examples: add a second generation repeater

The quantum repeater from https://arxiv.org/pdf/0809.3629.pdf with
repetition code is modelled.

fixes: tqsd#91

examples/repeater/second_gen_with_repetition_code.py

@@ -0,0 +1,323 @@
+from dataclasses import dataclass
+from statistics import mode
+
+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()
+        x = a.measure()
+        y = b.measure()
+        return Ebit((x, y))
+
+
+def send_epr(host, peer):
+    a, b = Qubit(host), Qubit(host)
+    a.H()
+    a.cnot(b)
+    host.send_qubit(peer.host_id, b)
+    return a
+
+
+@dataclass(init=False)
+class RepetitionCodedQubit:
+    physical: list[Qubit]
+    code_length: int
+
+    def __init__(self, h: Host, code_length: int = 3):
+        self.code_length = code_length
+        self.physical = [Qubit(h) for _ in range(code_length)]
+
+    def __getitem__(self, index):
+        return self.physical[index]
+
+    def H(self):  # this maps ⌈|0>⌋ to ⌈|+>⌋
+        self.physical[0].H()
+        for k in range(1, self.code_length):
+            self.physical[0].cnot(self.physical[k])
+
+
+# This circuit is from https://arxiv.org/pdf/quant-ph/0002039.pdf, page 9. It
+# lets two peers perform a remote CNOT using a single EPR pair.
+@dataclass()
+class RemoteCNOT:
+    """
+    RemoteCNOT teleports qubits, |alpha> and |beta>, through an EPR pair
+    composed of |red> and |blue>. The result of the protocol is that
+        |red>  = |alpha>
+        |blue> = |beta ⊕ alpha>
+    """
+    left: Host
+    right: Host
+
+    def left_protocol(self, alpha: Qubit, red: Qubit):
+        red.cnot(alpha)
+        x = alpha.measure()
+        if x == 1:
+            red.X()
+        self.left.send_classical(self.right.host_id, str(x), await_ack=True)
+
+        z = self.left.get_next_classical(self.right.host_id, wait=-1).content
+        if z == '1':
+            red.Z()
+
+    def right_protocol(self, blue: Qubit, beta: Qubit):
+        beta.cnot(blue)
+        beta.H()
+
+        x = self.right.get_next_classical(self.left.host_id, wait=-1).content
+        if x == '1':
+            blue.X()
+
+        z = beta.measure()
+        self.right.send_classical(self.left.host_id, str(z), await_ack=True)
+        if z == 1:
+            blue.Z()
+
+
+@dataclass(init=False)
+class EncodedGenerationProtocol:
+    """
+    EncodedGenerationProtocol establishes an encoded Φ^+ between left and right
+    hosts. This is done as follows.
+
+    1. locally prepare encoded states ⌈|+>⌋ and ⌈|0>⌋
+
+    For each each physical qubit:
+
+    2. left creates an EPR pair
+    3. left distributes half of the EPR pair to right
+    4. peers use the EPR pair to perform a transverse teleportation-based CNOT
+    """
+    left: Host
+    right: Host
+    remote_cnot: RemoteCNOT
+    code_length: int
+
+    def __init__(self, left, right, code_length=3):
+        self.left = left
+        self.right = right
+        self.remote_cnot = RemoteCNOT(left, right)
+        self.code_length = code_length
+
+    def left_protocol(self, left: Host, n: int):
+        logical = RepetitionCodedQubit(self.left, self.code_length)
+        logical.H()
+
+        for k, physical in enumerate(logical):
+            epr = send_epr(self.left, self.right)
+            self.remote_cnot.left_protocol(physical, epr)
+            self.left.add_qubit(self.left.host_id, epr, f"{n}>{k}")
+
+    def right_protocol(self, right: Host, n: int):
+        # prepare an encoded |0>
+        logical = RepetitionCodedQubit(right, self.code_length)
+
+        out = []
+        for k, physical in enumerate(logical):
+            epr = self.right.get_qubit(self.left.host_id, wait=-1)
+            self.remote_cnot.right_protocol(epr, physical)
+            right.add_qubit(right.host_id, epr, f"{n}<{k}")
+            out.append(epr)
+
+
+def encoded_connection(host: Host, left: Host, right: Host, logical_qubit: int,
+                       code_length: int = 3):
+    """
+    Perform transverse measurements of the code block for logical_qubit in the
+    Bell basis.
+
+    The logical measurement result is the mode of the physical measurement
+    results.
+
+    The logical measurement result is sent to the repeater's neighbours, hosts
+    `left` and `right`.
+    """
+    ms = []
+    for k in range(code_length):
+        p = host.get_qubit_by_id(f"{logical_qubit}>{k}")
+        q = host.get_qubit_by_id(f"{logical_qubit}<{k}")
+        ms.append(str(Ebit.from_bell_measurement(p, q)))
