examples: add an second generation repeater

The idealized quantum repeater from https://arxiv.org/pdf/0809.3629.pdf
is modelled with three repeater stations.

fixes: tqsd#91

examples/repeater/swap_and_distil.py

@@ -0,0 +1,102 @@
+from dataclasses import dataclass
+
+from qunetsim.components import Host
+from qunetsim.objects import Logger, Qubit
+from qunetsim.components import Network
+
+Logger.DISABLED = True
+
+
+@dataclass()
+class Ebit:
+    val: tuple[int, int]
+
+    def __str__(self):
+        return {
+            (0, 0): "phi+",
+            (0, 1): "psi+",
+            (1, 0): "phi-",
+            (1, 1): "psi-",
+        }[self.val]
+
+    @staticmethod
+    def from_bell_measurement(a: Qubit, b: Qubit):
+        a.cnot(b)
+        a.H()
+        return Ebit((a.measure(), b.measure()))
+
+
+def epr(left, right):
+    a = Qubit(left)
+    b = Qubit(right)
+
+    a.H()
+    a.cnot(b)
+    left.send_qubit(right.host_id, b)
+    b = right.get_qubit(left.host_id, wait=-1)
+
+    return a, b
+
+
+def main():
+    network = Network.get_instance()
+    nodes = ["Alice", "Polly", "Bob"]
+
+    network.start(nodes)
+    network.delay = 0.1
+
+    alice = Host("Alice")
+    alice.add_connection("Polly")
+    alice.start()
+
+    bob = Host("Bob")
+    bob.add_connection("Polly")
+    bob.start()
+
+    polly = Host("Polly")
+    polly.add_connection("Alice")
+    polly.add_connection("Bob")
+    polly.start()
+
+    network.add_host(alice)
+    network.add_host(polly)
+    network.add_host(bob)
+    network.start()
+
+    alices = []
+    bobs = []
+    for _ in range(10):
+        # Swap: Build eprs, Polly measures, Polly broadcasts results.
+        a, p1 = epr(alice, polly)
+        p2, b = epr(polly, bob)
+        ebit = Ebit.from_bell_measurement(p1, p2)
+        polly.send_broadcast(str(ebit))
+
+        # Apply local ops to transform |ab> into |Φ+> (modulo phase).
+        m = alice.get_next_classical(polly.host_id)
+        if m.content == 'psi-':
+            a.Y()
+
+        m = bob.get_next_classical(polly.host_id)
+        if m.content == 'psi+':
+            b.X()
+        elif m.content == 'phi-':
+            b.Z()
+
+        alices.append(a)
+        bobs.append(b)
+
+    # Check that we're establishing |Φ+>
+    for i in range(len(alices)):
+        a = alices[i].measure()
+        b = bobs[i].measure()
+        if a == b:
+            print(f"qubit pair {i} were probably Φ+!")
+        else:
+            print(f"qubit pair {i} were probably not Φ+!")
+
+    network.stop(True)
+
+
+if __name__ == "__main__":
+    main()