Indirect-Control VQE and ZNE Error Mitigation

Installation

• Python Version: 3.11
  
• To install dependencies, run:
  bash pip install -r requirements.txt

Usage

To run the program, use:
bash python3 main.py <config.yml>

Configuration Details

The program uses a YAML configuration file to define its parameters. Below is a detailed description of the configuration categories and their parameters:

| Section | Key | Type | Description | |-------------------------------------|-----------------------------------|--------------------------------------|----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| | Run Configuration | run | String | Defines the algorithm to run. Options: 'vqe', 'redundant', 'zne'. | | System Configuration | nqubits | Integer | Specifies the number of qubits in the quantum system. | | | state | String | Defines the state representation. Options: 'dmatrix' (density matrix) or 'statevector'. | | Observable (Target Hamiltonian) | def | String | Defines the type of Hamiltonian. Options: 'custom', 'ising', 'heisenberg'. Warning: Coefficients are overwritten based on the selected type. For 'ising', cn values are set to [0.5], bn values are set to [1], and r is set to 1. For 'heisenberg', only cn is used. | | | coefficients | Object | Contains coefficients for the Hamiltonian terms: | | | | cn | List of Floats | Defines the coefficients for the interaction term. Example: [0.5, 0.5, 0.5]. | | | | bn | List of Floats | Defines the coefficients for the coupling terms. Example: [1.0, 1.0, 1.0, 1.0]. | | | | r | Float | Defines the coefficient for the scaling term. Example: 1. | | Output Configuration | file_name_prefix | String | Specifies the prefix for the output file name. | | | draw | Object | Configures drawing options for output files: | | | | status | Boolean | If True, enables figure drawing. Example: False. | | | | fig_dpi | Integer | Specifies the resolution of the output figure. Example: 100. | | | | type | String | Specifies the type of output file. Example: "png". | | VQE Configuration | iteration | Integer | Specifies the number of iterations for the VQE algorithm. | | | optimization | Object | Configures optimization settings: | | | | status | Boolean | If True, enables optimization. Example: True. | | | | algorithm | String | Specifies the optimization algorithm. Options: "SLSQP". | | | | constraint | Boolean | If True, enables constraint optimization. Example: False. | | | ansatz | Object | Configures the ansatz circuit: | | | | type | String | Defines the type of the ansatz. Options: 'custom', 'xy-iss', 'ising', 'heisenberg'. Warning: Must be 'xy-iss' for ZNE redundant circuits. | | | | layer | Integer | Specifies the number of layers for the ansatz. Example: 10. | | | | gateset | Integer | Specifies the gate set used. Example: 1. | | | | ugate | Object | Defines the U gate settings: | | | | | coefficients | Object | Contains coefficients for the U gate: | | | | | cn | List of Floats | Defines the coefficients for the interaction terms in the U gate. Example: [0.5, 0.5, 0.5]. | | | | | bn | List of Floats | Defines the coefficients for the coupling terms in the U gate. Example: [0, 0, 0, 0]. | | | | | r | Float | Defines the coefficient for the scaling term in the U gate. Example: 0. | | | | | time | Object | Defines the time range for the gate: | | | | | min | Float | Minimum time. Example: 0.0. | | | | | max | Float | Maximum time. Example: 10.0. | | | | noise | Object | Defines noise parameters: | | | | | status | Boolean | If True, enables noise. Example: True. | | | | | value | List of Floats | Specifies noise probabilities for different gate types in the order [r, cz, u, y]. Example: [0.001, 0.01, 0.001, 0.01]. | | | init_param | String | Defines the initialization method for parameters. Options: 'random', etc. Example: "random". | | Redundant Circuit Configuration | identity_factors | List of Lists | Specifies the identity scaling factors for gates. Example: [[1, 0, 0, 1], [2, 3, 2, 1], ...]. | | | Warning | String | Warning: Identity scaling for the U gate is supported only if the ansatz type is 'xy-iss'. For other types, the identity scaling factor for the U gate must be set to 0. | | Zero Noise Extrapolation (ZNE) | method | String | Defines the method for zero-noise extrapolation. Options: 'linear', 'polynomial', 'richardson', 'richardson-mul'. | | | degree | Integer | Sets the degree for polynomial or Richardson methods. Used for regression. | | | sampling | String | Specifies the sampling method for extrapolation. Options: 'default', 'default-N', 'random-N', where N is an integer. | | | data_points | List of Lists | Provides the data points for extrapolation. Each entry contains several values, such as time and noise levels. Example: [[12, 1, 0, 3, -3.3480294367352315], [20, 7, 10, 3, -0.05316450776222178], ...]. |

Warnings and Important Notes

1. Observable (Target Hamiltonian) Coefficients Overwritten:

   • For the ising Hamiltonian (observable.def: "ising"), the coefficients are automatically overwritten as follows:
     • cn: [0.5]
     • bn: [1.0]
     • r: 1
   • For the heisenberg Hamiltonian (observable.def: "heisenberg"), only the cn coefficient is used, and bn and r are ignored.

2. Ansatz Type for Zero Noise Extrapolation (ZNE):

   • When using Zero Noise Extrapolation (ZNE) with redundant circuits, the ansatz type must be set to 'xy-iss' (vqe.ansatz.type: "xy-iss"). This is required for identity-scaling the circuit gates (U, Y, and CZ).
   • Warning: The identity-scaling for the U gate is only supported if the ansatz type is 'xy_model-xz-z'. For other ansatz types, the identity scaling for the U gate must be set to 0.

3. VQE Ansatz Coefficients Overwritten:

   • When using the VQE algorithm with certain ansatz types ('xy-iss'), the coefficients are automatically overwritten as follows:
     • cn: [0.5]
     • bn: [0]
     • r: 0
   • For ansatz types such as 'ising' or 'heisenberg', the coefficients are predefined according to the selected type.

4. Initialization of Parameters:

   • The initial parameters for the ansatz are set to random by default (vqe.ansatz.init_param: "random"). If you need to modify the initialization method, ensure to update this value accordingly.

5. Sampling Method for Zero Noise Extrapolation:

   • The sampling method should be selected appropriately:
     • 'default' - All points are sampled.
     • 'default-N' - The first N points are sampled.
     • 'random-N' - N points are sampled randomly.
   • Ensure that the method aligns with the desired sampling strategy for extrapolation.

Testing

For testing, use pytest.
To run the tests, execute:
bash pytest test/.

Linting and Formatting

• Use flake8 for linting.
  
• Use black and isort for formatting the code.
  ```bash # Run linting flake8 .

# Run formatting black . isort . ```