#
# Copyright 2021 Keysight Technologies Inc.
#
"""
Simulating Leakage
==================
"""
#%%
# The simulator is capable of adding extra energy levels to allow noise models that
# include leakage. For example, if a circuit acts on qubits, so that gates are either
# 2-by-2 for single qubit gates and 4-by-4 for two-qubit gates, then one can direct the
# simulator to add an extra energy level to each qubit, so that each subsystem is
# simulated with 3 dimensions. Noise models can interact with the extra level(s).
#
# Extra leakage dimensions are added by the simulator whenever some noise source
# explicitly asks for a specific dimension. Certain noise sources, such as overrotation,
# work no matter how many extra levels are included.
import trueq as tq
import trueq.simulation as tqs
import numpy as np
import scipy.linalg as la
#%%
# Kraus Noise
# -----------
# The most versatile method of adding leakage is through Kraus operator noise with the
# :py:meth:`~trueq.Simulator.add_kraus` method. Recall that Kraus noise is specified as
# a set of operators :math:`\{K_i\}_{i=1}^m` and acts on a given density matrix as
# :math:`\rho\mapsto\sum_{i=1}^m K_i\rho K_i^\dagger`. To add leakage to a model, we
# construct Kraus operators with a dimension strictly bigger than the dimension of our
# gates, and add terms that cause population transfer into these new levels, either
# stochastically or coherently. The increased dimension must be specified using the
# ``dim`` argument of the :py:meth:`~trueq.Simulator.add_kraus` method.
#
# In the following toy example, we add Kraus operators that add no noise with 95%
# probability, but apply a random (but fixed) qutrit unitary with probability 5%.
# This induces a stochastic population transfer into the leakage level.
p = 0.05
sim = tq.Simulator()
sim.add_kraus(
[np.sqrt(1 - p) * np.eye(3), np.sqrt(p) * tq.math.random_unitary(3)], dim=3
)
circuit = tq.Circuit([{0: tq.Gate.x}])
tq.visualization.plot_mat(sim.state(circuit).mat())
#%%
# In the next example, we add a coherent leakage term to a CNOT gate with the
# transitions :math:`|00\rangle\leftrightarrow|20\rangle` and
# :math:`|10\rangle\leftrightarrow|12\rangle` that occur at different rates.
sim = tq.Simulator()
ham = np.zeros((9, 9), dtype=np.complex128)
ham[([0, 6], [6, 0])] = 0.5
ham[([3, 5], [5, 3])] = 1
ops = la.expm(-1j * 0.3 * ham)
sim.add_kraus([ops], match=tqs.GateMatch(tq.Gate.cnot), dim=3)
circuit = tq.Circuit([{0: tq.Gate.h}, {(0, 1): tq.Gate.cx}])
tq.visualization.plot_mat(sim.state(circuit).mat(), xlabels=3, ylabels=3)
#%%
# Measurement Classification
# --------------------------
# In the first example, we add asymmetric classification error to all three levels,
# where a :math:`|0\rangle` is reported as a '0' 99% of the time, a :math:`|1\rangle` is
# reported as a '1' 92% of the time, and a :math:`|2\rangle` is reported as a '2' 80% of
# the time. Off-diagonals are the probabilities of misclassification into specific
# outcomes corresponding to the row they are located in. We do this by using the
# :py:meth:`~trueq.Simulator.add_readout_error` simulator method that supports confusion
# matrix inputs.
# define a confusion matrix for a qutrit
confusion = [[0.99, 0.03, 0.02], [0.005, 0.92, 0.18], [0.005, 0.05, 0.8]]
# simulate the effects on all three basis states
circuit = tq.Circuit([{0: tq.Prep()}, {0: tq.Meas()}])
for idx, prep_state in enumerate(np.eye(3)):
sim = tq.Simulator().add_readout_error(errors={0: confusion}).add_prep(prep_state)
sim.run(circuit, n_shots=np.inf, overwrite=True)
print(f"Prepare |{idx}>:", circuit.results)
#%%
# In the next example, we simulate with a qutrit, but we only classify into bits. This
# situation arises, for example, in superconducting qubits when there is leakage into
# the third level of the anharmonic oscillator, but readout always reports a '0' or a
# '1'. We achieve this by defining a rectangular confusion matrix where
# :math:`|2\rangle` is classified as a '0' 70% of the time, and as a '1' 30% of the
# time. Additionally, :math:`|0\rangle` and :math:`|1\rangle` also have their own
# classification errors, too.
confusion = [[0.99, 0.08, 0.7], [0.01, 0.92, 0.3]]
# simulate the effects on all three basis states
circuit = tq.Circuit([{0: tq.Prep()}, {0: tq.Meas()}])
for idx, prep_state in enumerate(np.eye(3)):
sim = tq.Simulator().add_readout_error(errors={0: confusion}).add_prep(prep_state)
sim.run(circuit, n_shots=np.inf, overwrite=True)
print(f"Prepare |{idx}>:", circuit.results)
#%%
# We can see the effect that this has on a 1-qubit benchmarking experiment.
# Here, we add gate noise that stochastically populates the third level with probability
# 1% every time a gate is applied.
p = 0.01
perm02 = np.array([[0, 0, 1], [0, 1, 0], [1, 0, 0]])
perm12 = np.array([[1, 0, 0], [0, 0, 1], [0, 1, 0]])
sim.add_kraus(
[np.sqrt(1 - p) * np.eye(3), np.sqrt(p / 2) * perm02, np.sqrt(p / 2) * perm12],
dim=3,
)
circuits = tq.make_srb(0, np.linspace(4, 100, 10).astype(int))
sim.run(circuits)
circuits.plot.raw()