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\(XX\) all-to-all Ising interactions

import itertools

import equinox as eqx
import jax
import jax.numpy as jnp
import seaborn as sns
import ultraplot as uplt
from rich.pretty import pprint

from squint import Circuit
from squint.interface.base import SharedGate, Wire
from squint.interface.dv import DiscreteVariableState, HGate, RXXGate, RZGate
from squint.backends.tensornetwork.simulator import Simulator
from squint.math.information_matrices import quantum_fisher_information_matrix, classical_fisher_information_matrix
from squint.utils import partition_op
from squint.visualize import draw

dim = 2
n = 4
wires = [Wire(dim=dim, idx=i) for i in range(n)]

circuit = Circuit()

for w in wires:
    circuit.add(DiscreteVariableState(wires=(w,), n=(0,)))

for i, j in itertools.combinations(list(range(n)), 2):
    circuit.add(RXXGate(wires=(wires[i], wires[j]), angle=jnp.pi / 4))

circuit.add(
    SharedGate(op=RZGate(wires=(wires[0],), phi=0.1 * jnp.pi), wires=tuple(wires[1:])),
    "phase",
)

for w in wires:
    circuit.add(HGate(wires=(w,)))

pprint(circuit)

fig = draw(circuit)

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params, static = partition_op(circuit, "phase")
sim = Simulator(static=static, params=params).jit()

def forward_probs(p):
    return jnp.abs(sim.forward(p)) ** 2

grad_probs = jax.jacfwd(forward_probs)

prob = forward_probs(params)
dprob = grad_probs(params)
cfi = classical_fisher_information_matrix(forward_probs, grad_probs, params).squeeze()

print(f"CFI is {cfi}")

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CFI is 15.999999999948939

phis = jnp.linspace(-jnp.pi, jnp.pi, 100)
params = eqx.tree_at(lambda pytree: pytree.ops["phase"].op.phi, params, phis)

probs = jax.vmap(forward_probs)(params)
grads = jax.vmap(grad_probs)(params).ops["phase"].op.phi
qfims = jax.vmap(lambda p: quantum_fisher_information_matrix(sim.forward, sim.grad, p))(params)
cfims = jax.vmap(lambda p: classical_fisher_information_matrix(forward_probs, grad_probs, p))(params)

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colors = sns.color_palette("Set2", n_colors=jnp.prod(jnp.array(probs.shape[1:])))
fig, axs = uplt.subplots(nrows=3, figsize=(6, 4), sharey=False)

for i, idx in enumerate(
    itertools.product(*[list(range(ell)) for ell in probs.shape[1:]])
):
    axs[0].plot(phis, probs[:, *idx], label=f"{idx}", color=colors[i])

    axs[1].plot(phis, grads[:, *idx], label=f"{idx}", color=colors[i])

axs[0].set(ylabel=r"$p(\mathbf{x} | \varphi)$")
axs[1].set(ylabel=r"$\partial_{\varphi} p(\mathbf{x} | \varphi)$")

axs[2].plot(phis, qfims.squeeze(), color=colors[0], label=r"$\mathcal{I}_\varphi^Q$")
axs[2].plot(phis, cfims.squeeze(), color=colors[-1], label=r"$\mathcal{I}_\varphi^C$")
axs[2].set(
    xlabel=r"Phase, $\varphi$",
    ylabel=r"$\mathcal{I}_\varphi^C$",
    ylim=[0, 1.05 * jnp.max(qfims)],
)
axs[2].legend();

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