Analog Evolution

The AnalogEvolution functional simulates analog evolution of a quantum system under one or more Hamiltonians, following a specified time-dependent schedule. Its parameter interface mirrors that of Schedule, making it straightforward to sweep control waveforms or pulse amplitudes from classical optimizers.

Observables and shot counts are specified separately via readout objects passed to execute().

Parameters

schedule (Schedule): Defines total evolution time, time steps, Hamiltonians, and their time-dependent coefficients.
initial_state (QTensor): Initial state of the system.
store_intermediate_results (bool, optional): If True, records the state at each time step. Default is False.

Returns

FunctionalResult: Inspect get_expectation_values() for measured observables, get_state() for the closing state, and get_intermediate_states() and get_intermediate_expectation_values() when store_intermediate_results is enabled.

Usage Example

import numpy as np
from qilisdk.analog import Schedule, X, Z, Y
from qilisdk.core import QTensor
from qilisdk.core.interpolator import Interpolation
from qilisdk.backends import QiliSim, CudaBackend
from qilisdk.functionals import AnalogEvolution

# Define total time and timestep
T = 10.0
dt = 0.5
nqubits = 1

# Define Hamiltonians
Hx = -sum(X(i) for i in range(nqubits))
Hz = sum(Z(i) for i in range(nqubits))

# Create the AnalogEvolution functional
analog_evolution = AnalogEvolution(
    schedule=Schedule.linear(Hx, Hz, total_time=T, dt=dt),
    initial_state=QTensor.uniform(nqubits),
    store_intermediate_results=False,
)

we can execute it on the QiliSim backend:

from qilisdk.readout import Readout

# Execute on QiliSim backend and inspect results
backend = QiliSim()
results = backend.execute(
    analog_evolution,
    Readout().with_expectation(observables=[Z(0), X(0), Y(0)]),
)
print(results)

Output

- Functional Results: [

Expectation Value Results: (
    expectation_values=[-0.99388223, 0.0467696, -0.10005353],
)

]