Monte Carlo simulations of noisy Clifford circuits

Import with using QuantumClifford.Experimental.NoisyCircuits.

This module enables the simulation of noisy Clifford circuits through a Monte Carlo method where the same circuit is evaluated multiple times with random errors interspersed through it as prescribed by a given error model.

Below is an example of a purification circuit. We first prepare the circuit we desire to use, including a noise model. Quantikz.jl was is used to visualize the circuit.

good_bell_state = S"XX
                    ZZ"
initial_state = MixedDestabilizer(good_bell_state⊗good_bell_state)

g1 = sCNOT(1,3) # CNOT between qubit 1 and qubit 3 (both with Alice)
g2 = sCNOT(2,4) # CNOT between qubit 2 and qubit 4 (both with Bob)
m = BellMeasurement([sMX(3),sMX(4)]) # Bell measurement on qubit 3 and 4
v = VerifyOp(good_bell_state,[1,2]) # Verify that qubit 1 and 2 indeed form a good Bell pair
epsilon = 0.01 # The error rate
n = NoiseOpAll(UnbiasedUncorrelatedNoise(epsilon))

# This circuit performs a depolarization at rate `epsilon` to all qubits,
# then bilater CNOT operations
# then a Bell measurement
# followed by checking whether the final result indeed corresponds to the correct Bell pair.
circuit = [n,g1,g2,m,v]

And we can run a Monte Carlo simulation of that circuit with mctrajectories.

mctrajectories(initial_state, circuit, trajectories=500)

Dict{CircuitStatus, Float64} with 4 entries:
  continue:CircuitStatus(0)      => 0.0
  true_success:CircuitStatus(1)  => 487.0
  false_success:CircuitStatus(2) => 9.0
  failure:CircuitStatus(3)       => 4.0

For more examples, see the notebook comparing the Monte Carlo and Perturbative method or this tutorial on entanglement purification for many examples.

Interface for custom operations

If you want to create a custom gate type (e.g. calling it Operation), you need to definite the following methods.

applywstatus!(s::T, g::Operation)::Tuple{T,Symbol} where T is a tableaux type like Stabilizer or a Register. The Symbol is the status of the operation. Predefined statuses are kept in the registered_statuses list, but you can add more. Be sure to expand this list if you want the trajectory simulators using your custom statuses to output all trajectories.

There is also applynoise! which is convenient wait to create a noise model that can then be plugged into the NoisyGate struct, letting you reuse the predefined perfect gates and measurements. However, you can also just make up your own noise operator simply by implementing applywstatus! for it.

You can also consult the list of implemented operators.