Add lattice gauge theory compilation test (#933)

* Add lattice gauge theory compilation test

* remove unused imports:

* run black

---------

Co-authored-by: Phillip Weinberg <[email protected]>

tests/test_lattice_gauge_theory_compile.py

@@ -0,0 +1,52 @@
+from bloqade import cast, piecewise_linear
+from bloqade.ir.location import Chain
+
+import numpy as np
+
+
+def test_lattice_gauge_theory_compile():
+    N_atom = 13
+
+    detuning_ratio = [0] * N_atom
+    detuning_ratio[1 : (N_atom - 1) : 2] = [1, 1, 1, 1, 1, 1]
+    detuning_ratio[(N_atom - 1) // 2] = 1
+
+    run_time = cast("run_time")
+
+    rabi_amplitude_wf = piecewise_linear(
+        durations=[0.1, 2.0, 0.05, run_time, 0.05],
+        values=[0, 5 * np.pi, 5 * np.pi, 4 * np.pi, 4 * np.pi, 0],
+    )
+    uniform_detuning_wf = piecewise_linear(
+        durations=[2.1, 0.05, run_time + 0.05], values=[-6 * np.pi, 8 * np.pi, 0, 0]
+    )
+    local_detuning_wf = piecewise_linear(
+        [0.1, 2.0, 0.05, run_time + 0.05],
+        values=[0, -8 * 2 * np.pi, -8 * 2 * np.pi, 0, 0],
+    )
+
+    program = (
+        Chain(N_atom, lattice_spacing=5.5, vertical_chain=True)
+        .rydberg.rabi.amplitude.uniform.apply(rabi_amplitude_wf)
+        .detuning.uniform.apply(uniform_detuning_wf)
+        .scale(detuning_ratio)
+        .apply(local_detuning_wf)
+    )
+
+    run_times = np.arange(0.0, 1.05, 0.05)
+    batch = program.batch_assign(run_time=run_times)
+
+    bloqade_emu_target = batch.bloqade.python()
+    braket_emu_target = batch.braket.local_emulator()
+    quera_aquila_target = batch.parallelize(15).quera.aquila()
+    braket_aquila_target = batch.parallelize(15).braket.aquila()
+
+    targets = [
+        bloqade_emu_target,
+        braket_emu_target,
+        quera_aquila_target,
+        braket_aquila_target,
+    ]
+
+    for target in targets:
+        target._compile(10)