Quantum ansatz (parameterized circuit) construction for variational algorithms.

This namespace provides various ansatz types used in VQE and other variational
quantum algorithms. Each ansatz is designed for specific problem types and
hardware constraints.

Key Responsibilities:
- Hardware-efficient ansatz for NISQ devices
- Chemistry-inspired ansatz for molecular systems
- UCCSD-inspired ansatz for quantum chemistry
- Symmetry-preserving ansatz for fermionic systems
- Parameter initialization strategies
   
Design Principles:
- Pure functions returning circuit constructors
- Configurable parameters for flexibility
- Hardware-aware circuit structures
- Reusable across different algorithms

Quantum channel domain layer providing pure quantum mechanical channel operations.

This namespace contains the core quantum channel functionality separated from
implementation details. It focuses on the mathematical representation and 
application of quantum channels through Kraus operators.

Quantum channels represent the most general form of quantum operations,
describing how quantum states evolve under the influence of noise, decoherence,
and other physical processes. Every quantum channel can be represented using
the Kraus representation: Ε(ρ) = Σᵢ KᵢρKᵢ†

Key concepts implemented:
- Kraus operator generation for standard noise models
- Quantum channel application to quantum states
- Decoherence parameter calculations
- Matrix operations for quantum channel mathematics

Quantum circuit representation and execution

Circuit transformation utilities for quantum backends.

This namespace provides functionality for adapting quantum circuits
to specific hardware backends by transforming operations not supported
by the backend into equivalent sequences of supported operations.

Quantum gate operations for quantum state manipulation

;; Decompose Toffoli gate for CNOT+T gate set
(decompose-operation 
  {:operation-type :toffoli 
   :operation-params {:control1 0 :control2 1 :target 2}}
  :cnot-t)

;; Decompose rotation gate with specific angle
(decompose-operation
  {:operation-type :ry :operation-params {:target 0 :angle (/ Math/PI 3)}}
  #{:rz :x :cnot})

Quantum gate decomposition and circuit transformation for quantum hardware compatibility.

This namespace provides functionality to decompose complex quantum gates into simpler,
hardware-native operations. It enables quantum circuits to be transformed to match the
specific gate sets supported by different quantum hardware platforms and simulators.
  
Gate Decomposition:
- Decomposes complex gates (Toffoli, Fredkin, etc.) into universal gate sets
- Handles parametric gates (rotation gates with arbitrary angles)
- Supports multiple decomposition strategies based on target hardware

Circuit Transformation:
- Transforms entire quantum circuits to use only supported operations
- Preserves quantum circuit semantics while changing implementation
- Provides iterative decomposition with cycle detection

Gate Decomposition Examples

```clojure
;; Decompose Toffoli gate for CNOT+T gate set
(decompose-operation 
  {:operation-type :toffoli 
   :operation-params {:control1 0 :control2 1 :target 2}}
  :cnot-t)

;; Decompose rotation gate with specific angle
(decompose-operation
  {:operation-type :ry :operation-params {:target 0 :angle (/ Math/PI 3)}}
  #{:rz :x :cnot})
```

See also: `org.soulspace.qclojure.domain.operation-registry` for gate definitions.

Gate optimization functions for quantum circuits

This namespace provides functions to optimize quantum circuits by removing
redundant gates and simplifying gate sequences. The primary optimization
implemented is cancellation of consecutive self-inverse gates.

Self-inverse gates include:
- Single-qubit gates: X, Y, Z, H (Pauli gates and Hadamard)
- Two-qubit gates: CNOT (controlled-X gate), CX, CY, CZ, SWAP
- Three-qubit gates: Toffoli (CCX), Fredkin (CSWAP)
 
When two identical self-inverse gates are applied consecutively to the same
qubit(s), they cancel out and can be removed from the circuit without
changing the quantum computation.

Core Hamiltonian representation and manipulation for quantum systems.

This namespace provides the fundamental building blocks for working with
quantum Hamiltonians in the VQE algorithm and other quantum algorithms.

Key Responsibilities:
- Pauli term creation and validation
- Hamiltonian expectation value calculations  
- Measurement grouping for hardware efficiency
- Commuting term analysis

Design Principles:
- Pure functions with no side effects
- Hardware-agnostic mathematical operations
- Composable building blocks for higher-level algorithms

Mathematical operations and utilities for quantum algorithms.

Backend for Clojure complex numbers.

Facade for linear algebra operations with pluggable backends.

Goals:
 - Provide a single, meaningful API for matrix and vector operations.
 - Allow swapping implementations (pure Clojure Math, Fastmath, Neanderthal) without changing call sites.
 - Keep data shapes simple: matrices as vectors of row vectors; vectors as vectors of numbers.
 - Handle conversions between FastMath Vec2 format and backend-specific representations.
 
 Default backend: :pure, implemented via org.soulspace.qclojure.domain.math.clojure-math.
 
 Use `set-backend!` to change the global backend, or `with-backend` to override in a dynamic scope.

Backend for fastmath complex numbers.

Core mathematical protocols for matrix algebra, decompositions, and quantum state operations.

Provides a contract for implementing backends to support linear algebra operations
over numeric fields (ℝ or ℂ) with a focus on immutability and pure functions.

Domain for quantum observables - Hermitian operators representing measurable quantities.

Observables in quantum mechanics are represented by Hermitian matrices.
This namespace provides functions for creating and manipulating observables,
calculating expectation values, and working with composite observables.

Design Philosophy:
- Observables are simple data (matrices) - no complex wrapping
- Pure functions for all operations
- Compose complex observables from simple primitives
- Separate representation, computation, and measurement concerns

Operation registry and catalog for quantum backends.

This namespace provides a comprehensive catalog of operations,
quantum gates and measurements, that can be supported by
different quantum backends. Backends can reference this registry
to declare their supported operation sets.

Functions for analyzing and optimizing qubit usage in quantum circuits.

Core quantum state representation and operations