RELER consistently outperforms InfoNCE and LambdaLoss in average nDCG@10 when post-training BGE-M3 and Qwen3-Embedding backbones. We further evaluate downstream utility through retrieval-augmented generation (RAG), where we adapt only the query encoder while keeping the document index and generator fixed. Across seven QA datasets, jointly optimizing retrieval and answer rewards improves both average retrieval performance and answer quality in RAG.

Qi Liu, Fengming Liang, Yiqun Chen +2

Renmin University of China

RL for IR Text Embedding Models

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Abstract

Quantum-Inspired ML

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