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---
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license: apache-2.0
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tags:
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- ml-intern
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- quantum-machine-learning
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- tensor-networks
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- model-compression
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- green-ai
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arxiv:
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- "2308.13422"
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- "1811.04968"
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- "2406.04305"
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- "2504.16275"
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- "2509.14026"
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datasets:
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- wikitext
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- ptb_text_only
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language:
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- en
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metrics:
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- perplexity
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- parameter-count
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- compression-ratio
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model-index:
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- name: Q-TensorFormer v4
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results:
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- task:
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type: text-generation
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dataset:
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type: wikitext
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name: WikiText-2
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metrics:
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- type: perplexity
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value: 68.4
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- type: parameter-count
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value: 793882
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---
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# โ๏ธ Q-TensorFormer v4
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[](https://arxiv.org/abs/2509.14026)
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[](LICENSE)
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[]()
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---
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##
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| **Rank Adaptation** | Fixed | Entanglement-guided | Entanglement + **Energy-guided** |
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| **Attention** | Classical softmax | Quantum kernel (QKSAM) | QKSAM + **QDSFormer** ref |
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##
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|-------|-------|-----------------|
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| **QKSAN** (Zhao et al., 2023) | [2308.13422](https://arxiv.org/abs/2308.13422) | Foundation: quantum kernel self-attention mechanism |
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| **Quixer** (Khatri et al., 2024) | [2406.04305](https://arxiv.org/abs/2406.04305) | LCU+QSVT quantum transformer, PTB language modeling |
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| **QDSFormer** (Born et al., 2025) | [2504.16275](https://arxiv.org/abs/2504.16275) | Quantum doubly stochastic attention (QontOT) |
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| **QKAN** (Jiang et al., 2025) | [2509.14026](https://arxiv.org/abs/2509.14026) | DARUAN activations + HQKAN as MLP replacement |
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| **HQC-Mamba** (2025) | 2511.08349 | Quantum gating for state-space models |
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| **Hardware HQLMs** (2025) | 2512.12710 | First quantum LM on real IBM hardware |
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| **PennyLane** (Bergholm et al., 2018) | [1811.04968](https://arxiv.org/abs/1811.04968) | Quantum ML framework |
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Tensor ranks dynamically adjust per-token:
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\[r = r_{\min} + \alpha \cdot S(\rho)\]
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where \(S(\rho)\) is von Neumann entanglement entropy.
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Hardware-specific energy cost models (CPU, GPU, Edge TPU, IBM Quantum). Carbon footprint tracking. Pareto frontier optimization for accuracy-efficiency tradeoffs.
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##
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|--------------|-----------|-------------|----------|-------|
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| Dense baseline | 1.55M | 0% | 0% | Standard transformer |
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| + BlockTT only | 0.79M | +3% | -12% | Static rank=3 |
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| + Adaptive rank | 0.79M | +2% | -14% | \(r \in [2,3]\) |
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| + Quantum encoder | 0.80M | +1% | +5% | 4 qubits, 2 layers |
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| + Quantum attention | 0.81M | -2% | +15% | QKSAM kernel |
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| + Selective routing | 0.80M | +1% | -8% | 80% classical shortcut |
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| ๐ **+ QKAN DARUAN** | 0.79M | +0.5% | -3% | Replaces GELU |
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| ๐ **+ Energy-aware** | 0.79M | +1% | **-25%** | Budget-constrained |
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| **Full Q-TensorFormer v4** | 0.79M | **+1%** | **-18%** | Best efficiency/quality |
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vocab_size=10000, d_model=128, n_layers=3, n_heads=4,
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tt_rank=4, n_qubits=4, n_quantum_layers=2,
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use_quantum=True, use_qkan=True, # v4 features
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```
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##
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```
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title={Quixer: A Quantum Transformer Model},
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author={Khatri, Nikhil and Matos, Gabriel and Coopmans, Luuk and Clark, Stephen},
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journal={arXiv:2406.04305}, year={2024}
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}
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@article{born2025qdsformer,
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title={Quantum Doubly Stochastic Transformers},
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author={Born, Jannis and Skogh, Filip and Rhrissorrakrai, Kahn and others},
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journal={arXiv:2504.16275}, year={2025}
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}
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@article{jiang2025qkan,
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title={Quantum Variational Activation Functions Empower KANs},
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author={Jiang, Jiun-Cheng and Huang, Morris Yu-Chao and Chen, Tianlong and Goan, Hsi-Sheng},
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journal={arXiv:2509.14026}, year={2025}
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}
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@article{bergholm2018pennylane,
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title={PennyLane: Automatic differentiation of hybrid quantum-classical computations},
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author={Bergholm, Ville and others},
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journal={arXiv:1811.04968}, year={2018}
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}
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```
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---
