Getting the wavefunction of a qumode of a two-qumode system

Photonic Software Strawberry Fields
1

A circuit to displace a wavefunction \psi(x) = \langle x | \psi \rangle using its quantum state |\psi\rangle which for illustration I will take to be the ground state |0\rangle (i.e. my wavefunction is just the ground state wavefunction of the Harmonic oscillator) could be constructed as follows. (I take the state to be qumode \texttt{q[1]})

prog = sf.Program(2)
with prog.context as q:
    Fock(0) | q[0] #auxillary qumode set up
    Fock(0) | q[1] #state of the system
    CXgate(2) | (q[0],q[1])
    MeasureHomodyne(phi=0,select=1) | q[0]

This displaces \psi(x) \to \psi(x-2). Suppose that I want to plot the PMF |\langle x |\psi\rangle|^2 = |\psi(x)|^2 of the system, after I’ve done this operation. One way to do this is to put the above circuit in a loop and then act with \texttt{MeasureX} on \texttt{q[1]}. From the histogram one can obtain the normalized pmf easily. However, one needs a large sample size and hence a large loop.

num_samples = 10000
samples = []

for _ in range(num_samples):
    prog = sf.Program(2)
    with prog.context as q:
        Fock(0) | q[0] #auxillary qumode set up
        Fock(0) | q[1] #state of the system
        CXgate(2) | (q[0],q[1])
        MeasureHomodyne(phi=0,select=1) | q[0]
        MeasureX | q[1]
    
    eng = sf.Engine("fock", backend_options={"cutoff_dim":some_cutoff})
    result = eng.run(prog)
    state = result.samples[0][1]
    samples.append(state)

Is there a built in functionality for a two-qumode system that will extract the Fock modes of a qumode after a homodyne measurement has been done on its partner? I would want to obtain the Fock expansion of \texttt{q[1]} after I have performed the homodyne measurement on \texttt{q[0]} at y = 0 so that I can feed it into another circuit. Thanks. Sorry if this is trivial I am new to \texttt{StrawberryFields}.

2

Hi @tenebr1s ,

Thanks for your question. I’ll forward it to one of my colleagues. We’ll get back to you soon.

3

Hi @tenebr1s ,

I heard back from my colleagues.

Instead of measuring the second mode, leave it unmeasured. Then the program will return a state, and you can call the ket method of the state to get back the probability amplitudes in the Fock basis (see ket in the docs).

I hope this helps!