Support the graph visualization for Gaussian pure states

[Hugh-888]

• Implementing a unified graphical calculus for Gaussian pure states based on the paper "Graphical calculus for Gaussian pure states" (Menicucci et al., 2011). It allows representing any Gaussian pure state as an undirected graph with complex-weighted edges (Z=V+iU), where:

  • V (Real part): Represents the entanglement structure (equivalent to Cz interaction strengths).
  • U (Imaginary part): Represents the squeezing properties of the state.

• Code example

nmode = 4
cir = dq.QumodeCircuit(nmode, init_state='vac', backend='gaussian')
for i in range(nmode):
    cir.s(i, 1)
for i in range(nmode-1):
    cir.cz([i, i+1], [np.pi/3, np.pi/3])
re = cir()
cir.draw()

s = dq.GaussianState(re)
test = s.graph()

nmode = 4
cir = dq.QumodeCircuit(nmode, init_state='vac', backend='gaussian')
for i in range(nmode):
    cir.s(i, 1)

for i in range(nmode-1):
    cir.bs([i, i+1], [np.pi/3, np.pi/3])

for i in range(1, nmode):
    cir.bs([nmode-i, nmode-i-1], [np.pi/3, np.pi/3])
re = cir()
cir.draw()

s = dq.GaussianState(re)
test = s.graph(mode='simplified')

s = dq.GaussianState(re)
test = s.graph(mode='full')

[sansiro77]

LGTM