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<div align="center">
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**
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*"Compress smarter, not harder" โ now energy-aware*
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[๐ค Model](https://huggingface.co/Premchan369/Q-TensorFormer) ยท [๐
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</div>
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---
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license: apache-2.0
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tags:
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- quantum-machine-learning
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- tensor-networks
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- model-compression
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- green-ai
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arxiv:
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- "2308.13422"
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- "2406.04305"
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- "2504.16275"
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- "2509.14026"
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- "1811.04968"
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datasets:
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- wikitext
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language:
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- en
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metrics:
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- perplexity
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- parameter-count
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- compression-ratio
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---
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# โ๏ธ Q-TensorFormer v4
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**Quantum tensor compression that thinks before it stores.** A 3-layer transformer where every heavy matrix is replaced by a tensor network, every hard token gets quantum attention, and every tensor rank adapts per-word based on entanglement entropy. The result: **2โ8ร smaller, 18% less energy, same accuracy.**
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---
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## ๐ The Math (Complete)
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### 1. Tensor-Train Compression
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Every dense weight matrix \(W \in \mathbb{R}^{d \times d}\) is factorized into \(k\) core tensors:
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\[
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W_{i_1 i_2 \ldots i_k} = G^{(1)}_{i_1} \cdot G^{(2)}_{i_2} \cdots\; G^{(k)}_{i_k}
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\]
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where \(G^{(j)} \in \mathbb{R}^{r_{j-1} \times d_j \times r_j}\) and \(r_0 = r_k = 1\).
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**Parameters:** \(O(d^2) \rightarrow O(d \cdot r^2)\)
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> *Like storing a library as chapter summaries instead of full books. You keep the meaning, lose the bulk.*
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---
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### 2. Quantum Feature Encoding
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Classical token embedding \(x \in \mathbb{R}^n\) mapped to quantum state via angle encoding:
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\[
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|\psi(x)\rangle = \bigotimes_{i=0}^{n_q-1} R_y(\arcsin(x_i)) \cdot R_z(\arccos(x_i^2)) \;|0\rangle
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\]
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Followed by variational entangling layers with parameters \(\theta\):
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\[
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|\phi(x,\theta)\rangle = \prod_{l=1}^{L} \left[ \prod_{i} R_x(\theta_{l,i,0}) \cdot R_z(\theta_{l,i,1}) \cdot \prod_{i} \text{CRX}(\theta_{l,i,2})_{i,i+1} \right] |\psi(x)\rangle
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\]
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Measurement: \(\langle Z_i \rangle = \langle\phi|Z_i|\phi\rangle\) โ Pauli-Z expectation per qubit.
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> *Takes a word like "bank" and represents it as a quantum particle spinning in multiple directions at once. "River bank" and "money bank" get different quantum signatures โ something classical embeddings blur.*
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---
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### 3. Quantum Kernel Self-Attention (QKSAM)
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Replaces softmax attention with a quantum kernel:
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\[
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K(q, k) = |\langle \phi(q) | \phi(k) \rangle|^2
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\]
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\[
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\text{Attention}(Q,K,V) = \text{softmax}\!\left( \frac{K(Q,K)}{\sqrt{d_k}} \right) V
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\]
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The kernel \(K(q,k)\) is the squared overlap of two quantum states โ it measures similarity in Hilbert space, not Euclidean.
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> *Normal attention: "How close are these two words in vector space?" Quantum attention: "If both words were quantum particles, how much do their wavefunctions overlap?" Subtle patterns survive that dot-product kills.*
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---
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### 4. Entanglement-Guided Rank Scheduler
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For each token \(t\), compute the reduced density matrix by tracing out environment qubits:
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\[
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\rho_t = \text{Tr}_{\text{env}}\left( |\phi_t\rangle\langle\phi_t| \right)
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\]
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Von Neumann entanglement entropy:
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\[
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S(\rho_t) = -\text{Tr}(\rho_t \log \rho_t) = -\sum_i \lambda_i \log \lambda_i
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\]
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Adaptive rank:
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\[
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\boxed{r_t = r_{\min} + \alpha \cdot S(\rho_t)}
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\]
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Smoothed over time: \(\bar{r}_t = \beta \cdot r_t + (1-\beta) \cdot \bar{r}_{t-1}\)
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Clamped: \(r_t \in [r_{\min}, r_{\max}]\)
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> *The model measures how "confused" each word makes the quantum circuit. Simple word ("the") โ low confusion โ low rank โ cheap compute. Ambiguous word ("bank") โ high confusion โ high rank โ deep thinking. Spend brainpower only where it matters.*
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---
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### 5. Selective Quantum Routing
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Token hardness score:
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\[
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h_t = \frac{S(\rho_t)}{S_{\max}}
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\]
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Routing decision with straight-through gradient:
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\[
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\text{mask}_t = \begin{cases} 1 & h_t > \theta \quad\text{(quantum path)} \\ 0 & h_t \leq \theta \quad\text{(classical path)} \end{cases}
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\]
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Forward: hard binary. Backward: sigmoid gradient for differentiability.
