Submitted:
01 November 2025
Posted:
03 November 2025
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Abstract
Keywords:
1. Introduction
2. Background
2.1. Quantum Computing Fundamentals
2.2. Quantum Machine Learning Foundations
2.3. Natural Language Processing
2.4. Quantum Classical Hybrids
3. Computational Models for QNLP
3.1. Categorical Compositional Models
3.2. Quantum Circuit-Based Models
3.3. Variational Quantum Models

3.4. Quantum Kernel Methods
4. Encoding Paradigms
4.1. Basic Encoding
4.2. Amplitude Encoding
4.3. Entanglement-Based Encodings
4.4. Hybrid Embedding Strategies
4.5. Space-Efficient Tensorized Embeddings
4.6. Trainable Quantum Embedding Circuits
4.7. Resource Cost Modeling
5. Evaluation Frameworks
6. Challenges and Future Directions
7. Conclusion
Appendix A
| Task | Method | Design Highlights | Input Data Type | Label Type | Loss |
|---|---|---|---|---|---|
| Sentence Classification | DisCoCat Coecke et al. (2010) | Maps grammatical reductions to tensor contractions in Hilbert space (compact-closed categories); sentence meaning via categorical compositionality with quantum-ready tensors. | Tokenized sentences | Sentiment / Topic | Cross-entropy |
| VQC-QNLP Gujju et al. (2025) | Parameterized quantum circuit on encoded tokens; hybrid loop minimizes expectation; entanglement captures long-range dependencies under NISQ. | Token embeddings | Binary / Multi-class | Weighted cross-entropy | |
| Semantic Similarity | QBW Lorenz et al. (2021a) | Quantum Bag-of-Words; embeds words as quantum states; measures similarity via state fidelity/overlaps instead of cosine distance. | Sentence pairs | Similarity / Paraphrase | Fidelity or MSE |
| Quantum Kernel (QK-NLP) Schuld and Killoran (2019);Wang et al. (2025) | Quantum feature map induces kernel ; classical SVM/GP on quantum kernel matrix. | Sentences / embeddings | STS / Entailment | Hinge loss / GP NLL | |
| Sequence Labeling | DisCoCirc Chang et al. (2023) | Discourse-aware extension of DisCoCat; circuit evolution updates word states across context; syntax–semantics via variational updates. | Token sequences | POS / NER / chunks | Token-level cross-entropy |
| QCSE Liu et al. (2025b) | Quantum Context-Sensitive Embeddings: context unitary entangles tokens; contextual vectors in Hilbert space for tagging. | Token sequences | Sequence tags | MSE / cross-entropy | |
| Hybrid Embedding Learning | Hybrid-QNN Chen et al. (2025) | Classical encoder (e.g., BERT) → amplitude/angle map → shallow PQC refinement; few-qubit head for NISQ robustness. | Pretrained text embeddings | Sentiment / Intent | Cross-entropy (hybrid) |
| Low-Resource / Multi-Modal | MultiQ-NLP Wang et al. (2024) | Entangles text–image qubits; cross-modal attention via controlled rotations; improves transfer in few-shot regimes. | Text–image pairs | Match / Tags | Contrastive (InfoNCE) |
| Sense Modeling / Pretraining | QTP-Net Zhang et al. (2025) | Encodes word senses as quantum superpositions ; learns sense mixture via measurement-driven objectives. | Large text corpora | Sense / Masked tokens | NLL; superposition reconstruction |
| Encoding Learning | Trainable Basic Encoding Munikote (2024) | Learnable encoder on basis states prior to PQC; low-depth, NISQ-friendly alternative to fixed angle/amplitude maps. | Token indices | Task-specific | Task loss + encoder reg. |
| Resource-Efficient Embeddings | word2ket / Tensorized Panahi et al. (2019) | Factorizes embedding matrix into low-order tensor products; quantum-ready prep with shallow circuits; large parameter compression. | Vocabulary embeddings | Task-specific | Task loss; tensor-factor regs |
| Encoding Paradigm | Core Idea / Map | Qubits q | State-Prep Cost | Strengths | Limitations |
|---|---|---|---|---|---|
| Basic / Learnable Encoding | Token index with shallow trainable unitary | (index map) | Low (shallow ) | Very low depth; parameter-efficient; preserves discrete identity; NISQ-friendly | Needs downstream entanglers/PQC for expressivity; tuning still task-dependent |
| Angle / Rotation Encoding | Map features to single-qubit rotations (e.g., /) per dimension; supports data re-uploading | Simple, robust, transparent geometry; pairs well with re-uploading in VQCs | Linear qubit growth with d; underuses Hilbert space unless combined with entanglement | ||
| Amplitude Encoding | (inner-products preserved) | (state loading) | Exponential compression of d; strong for kernel/similarity tasks; unitary-friendly | Expensive loaders; noise-sensitive; benefits from high-fidelity prep | |
| Entanglement-based Composition | Apply (CNOT/CZ) to correlate token subsystems; syntax/relations via entanglers | Task-dependent | Entanglers dominate | Directly captures compositional/relational structure; aligns with categorical semantics | Increases depth and error on NISQ; careful compilation needed |
| Hybrid Embedding Strategies | Classical embedding (e.g., BERT/Word2Vec) → quantum feature map → PQC | Few-qubit heads common | Modest; depends on chosen feature map | Best near-term trade-off; leverages pretrained semantics; smaller q / shots | Classical front-end may dominate compute; quantum benefit is task- and map-dependent |
| Space-efficient Tensorized (word2ket) | Factorize embedding matrix into low-order tensor products; shallow quantum prep from factors | By factorization design | Low (from tensor factors) | compression reported; principled bridge to tensor networks; shallow circuits | Quality depends on factorization rank/structure; extra design choices required |
| Trainable Quantum Embedding Circuits | Small reusable quantum cell learns token/context encoding in-circuit; reused across positions | Few (cell reused) | Low–moderate (per-cell) | Parameter-efficient; context-aware; fewer qubits/shots than naïve per-token circuits | Requires careful training/stability on NISQ; generalization may be dataset-dependent |
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