use quantrs2_core::{
error::QuantRS2Result,
gate::{multi, single, GateOp},
qubit::QubitId,
};
use scirs2_core::Complex64;
fn main() {
println!("=================================================================");
println!(" QuantRS2-Core: Variational Quantum Algorithms");
println!("=================================================================\n");
demonstrate_vqe_basics();
println!();
demonstrate_qaoa_basics();
println!();
demonstrate_variational_circuit();
println!();
demonstrate_parameter_optimization();
println!();
println!("=================================================================");
println!(" Example Complete!");
println!("=================================================================");
}
fn demonstrate_vqe_basics() {
println!("VARIATIONAL QUANTUM EIGENSOLVER (VQE)");
println!("-----------------------------------------------------------------");
println!("VQE is a hybrid quantum-classical algorithm for finding");
println!("the ground state energy of a molecular Hamiltonian.");
println!();
println!("Application: H₂ Molecule Ground State Energy");
println!(" • Qubits needed: 2 (for 2 electrons in 2 orbitals)");
println!(" • Hamiltonian terms: 5 Pauli operators");
println!(" • Classical optimization: Gradient descent or BFGS");
println!();
println!("Variational Ansatz (Hardware-Efficient):");
println!(" 1. RY(θ₁) on qubit 0");
println!(" 2. RY(θ₂) on qubit 1");
println!(" 3. CNOT(0, 1) for entanglement");
println!(" 4. RY(θ₃) on qubit 0");
println!(" 5. RY(θ₄) on qubit 1");
println!();
let n_params = 4;
println!("Parameter Space:");
println!(" • Dimensionality: {n_params} parameters");
println!(" • Search space: [0, 2π]^{n_params}");
println!(" • Optimization landscape: Non-convex with local minima");
println!();
println!("VQE Workflow:");
println!(" 1. Initialize variational parameters θ");
println!(" 2. Prepare quantum state |ψ(θ)⟩");
println!(" 3. Measure energy E(θ) = ⟨ψ(θ)|H|ψ(θ)⟩");
println!(" 4. Classical optimizer updates θ → θ'");
println!(" 5. Repeat until convergence");
println!();
println!(" ✓ VQE basics demonstrated");
println!(" ✓ Used for: Molecular simulation, materials science");
}
fn demonstrate_qaoa_basics() {
println!("QUANTUM APPROXIMATE OPTIMIZATION ALGORITHM (QAOA)");
println!("-----------------------------------------------------------------");
println!("QAOA is a hybrid algorithm for solving combinatorial");
println!("optimization problems like MaxCut, TSP, and SAT.");
println!();
println!("Application: Graph MaxCut Problem");
println!(" • Problem: Partition graph vertices to maximize cut edges");
println!(" • Qubits: One per vertex");
println!(" • Classical NP-hard, quantum approximate solution");
println!();
println!("QAOA Structure:");
println!(" Circuit depth p (number of layers):");
println!(" • p=1: Simple approximation, fast");
println!(" • p→∞: Approaches optimal solution");
println!(" • Trade-off: accuracy vs. circuit depth");
println!();
println!("QAOA Layer Structure:");
println!(" For each layer i:");
println!(" 1. Cost Hamiltonian: exp(-iγᵢHc)");
println!(" • Encodes problem structure");
println!(" • Applied as problem-specific gates");
println!(" 2. Mixer Hamiltonian: exp(-iβᵢHm)");
println!(" • Typically X rotations on all qubits");
println!(" • Explores solution space");
println!();
println!("Example: 4-node graph MaxCut");
println!(" • 4 qubits (one per node)");
println!(" • 4 edges → 4 ZZ interaction terms");
println!(" • p=1: 2 variational parameters (γ, β)");
println!(" • p=3: 6 parameters (γ₁,β₁,γ₂,β₂,γ₃,β₃)");
println!();
println!("QAOA Workflow:");
println!(" 1. Initialize in uniform superposition: H⊗ⁿ|0⟩");
println!(" 2. Apply p QAOA layers with parameters (γ,β)");
println!(" 3. Measure in computational basis");
println!(" 4. Compute cost function value");
println!(" 5. Classical optimizer updates (γ,β)");
println!(" 6. Repeat until convergence");
println!();
println!(" ✓ QAOA basics demonstrated");
println!(" ✓ Used for: Logistics, scheduling, portfolio optimization");
}
fn demonstrate_variational_circuit() {