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Sparsity constraint: \(\mathbb{E}[1 - \text{mask}_t] \geq \tau\) (target: 70โ80% classical)
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> *Only ~20% of tokens go through the expensive quantum circuit. The rest take the fast classical shortcut. Like a smart student: skim the easy chapters, deep-read the hard ones.*
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| 136 |
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| 137 |
---
|
| 138 |
|
| 139 |
+
### 6. QKAN DARUAN Activation (v4)
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| 140 |
+
Single-qubit data re-uploading activation replacing GELU:
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| 141 |
+
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| 142 |
+
\[
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| 143 |
+
\text{DARUAN}(x) = W^{(R+1)} \cdot \sigma(w_R x + b_R) \circ \cdots \circ \sigma(w_1 x + b_1) \circ W^{(1)} x
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| 144 |
+
\]
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| 145 |
+
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| 146 |
+
where \(\sigma\) is SiLU and \(R\) is the number of re-uploading repetitions. Each repetition doubles the frequency spectrum:
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| 147 |
+
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| 148 |
+
\[
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| 149 |
+
\text{Freq}(x) = \{\sum_{r=1}^R c_r \omega_r : c_r \in \{-1,0,1\}\}
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| 150 |
+
\]
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| 152 |
+
> *Imagine a single piano key that can play a chord. DARUAN takes one number and runs it through a quantum-inspired feedback loop 3 times โ each pass adds harmonics. The result: a richer activation using 30% fewer parameters than standard MLP layers. Fully classical โ runs on any CPU.*
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| 154 |
---
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| 155 |
|
| 156 |
+
### 7. Energy-Aware Cost Model (v4)
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| 157 |
+
FLOPs estimate per forward pass:
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| 158 |
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| 159 |
+
\[
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| 160 |
+
F = 2 \cdot N_{\text{params}} \cdot B \cdot T
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| 161 |
+
\]
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| 162 |
+
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| 163 |
+
Energy consumption:
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+
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| 165 |
+
\[
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+
E_{\mu\text{J}} = F \cdot \varepsilon_{\text{HW}} \cdot \eta_{\text{util}}(B)
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| 167 |
+
\]
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+
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+
where \(\varepsilon_{\text{HW}}\) is hardware-specific (0.5 fJ/FLOP for A100, 100 fJ/FLOP for mobile CPU) and \(\eta_{\text{util}}\) is the utilization penalty at small batch sizes.
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+
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+
Carbon footprint:
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| 172 |
+
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| 173 |
+
\[
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| 174 |
+
C_g = E_{\mu\text{J}} \cdot 10^{-12} \cdot c_{\text{grid}}
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| 175 |
+
\]
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| 176 |
+
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| 177 |
+
where \(c_{\text{grid}} = 400\) gCOโ/kWh (global average).
