Quantum data encoding strategies for quantum machine learning

Common infrastructure for quantum generative adversarial networks (QGANs)

Quantum Neural Networks (QNN) implementation.

QNNs are parameterized quantum circuits organized in layers that can approximate
arbitrary functions for both classification and regression tasks. This implementation
follows Clojure principles of simplicity and data orientation.

Key Features:
- Layer-based architecture using simple data maps
- Explicit parameter management per layer
- Sequential network composition using vectors
- Integration with existing variational algorithm infrastructure
- Hardware-compatible quantum operations
- Support for multiple activation patterns

Design Principles:
- Layers as data: Each layer is a simple map describing its configuration
- Explicit parameters: Clear parameter ownership and allocation per layer
- Functional composition: Networks as vectors of layers processed sequentially
- Data orientation: All network state represented as plain Clojure data structures

Architecture:
1. Input encoding layer (feature map)
2. Hidden quantum layers (parameterized unitaries)
3. Quantum activation functions (non-linear transformations)
4. Output measurement layer (classical readout)

Production-ready quantum kernel methods for quantum machine learning.

Quantum kernels compute similarity measures between classical data points by encoding
them into quantum states and measuring their overlap. This implementation provides
hardware-compatible kernel computation using measurement-based approaches suitable
for real quantum devices.

Key Features:
- Hardware-compatible adjoint/fidelity circuits for overlap estimation
- Support for multiple encoding strategies (angle, amplitude, basis, IQP)
- Efficient kernel matrix computation using transients
- Batched processing for large datasets
- Integration with QClojure backend protocols
- Production-ready error handling and validation

Algorithm:
1. Encode classical data points into quantum states using feature maps
2. Compute pairwise overlaps |⟨φ(x_i)|φ(x_j)⟩|² using adjoint/fidelity method
3. Build kernel matrix for use with classical ML algorithms
4. Support symmetric and asymmetric kernel computations

The adjoint method prepares |ψ⟩ = U_φ(x)|0⟩ then applies U†_φ(x') and measures
P(|0⟩) = |⟨φ(x)|φ(x')⟩|², avoiding ancilla qubits and working correctly for
feature-mapped superposition states (unlike SWAP test).

Training algorithms and cost functions for quantum machine learning

Variational Quantum Classifier (VQC) implementation.

VQC is a quantum machine learning algorithm that uses parameterized quantum circuits 
to perform classification tasks. It combines feature maps for encoding classical data
with variational ansatzes optimized to maximize classification accuracy.

Key Features:
- Multiple feature map types (angle, amplitude, basis, IQP)
- Integration with existing ansatz types from QClojure
- Classification-specific objective functions and metrics
- Support for binary and multi-class classification
- Comprehensive analysis including confusion matrix and decision boundaries

Algorithm Flow:
1. Encode classical features using quantum feature maps
2. Apply parameterized ansatz circuit
3. Measure classification outputs
4. Optimize parameters to maximize classification accuracy
5. Analyze results and performance metrics

This implementation is designed for production use with real quantum hardware.