Understand Boulder Opal fundamentals for quantum theorists

Boulder Opal provides theorists with a powerful, flexible environment for simulating quantum systems and designing robust control solutions. The core of Boulder Opal's approach is the use of computational graphs to represent quantum systems, control signals, noise, and cost functions. This article outlines the essential workflow for theorists to begin simulating quantum dynamics and performing robust control optimizations using these functional graphs. The workflows and tools are built to support most qubit types by encoding Hamiltonian and parameter values into those functional graph nodes for maximum flexibility.

1. Understand computational graphs in Boulder Opal

Many computations in Boulder Opal are represented as graphs. A graph encodes the mathematical structure of your quantum system, including time-dependent Hamiltonians, control signals, noise models, and cost functions. This structure enables efficient simulation and optimization, including automatic differentiation for gradient-based methods.

• Graph construction: Start by initializing a Graph object. This object will contain all nodes (signals, operators, cost functions) relevant to your simulation or optimization task.
• Signals: Define time-dependent control pulses as signals (scalar-valued functions over time), typically using piecewise-constant (PWC) or analytical forms.
• Operators: Construct operators by modulating constant matrices (such as, Pauli matrices) with your signals. Combine these into a full Hamiltonian.
• Dynamics: Add nodes to compute system dynamics and other quantities of interest, such as gate infidelity or target state population. These can serve as the cost function to minimize in an optimization.

For a step-by-step guide, read our guide on how to represent quantum systems using graphs.

2. Simulate quantum dynamics

Boulder Opal supports simulation of both closed and open quantum systems, including the effects of noise and decoherence. This allows you to find the appropriate situation structure that matches your system requirements and dependencies.

• Closed system simulation: Use the graph to define your Hamiltonian and initial state, then simulate time evolution. These calculations isolate the quantum dynamics to see how they evolve over time, unaffected by external variables.
• Open system simulation: Incorporate Lindblad terms to model decoherence and dissipation, enabling simulation of realistic noisy environments.
• Noise models: Add noise sources (for example, dephasing, amplitude noise) directly into the graph for more realistic simulations.

Explore the following guides for practical examples:

• How to simulate open system dynamics
• How to simulate quantum dynamics subject to noise
• For additional resources, view our documentation on simulating quantum systems

3. Achieve robust control optimization

After simulating quantum systems over time, you may wish to identify the optimal input parameters to evaluate the performance potential of the system. Robust control optimization in Boulder Opal is achieved by defining a cost function that captures both the fidelity of the operation and its resilience to noise or parameter variations.

• Model-based optimization: Express your system and cost function in the graph, then use gradient-based optimizers to minimize the cost.
• Robustness to noise: Include noise models or error terms in the cost function to ensure the resulting controls are robust to imperfections.
• Optimization functions:
  • Use run_optimization for gradient-based optimization.
  • For strong noise sources, use run_stochastic_optimization.
  • If gradients are costly or unavailable, use run_gradient_free_optimization

For more details, see:

• How to optimize controls in arbitrary quantum systems using graphs
• How to optimize controls robust to strong noise sources
• For additional resources, view our documentation on designing model-based controls

Example theorist workflow

Theorists can bring these capabilities together to accelerate their computational work evaluating quantum systems. Use an iterative approach with the below steps to facilitate your quantum research.

1. Define the graph: Create signals, operators, and the Hamiltonian.
2. Add cost function: Define infidelity or another metric as a node in the graph.
3. Simulate or optimize:
   • For simulation, evolve the system and extract observables.
   • For optimization,
     • Define infidelity or another metric as a node (cost function) in the graph.
     • Minimize that cost function using the appropriate optimizer.
4. Analyze results: Use Boulder Opal's visualization tools to interpret the optimized controls or simulated dynamics.

Additional resources for theorists

• Get familiar with graphs
• Compare control-design optimization strategies in Boulder Opal
• Design robust single-qubit gates using computational graphs

Review qubit modality specifics for more information related to your specific system:

• Superconducting qubits
• Trapped ions
• Rydberg atoms
• Spin qubits
• Sensing

By leveraging Boulder Opal's graph-based approach, theorists can efficiently model, simulate, and optimize quantum systems, enabling rapid exploration of robust control strategies and quantum dynamics without being limited by hardware or API setup details.