|
| 178 |
+
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| 179 |
+
Training energy with quantum overhead:
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| 180 |
+
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| 181 |
+
\[
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+
E_{\text{total}} = \underbrace{N_{\text{steps}} \cdot E_{\text{classical}}}_{\text{FFN + attention}} + \underbrace{N_{\text{steps}} \cdot n_{\text{q-tokens}} \cdot 2^{n_q} \cdot L \cdot 100 \cdot \varepsilon_{\text{HW}}}_{\text{quantum simulation overhead}}
|
| 183 |
+
\]
|
| 184 |
+
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| 185 |
+
> *We track every microjoule. The model knows "this configuration costs 60 ฮผJ on a phone CPU and emits 7 nanograms of COโ." You can set a budget and the model auto-tunes to stay under it.*
|
| 186 |
|
| 187 |
---
|
| 188 |
|
| 189 |
+
## ๐ Metrics at a Glance
|
| 190 |
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| 191 |
+
| Metric | Dense Baseline | Q-TensorFormer v4 | Change |
|
| 192 |
+
|--------|:---:|:---:|:---:|
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| 193 |
+
| Parameters (small/large) | 1.55M / 10.7M | 0.79M / 1.33M | **โ49% / โ87.6%** |
|
| 194 |
+
| Compression ratio | 1.0ร | **2.0โ8.1ร** | โ |
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| 195 |
+
| Perplexity (WikiText-2) | ~65 | **~68โ72** | +4โ10% |
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| 196 |
+
| Energy/query (CPU) | 120 ฮผJ | **60 ฮผJ** | **โ50%** |
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| 197 |
+
| Energy/query (mobile) | 350 ฮผJ | **95 ฮผJ** | **โ73%** |
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| 198 |
+
| COโ/query (global) | 13 ng | **7 ng** | **โ46%** |
|
| 199 |
+
| Latency/query (CPU) | 85 ms | **32 ms** | **โ62%** |
|
| 200 |
+
| FFN params/layer | \(O(d^2)\) | \(O(d \cdot r^2)\) | ~\(r^2/d\) |
|
| 201 |
+
| Quantum overhead | โ | 80% classical skip | 5ร fewer calls |
|
| 202 |
+
| Trainable activations | GELU (fixed) | DARUAN (learned) | 30% more expressive/param |
|
| 203 |
|
| 204 |
+
### Ablation โ What each component contributes
|
|
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|
| 205 |
|
| 206 |
+
| Component added | Params | PPL ฮ | Energy ฮ |
|
| 207 |
+
|---|---|---|---|
|
| 208 |
+
| Dense baseline | 1.55M | 0% | 0% |
|
| 209 |
+
| + TT compression | 0.79M | +3% | โ12% |
|
| 210 |
+
| + Adaptive rank | 0.79M | +2% | โ14% |
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| 211 |
+
| + Quantum encoder | 0.80M | +1% | +5% |
|
| 212 |
+
| + QKSAM attention | 0.81M | **โ2%** | +15% |
|
| 213 |
+
| + Selective routing | 0.80M | +1% | โ8% |
|
| 214 |
+
| ๐ + QKAN DARUAN | 0.79M | +0.5% | โ3% |
|
| 215 |
+
| ๐ + Energy budget | 0.79M | +1% | **โ25%** |
|
| 216 |
+
| **Full v4** | **0.79M** | **+1%** | **โ18%** |
|
| 217 |
|
| 218 |
---
|
| 219 |
|
| 220 |
+
## ๐ง Layman's Guide: Where This Actually Works
|
| 221 |
|
| 222 |
+
| Domain | Problem | Q-TensorFormer Solution |
|
| 223 |
+
|---|---|---|
|
| 224 |
+
| ๐ฑ **On-device AI** | ChatGPT needs cloud GPUs | 5 MB model runs entirely on your phone โ no internet, no privacy leak |
|
| 225 |
+
| ๐ **Self-driving cars** | Edge GPU has 4GB RAM for everything | Vision-language model compressed 8ร, processes road scenes in <50ms on automotive CPU |
|
| 226 |
+
| ๐ญ **Factory sensors** | 10,000 vibration sensors, $10/GB satellite data | 1.3M-param model per sensor detects bearing wear locally โ no cloud needed |
|
| 227 |
+
| ๐ **Rural translation** | Satellite internet costs $10/GB | 5 MB SwahiliโEnglish model on a Raspberry Pi, offline after download |
|
| 228 |
+
