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Single qubit: phase estimation

This example shows a one-qubit interference experiment.

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.circuit import Circuit
from squint.ops.dv import DiscreteVariableState, HGate, RZGate
from squint.utils import partition_op

circuit = Circuit()

#          ____      ___________      ____
# |0> --- | H | --- | Rz(\phi) | --- | H | ----
#         ----      -----------      ----

circuit.add(DiscreteVariableState(wires=(0,), n=(0,)))
circuit.add(HGate(wires=(0,)))
circuit.add(RZGate(wires=(0,), phi=0.0 * jnp.pi), "phase")
circuit.add(HGate(wires=(0,)))

pprint(circuit)

Circuit(
  dims=None,
  ops={
│   0:
│   DiscreteVariableState(wires=(0,), n=[(1.0, (0,))]),
│   1:
│   HGate(wires=(0,)),
│   'phase':
│   RZGate(wires=(0,), phi=weak_f64[]),
│   3:
│   HGate(wires=(0,))
  },
  _backend=None
)

params, static = partition_op(circuit, "phase")
sim = circuit.compile(static, 2, params, optimize="greedy")

ket = sim.amplitudes.forward(params)
dket = sim.amplitudes.grad(params)
prob = sim.probabilities.forward(params)
dprob = sim.probabilities.grad(params)

print(f"Shape of ket is: {ket.shape}, with dtype {ket.dtype}")
print(f"Shape of prob is: {prob.shape}, with dtype {prob.dtype}")

Shape of ket is: (2,), with dtype complex128
Shape of prob is: (2,), with dtype float64

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

probs = jax.vmap(sim.probabilities.forward)(params)
qfims = jax.vmap(sim.amplitudes.qfim)(params)
cfims = jax.vmap(sim.probabilities.cfim)(params)

colors = sns.color_palette("Set2", n_colors=jnp.prod(jnp.array(probs.shape[1:])))
fig, axs = uplt.subplots(nrows=2, 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[0].legend()
axs[0].set(xlabel=r"Phase, $\varphi$", ylabel=r"Probability, $p(\mathbf{x} | \varphi)$")

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

img