quantum-systems-control-simulation

name

quantum-systems-control-simulation

description

Quantum systems control theory and simulation framework. Covers coherent feedback control (H∞), physics-informed discrete-event simulation for quantum networks, and high-dimensional quantum photonics encoding. Use when: (1) designing control systems for quantum linear systems, (2) simulating polarization-encoded quantum networks, (3) implementing H∞ disturbance attenuation, (4) encoding quantum states in high-dimensional photonic modes, (5) analyzing quantum network stability and performance.

Quantum Systems Control and Simulation

Framework for designing, analyzing, and simulating quantum control systems with physics-informed models.

Core Concepts

1. Coherent Feedback H∞ Control

Design methodology for linear quantum systems with guaranteed stability and disturbance attenuation.

Key Principles:

• Closed-loop stability guarantee
• Prescribed disturbance attenuation level
• Simplified design for general linear quantum systems
• Riccati equation-based synthesis

Design Steps:

1. Define quantum linear system model (G)
2. Specify disturbance attenuation level (γ)
3. Solve H∞ Riccati equation
4. Construct coherent feedback controller (K)
5. Validate closed-loop stability

2. Physics-Informed Discrete-Event Simulation

Simulation framework integrating physical models with event-driven quantum network simulation.

Components:

• Jones calculus optical components
• SPDC Bell-state source models
• Wave plates and polarizing beam splitters
• Multi-section fiber models
• Quantum protocol timing

Implementation:

# Extend SeQUeNCe simulator with physics models
from sequence import QuantumNetworkSimulator

class PhysicsInformedQuantumSimulator(QuantumNetworkSimulator):
    def __init__(self):
        super().__init__()
        self.add_jones_calculus_components()
        self.add_spdc_source()
        self.add_polarization_components()
    
    def simulate_bell_state_distribution(self, topology):
        # Discrete-event simulation with physics models
        events = self.generate_events(topology)
        return self.run_simulation(events)

3. High-Dimensional Quantum Photonics

Encoding multi-level quantum states using photonic degrees-of-freedom.

Encoding Modes:

• Spatial modes: Path encoding, orbital angular momentum
• Temporal modes: Time-bin encoding, pulse shaping
• Spectral modes: Frequency encoding, wavelength channels

Workflow:

1. Select encoding dimension (d)
2. Design generation scheme (SPDC, waveguides)
3. Define manipulation operations (unitary transformations)
4. Implement detection scheme (mode projection)
5. Characterize encoding fidelity

Tools Used

• exec: Run simulation scripts, solve control equations
• read: Load reference materials, configuration files
• write: Save simulation results, controller designs
• python: Numerical computation (numpy, scipy, qutip)

Usage Patterns

Pattern 1: Design H∞ Quantum Controller

Design H∞ controller for quantum linear system with γ=0.5 attenuation

Process:

1. Parse system matrices (A, B, C, D)
2. Compute H∞ Riccati solution
3. Extract controller gains
4. Validate stability margin
5. Output controller transfer function

Pattern 2: Simulate Quantum Network

Simulate polarization-encoded quantum network with Bell-state distribution

Process:

1. Define network topology
2. Configure optical components (Jones matrices)
3. Set timing parameters (discrete events)
4. Run physics-informed simulation
5. Analyze fidelity and timing statistics

Pattern 3: Design High-Dimensional Encoding

Design 4-dimensional quantum encoding using temporal modes

Process:

1. Choose encoding scheme (time-bin)
2. Define generation parameters
3. Specify manipulation operations
4. Design detection protocol
5. Calculate information capacity

Instructions for Agents

Step 1: Identify Problem Type

Determine which quantum systems problem:

• Control: Stability, disturbance attenuation, feedback design
• Simulation: Network behavior, protocol timing, component modeling
• Encoding: State dimensionality, photonic modes, fidelity

Step 2: Gather System Parameters

For control problems:

• System matrices (A, B, C, D)
• Disturbance characteristics
• Performance requirements (γ level)

For simulation problems:

• Network topology
• Component specifications
• Timing constraints

For encoding problems:

• Target dimensionality
• Available photonic modes
• Fidelity requirements

Step 3: Apply Methodology

Execute appropriate design/analysis method:

• Solve Riccati equations for H∞ control
• Run discrete-event simulation with physics models
• Design encoding scheme with unitary transformations

Step 4: Validate Results

Check:

• Stability conditions satisfied
• Simulation timing and fidelity meet specs
• Encoding scheme achieves target dimension

Step 5: Document Output

Generate report with:

• Controller transfer function (for control)
• Simulation statistics (for simulation)
• Encoding protocol specification (for encoding)

References

H∞ Control Theory

See references/h-infinity-control.md for:

• Riccati equation derivation
• Stability conditions
• Disturbance attenuation proofs

Physics-Informed Simulation

See references/discrete-event-simulation.md for:

• Jones calculus fundamentals
• SPDC source modeling
• Component timing parameters

High-Dimensional Encoding

See references/high-dimensional-encoding.md for:

• Spatial/temporal/spectral mode theory
• Generation/manipulation/detection schemes
• Fidelity characterization methods

Examples

Example 1: H∞ Controller Design

User: "Design H∞ controller for quantum harmonic oscillator with γ=0.8"

Agent:

1. Parse oscillator model: A = [ω, 0; 0, -ω]
2. Solve H∞ Riccati: P = solve_riccati(A, B, γ)
3. Compute controller: K = -B^T P
4. Validate: ||Tzw||∞ < γ ✓
5. Output: K(s) = transfer_function(K)

Example 2: Quantum Network Simulation

User: "Simulate Bell-state distribution over 3-node quantum network"

Agent:

1. Define topology: Node_A → Fiber → Node_B
2. Configure: SPDC source, PBS, wave plates
3. Set events: Generate, transmit, detect
4. Run simulation: 10000 trials
5. Results: Fidelity = 0.92, Latency = 15μs

Related Skills

• quantum-algorithm-framework-designer: Algorithm design
• quantum-error-correction-gauge-theory: Error handling
• distributed-quantum-computing: Network architectures
• complex-valued-kuramoto-control: Oscillator control

Dependencies

pip install qutip numpy scipy matplotlib

Notes

• H∞ control requires linear system model
• Simulation accuracy depends on component models
• High-dimensional encoding limited by mode orthogonality
• Consider decoherence effects in all designs