feat(qml): Add QLSTM implementation based on arXiv:2009.01783

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Summary

This PR implements Quantum Long Short-Term Memory (QLSTM) with a 6-VQC architecture as described in Figure 5 of the paper arXiv:2009.01783.

New Features

QLSTM Module (src/qml/)

• QLSTMCell with 6 VQCs:
  • VQC₁-VQC₄: Forget, Input, Cell, Output gates
  • VQC₅: Hidden state processing (h_t = VQC₅(o_t ⊙ tanh(c_t)))
  • VQC₆: Output processing (y_t = VQC₆(h_t))
• QLSTM layer for sequence processing
• QLSTMTrainer for basic gradient descent training
• VQC types: Simple, BasicEntangling, StronglyEntangling
• Data encoding: Angle, Amplitude, IQP encoding strategies

Visualization (src/vis/qlstm.rs)

• SVG diagram generation for QLSTM cell architecture
• VQC circuit visualization with qubit lines, gates, and measurements
• Text-based diagram output

Example (examples/qlstm_demo.rs)

• Comprehensive demo showcasing QLSTM functionality
• Generates SVG diagrams: qlstm_cell.svg, qlstm_full.svg, qlstm_vqc.svg

Tests (tests/test_qml_qlstm.rs)

• Unit tests for QLSTM cell and layer
• Gradient accuracy tests using parameter-shift rule
• Smoke tests for training tasks (sine wave, addition, XOR)

Architecture Diagram

                          ┌─────┐
    c_{t-1} ─────────────→│  ⊗  │────────────────────→ c_t
                          └──┬──┘
                             │
    [x_t, h_{t-1}] ──┬─→ VQC₁ → σ ─→ f_t ─┘
                     ├─→ VQC₂ → σ ─→ i_t ─┬→ ⊗ ─┬→ ⊕
                     ├─→ VQC₃ → tanh → c̃_t ┘    │
                     └─→ VQC₄ → σ ─→ o_t ─┬→ ⊗ ─┤
                                          │      │
                                    tanh(c_t) ←──┘
                                          │
                                          └─→ VQC₅ ──→ h_t ──→ VQC₆ ──→ y_t

References

• arXiv:2009.01783 - Quantum Long Short-Term Memory
• PennyLane: Learning to Learn with Quantum Neural Networks

---

Note

Introduces a Quantum ML stack centered on a 6‑VQC QLSTM, plus visualization, examples, and tests.

• Adds src/qml/ with qlstm (6‑VQC cell, QLSTM layer, trainer, MSE/cross‑entropy losses), vqc (VQC types/builders/forward), and data_encoding (Angle/Amplitude/IQP)
• New QLSTM/VQC visualization (src/vis/qlstm.rs): text and SVG diagrams; implements Visualizable and re-exports in vis
• Example app examples/qlstm_demo.rs demonstrating forward pass, training, gradients, VQC types, and diagram generation
• Comprehensive tests tests/test_qml_qlstm.rs for forward/stacked behavior, gradients, basic tasks, and losses
• Public API: exports via src/lib.rs and src/prelude.rs

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