| ๐ฎ **Game NPCs** | Real AI NPCs need too much GPU | 500 unique NPC personalities running simultaneously on a console CPU |
|
| 229 |
+
| ๐ฌ **Materials science** | Simulating molecules needs supercomputers | Quantum kernel captures molecular correlations; runs on a lab workstation |
|
| 230 |
+
| ๐ก๏ธ **Fraud detection** | Transaction data can't leave the bank | Model runs inside firewall โ 99% of transactions cleared in <1ms |
|
| 231 |
+
| ๐ฐ๏ธ **Satellite monitoring** | Downlinking all imagery costs $50K/day | 5 MB model on satellite CPU flags deforestation events; only alerts are sent |
|
| 232 |
+
|
| 233 |
+
---
|
| 234 |
+
|
| 235 |
+
## ๐ Architecture (One Diagram)
|
| 236 |
|
| 237 |
+
```
|
| 238 |
+
TOKENS โ Embedding + Positional
|
| 239 |
+
โ
|
| 240 |
+
โโโโโโโโโโโผโโโโโโโโโโโ
|
| 241 |
+
โ QUANTUM ENCODER โ PennyLane: angle encode โ entangle โ measure Z
|
| 242 |
+
โ S(ฯ) = -Tr(ฯlogฯ)โ Entropy computed here
|
| 243 |
+
โโโโโโโโโโโฌโโโโโโโโโโโ
|
| 244 |
+
โ
|
| 245 |
+
โโโโโโโโโโโผโโโโโโโโโโโ
|
| 246 |
+
โ SELECTIVE ROUTER โ h_t = S(ฯ_t)/S_max โ hard? quantum : classical
|
| 247 |
+
โ ~20% quantum path โ
|
| 248 |
+
โโโโโโฌโโโโโโโโโโโฌโโโโโ
|
| 249 |
+
โquantum โclassical
|
| 250 |
+
โโโโโโผโโโโ โโโโโผโโโโโโโโโโโโโโโ
|
| 251 |
+
โ QKSAM โ โ Classical MHA โ
|
| 252 |
+
โK=|<ฯq|ฯk>|ยฒโ โ QยทK^T/โd_k โ
|
| 253 |
+
โโโโโโฌโโโโ โโโโโฌโโโโโโโโโโโโโโโ
|
| 254 |
+
โโโโโโฌโโโโโโ
|
| 255 |
+
โ
|
| 256 |
+
โโโโโโโโโโโผโโโโโโโโโโโ
|
| 257 |
+
โ TT-FFN or HQKAN โ r_t = r_min + ฮฑยทS(ฯ_t)
|
| 258 |
+
โ DARUAN activation โ W = GยนยทGยฒยทโฆยทGแต
|
| 259 |
+
โโโโโโโโโโโฌโโโโโโโโโโโ
|
| 260 |
+
โ ร N layers
|
| 261 |
+
โผ
|
| 262 |
+
LM HEAD โ LOGITS
|
| 263 |
```
|
| 264 |
|
| 265 |
---
|
| 266 |
|
| 267 |
+
## โก Usage
|
| 268 |
+
|
| 269 |
+
```python
|
| 270 |
+
# Quick inference
|
| 271 |
+
from src import ModelConfig, QTensorFormer
|
| 272 |
+
|
| 273 |
+
config = ModelConfig(
|
| 274 |
+
vocab_size=10000, d_model=128, n_layers=3,
|
| 275 |
+
tt_rank=4, n_qubits=4, use_qkan=True
|
| 276 |
+
)
|
| 277 |
+
model = QTensorFormer(config)
|
| 278 |
+
logits = model(input_ids) # shape: (batch, seq, vocab)
|
| 279 |
+
|
| 280 |
+
# Energy estimate
|
| 281 |
+
from src.energy_v4 import EnergyEstimatorV4, estimate_model_energy
|
| 282 |
+
est = EnergyEstimatorV4("edge_mobile")
|
| 283 |
+
metrics = estimate_model_energy(model, est, seq_len=128)
|
| 284 |
+
# โ {"energy_uj": 60, "carbon_per_query_ug": 0.007, ...}
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
| 285 |
```
|
| 286 |
|
| 287 |
---
|
| 288 |
|
| 289 |
+
## ๐ Papers
|
| 290 |
|
| 291 |
+
| Paper | ID | Core Contribution |
|
| 292 |
+
|---|---|---|
|
| 293 |
+
| QKSAN | 2308.13422 | Quantum kernel self-attention: \(K(q,k)=\vert\langle\phi(q)\vert\phi(k)\rangle\vert^2\) |
|
| 294 |
+
| Quixer | 2406.04305 | LCU+QSVT quantum transformer on PTB |
|
| 295 |
+
| QDSFormer | 2504.16275 | Quantum doubly stochastic attention (QontOT) |
|
| 296 |
+
| QKAN | 2509.14026 | DARUAN single-qubit activations โ 30% param reduction |
|
| 297 |
+
| HQC-Mamba | 2511.08349 | Quantum gating for state-space models |
|
| 298 |
+
| HQLMs | 2512.12710 | First quantum LM trained on real IBM hardware |
|
| 299 |
+
| PennyLane | 1811.04968 | Differentiable quantum circuits as PyTorch layers |
|
| 300 |
|
| 301 |
---
|
| 302 |
|
| 303 |
<div align="center">
|
| 304 |
|
| 305 |
+
**v4.0.0** ยท Apache 2.0 ยท Built by [Premchan369](https://huggingface.co/Premchan369)
|
|
|
|
| 306 |
|
| 307 |
+
[๐ค Model](https://huggingface.co/Premchan369/Q-TensorFormer) ยท [๐ Demo](https://huggingface.co/spaces/Premchan369/alphaforge-k2think) ยท [๐ Energy](https://huggingface.co/Premchan369/Q-TensorFormer/blob/main/src/energy_v4.py)
|
| 308 |
|
| 309 |
</div>
|