Pinn Quantum Pulse Optimization

---
name: pinn-quantum-pulse-optimization
description: "Use Physics-Informed Neural Networks (PINNs) for quantum pulse optimization and noise-aware gate fidelity. Specifically for optimizing quantum control pulses in exchange-only spin qubit systems, handling charge noise, and maximizing gate-level fidelity through noise-averaged training. Use when: optimizing quantum pulses, PINN-based quantum control, spin qubit noise mitigation, exchange-only qubits, quantum gate pulse design, charge noise optimization, silicon spin qubits."
---

# PINN Quantum Pulse Optimization

Two-stage Physics-Informed Neural Network (PINN) framework for per-gate pulse optimization in quantum systems, specifically exchange-only silicon spin qubits.

## Problem

Exchange-only spin qubits use pairwise Heisenberg exchange for electrical control. Charge noise couples multiplicatively to exchange coupling, degrading gate fidelity.

## Two-Stage PINN Framework

### Stage I: Noise-Averaged Gate Fidelity Maximization

- Train PINN to maximize noise-averaged gate fidelity
- Use iterations 1-100 for broad search
- Loss function: negative fidelity averaged over charge noise samples
- Physics constraint: Schrödinger equation with exchange Hamiltonian

### Stage II: Gate-Level Fidelity Refinement

- Fine-tune with gate-level specific constraints
- Add gradient-based robustness penalties
- Optimize pulse shape for specific noise distribution

## Implementation Pattern

```python
import torch
import torch.nn as nn

class PINNPulseOptimizer:
    def __init__(self, hamiltonian, noise_model, target_gate):
        self.H = hamiltonian  # Exchange-only Hamiltonian
        self.noise = noise_model  # Charge noise model
        self.target = target_gate  # Target unitary
        
    def fidelity_loss(self, params):
        U_opt = self.simulate(params)
        F = torch.abs(torch.trace(self.target.conj().T @ U_opt)) ** 2
        return -torch.mean(F)  # Negative for maximization
```

## Key Principles

1. **Noise-aware training**: Average fidelity over noise distribution during training
2. **Physics constraints**: Embed Hamiltonian dynamics directly into loss
3. **Two-stage approach**: Broad search → fine refinement
4. **Per-gate optimization**: Different pulse shapes for different gates

## Related Skills

- quantum-control-engineering
- quantum-robust-control