# Writing Custom Noise Sources¶

This example will demonstrate how to write a custom noise source for the simulator. See also this guide for more general information.

import numpy as np
import trueq as tq
import trueq.simulation as tqs


A custom noise source can be implemented by subclassing NoiseSource and overriding its apply() method.

The apply() method will be passed three arguments: cycle_wrapper, state, and circuit_cache. The job of apply is to mutate state based on the contents of cycle_wrapper. The state refers to “the state of simulation” and can either be a StateTensor (which can store either a pure state or a mixed state), or a OperatorTensor (which can store either a unitary or a superoperator). Each of these four possibilities share the method apply_matrix() which can always accept a unitary or superoperator as input, and for example upgrades pure states to mixed states when necessary, and so the distinction between these various types of states becomes irrelevant to the implementation of a noise source.

Note that cycle_wrapper is not a Cycle instance as one might expect, but instead a thin wrapper called CycleWrapper which in turn wraps each cycle operation as OpWrapper.

These wrapper types are required to store metadata on each operation (also discussed further below). However, noise sources will rarely need to deal with these wrapper objects directly. This is because noise sources (by strongly encouraged convention, though not by contract) own a Match instance which takes ownership of the mechanics of these wrappers. This is seen in the example below, where the iter_gates method is used to yield gate objects with their corresponding gate labels.

# predefine noise matrices to be applied to qubits following ideal gates
# note that rowstack_subsys is the superoperator convention required by the simulator
p = 0.01
s = tq.math.Superop.from_kraus([np.sqrt(1 - p) * np.eye(2), np.sqrt(p) * tq.Gate.x.mat])
s1 = s.rowstack_subsys()

p = 0.02
s = tq.math.Superop.from_kraus(
[np.sqrt(1 - p) * np.eye(4), np.sqrt(p) * tq.math.random_unitary(4)]
)
s2 = s.rowstack_subsys()

class ExampleNoise(tqs.NoiseSource):
def __init__(self, match=None):
# this simulator hardcodes the subsystem dimension to 2
super().__init__(dim=2, match=match)

def make_circuit_cache(self, circuit):
# this return will be made available to apply() as circuit_cache for every
# cycle in the circuit
return set(circuit.labels)

def apply(self, cycle_wrapper, state, circuit_cache):
# in this method we need to mutate state by inspecting cycle_wrapper

used_labels = set()
# loop through the gates in the cycle and mutate the state
# note that we must set noise_only=False since we are simulating each gate
for labels, gate in self.match.iter_gates(cycle_wrapper, noise_only=False):
used_labels.update(labels)
# first do ideal simulation of this gate
state.apply_matrix(labels, gate.mat)

# now add some noise to each qubit the gate acts on
if len(labels) == 1:
state.apply_matrix(labels, s1)
elif len(labels) == 2:
state.apply_matrix(labels, s2)

# apply a 20 degree Z rotation to every qubit without a gate in this cycle
for label in circuit_cache.difference(used_labels):
state.apply_matrix((label,), tq.Gate.rp("Z", 20))


Now we can instantiate a simulator that uses this noise source and do any simulator calculation. Here, we use the simulator to predict the output of a hypothetical KNR experiment.

sim = tq.Simulator().append_noise_source(ExampleNoise())

cycle = {(0, 1): tq.Gate.cnot, 2: tq.Gate.x}
fit = sim.predict_knr(cycle, twirl=tq.Twirl("P", range(5)))
fit.plot.knr_heatmap()


## Caching¶

There are two distinct caches available to a noise source. The first is a private noise source attribute that is called _cache (by convention, not by contract) in built-in noise models which persists throughout the lifetime of the noise source. For example, a gate-dependent noise model may consider caching gate noise if it is expensive to recompute everytime the same gate is encountered.

The second cache comes as the third argument to the apply method. This cache is instantiated by make_circuit_cache() just before a new circuit is simulated and is presented as the third argument to the apply method for every cycle within that circuit. It typically stores information about the circuit that is not available in every cycle, such as all of the labels the circuit acts on, or which measurements it performs at the end.

The variable cycle_wrapper in the example above has type CycleWrapper which is a thin wrapper for a cycle and also wraps every cycle operation with OpWrapper. During simulation, everytime a new cycle is encountered it is wrapped once, and the same wrapped cycle instance is passed to all noise sources. The cycle wrapper exists to enable efficient looping logic used by Match and to persist operation wrappers for multiple noise sources. The operation wrapper exists to store two important pieces of information:
1. Whether some noise source has previously simulated the same operation of the cycle. This is stored as a boolean called has_been_simulated and is set to true whenever a match method is called with the argument noise_only=False, as it is in the above example.
2. Whether no noise sources (except the ideal final simulation if relevant) should touch the operation again. This is stored as a boolean called no_more_noise and is set to true whenever it is yielded by a match method whose exclusive value is true.