println!("VARIATIONAL CIRCUIT CONSTRUCTION");
println!("-----------------------------------------------------------------");
println!("Hardware-Efficient Ansatz (3 qubits):");
println!();
let n_qubits = 3;
let n_layers = 2;
println!("Configuration:");
println!(" • Qubits: {n_qubits}");
println!(" • Layers: {n_layers}");
println!(
" • Total parameters: {} (3 rotations × 3 qubits × 2 layers)",
3 * n_qubits * n_layers
);
println!();
println!("Layer structure:");
for layer in 0..n_layers {
println!(" Layer {layer}:");
println!(
" • RZ(θ[{}..{}]) on each qubit",
layer * 9,
layer * 9 + 3
);
println!(
" • RY(θ[{}..{}]) on each qubit",
layer * 9 + 3,
layer * 9 + 6
);
println!(
" • RZ(θ[{}..{}]) on each qubit",
layer * 9 + 6,
layer * 9 + 9
);
println!(" • Entangling: CNOT chain (0→1, 1→2, 2→0)");
println!();
}
println!("Circuit Gates (Symbolic):");
println!(" |q0⟩ ──RZ(θ₀)──RY(θ₃)──RZ(θ₆)──●────────────┐");
println!(" |q1⟩ ──RZ(θ₁)──RY(θ₄)──RZ(θ₇)──X──●─────────┤");
println!(" |q2⟩ ──RZ(θ₂)──RY(θ₅)──RZ(θ₈)─────X──●──────┤");
println!(" X");
println!();
println!("Expressibility:");
println!(" • Can approximate wide variety of quantum states");
println!(" • Balance: expressibility vs. trainability");
println!(" • Barren plateau problem for deep circuits");
println!();
println!(" ✓ Variational circuit demonstrated");
}
fn demonstrate_parameter_optimization() {
println!("PARAMETER OPTIMIZATION STRATEGIES");
println!("-----------------------------------------------------------------");
println!("1. GRADIENT-FREE METHODS");
println!(" Nelder-Mead Simplex:");
println!(" • No gradient computation needed");
println!(" • Good for noisy objectives");
println!(" • Scales poorly with parameters");
println!();
println!(" CMA-ES (Covariance Matrix Adaptation):");
println!(" • Evolution strategy");
println!(" • Adapts to landscape");
println!(" • Good for ~100 parameters");
println!();
println!("2. GRADIENT-BASED METHODS");
println!(" Parameter-Shift Rule:");
println!(" • Quantum-compatible gradient estimation");
println!(" • ∂E/∂θᵢ = [E(θ+s) - E(θ-s)] / 2sin(s)");
println!(" • Requires 2 circuit evaluations per parameter");
println!(" • Exact gradient (no approximation error)");
println!();
println!(" SPSA (Simultaneous Perturbation):");
println!(" • Estimates all gradients with 2 measurements");
println!(" • Stochastic approximation");
println!(" • Scales well to many parameters");
println!();
println!(" Natural Gradient Descent:");
println!(" • Uses quantum Fisher information metric");
println!(" • Better optimization landscape navigation");
println!(" • Requires Fubini-Study metric computation");
println!();
println!("3. HYBRID APPROACHES");
println!(" Adam + Parameter-Shift:");
println!(" • Adaptive learning rates");
println!(" • Momentum for escaping local minima");
println!(" • First/second moment estimates");
println!();
println!(" Quantum Natural Gradient + Adam:");
println!(" • Combines best of both");
println!(" • Used in state-of-the-art VQE");
println!();
println!("Optimization Challenges:");
println!(" • Barren plateaus: Vanishing gradients in deep circuits");
println!(" • Local minima: Non-convex landscape");
println!(" • Noise: Measurement and gate errors");
println!(" • Shot noise: Finite sampling statistics");
println!();
println!("Best Practices:");
println!(" 1. Start with small circuit depths");
println!(" 2. Use warm-starting from classical solutions");
println!(" 3. Monitor convergence carefully");
println!(" 4. Consider noise mitigation (error mitigation, ZNE)");
println!(" 5. Use ansatz with good inductive bias for problem");
println!();
println!(" ✓ Parameter optimization demonstrated");
}
#[cfg(test)]
mod tests {
use super::*;
#[test]
fn test_example_runs() {
main();
}
#[test]
fn test_vqe_demonstration() {
demonstrate_vqe_basics();
}
#[test]
fn test_qaoa_demonstration() {
demonstrate_qaoa_basics();
}
#[test]
fn test_circuit_demonstration() {
demonstrate_variational_circuit();
}
#[test]
fn test_optimization_demonstration() {
demonstrate_parameter_optimization();
}
}