+    host.send_classical(left.host_id, mode(ms), await_ack=True)
+    host.send_classical(right.host_id, mode(ms), await_ack=True)
+
+
+def pauli_frame_left(host: Host, right: Host, n: int, code_length: int = 3):
+    msg = host.get_next_classical(right.host_id, wait=-1).content
+    for k in range(code_length):
+        q = host.get_qubit_by_id(f"{n}>{k}")
+        if msg == 'psi+':
+            q.X()
+        elif msg == 'phi-':
+            q.Z()
+
+
+def pauli_frame_right(host: Host, left: Host, logical_qubit: int,
+                      code_length: int = 3):
+    msg = host.get_next_classical(left.host_id, wait=-1).content
+    for k in range(code_length):
+        q = host.get_qubit_by_id(f"{logical_qubit}<{k}")
+        if msg == 'psi-':
+            q.Y()
+
+
+def pretty_print_logical_qubit(h, n, code_length, left_side=True):
+    if n > 0:
+        print('|', end='')
+    for k in range(code_length):
+        if left_side:
+            p = h.get_qubit_by_id(f"{n}>{k}")
+        else:
+            p = h.get_qubit_by_id(f"{n}<{k}")
+        print(f"{p.measure()}", end='')
+
+
+def check_correlations(hosts: list[Host], logical_qubits: int,
+                       code_length: int = 3):
+    print("Checking correlations")
+    print("Alice: ", end='')
+    for n in range(logical_qubits):
+        pretty_print_logical_qubit(hosts[0], n, code_length)
+    print()
+    print("Bob:   ", end='')
+    for n in range(logical_qubits):
+        pretty_print_logical_qubit(hosts[-1], n, code_length, left_side=False)
+    print()
+
+
+@dataclass(init=False)
+class LinearRelayNetwork:
+    """
+    LinearRelaynetwork creates a line topology where boundary nodes, Alice and
+    Bob, are separated by repeaters-many repeater nodes.
+
+    The method `run_with_repetition_code` will establish an encoded Φ^+ between
+    Alice and Bob in three steps.
+
+    1. Encoded generation. An encoded Φ^+ is established between neighbours in
+    three steps:
+    1.1. memory qubits are prepared in encoded states |+> and |0> at
+         neighbouring stations.
+    1.2. a physical Bell pair is generated and shared for each physical qubit
+         in the code block
+    1.3. the prepared memory qubits are teleported through remote CNOT gates to
+         create an encoded |00> + |11>
+
+    2. Encoded Connection. A transverse Bell basis measurement is performed at
+    each repeater node. The measurement result is sent to the appropriate
+    neighbours.
+
+    3. Pauli Frame Correction. A local gate is applied transversely to account
+    for the measurement outcome and create an encoded Φ+ between non-
+    neighbouring peers.
+    """
+    network: Network
+    hosts: list[Host]
+
+    def __init__(self, repeaters, delay=0.1, x_error_rate=0.3):
+        self.network = Network.get_instance()
+        peers = ["Alice"] + [f"Polly_{k}" for k in range(repeaters)] + ["Bob"]
+        self.network.delay = delay
+        self.network.x_error_rate = x_error_rate
+
+        hosts = list(map(lambda x: Host(x), peers))
+        self.hosts = hosts
+
+        for k in range(len(peers)-1):
+            hosts[k].add_connection(hosts[k+1].host_id)
+            hosts[k+1].add_connection(hosts[k].host_id)
+
+        for host in hosts:
+            self.network.add_host(host)
+            host.start()
+
+        self.network.start(nodes=peers)
+
+    def __len__(self):
+        return len(self.hosts)
+
+    def __getitem__(self, i):
+        return self.hosts[i]
+
+    def __enter__(self):
+        return self
+
+    def __exit__(self, *args):
+        self.network.stop()
+
+    @property
+    def num_repeaters(self):
+        return len(self.hosts) - 2
+
+    def run_with_repetition_code(self, logical_qubits: int = 3,
+                                 code_length: int = 3):
+        print(f"Establishing {logical_qubits} logical Φ^+"
+              f" with code length {code_length}"
+              f" using {self.num_repeaters} intermediate repeater nodes")
+
+        egs = [EncodedGenerationProtocol(self[i], self[i+1],
+                                         code_length=code_length)
+               for i in range(len(self)-1)]
+
+        # Repeat the protocol to assemble encoded entangled qubits.
+        for n in range(logical_qubits):
+            # 1. Encoded Generation. Generate one logical Φ^+ between
+            # neighbours.
+            ts = []
+            for eg in egs:
+                ts.append(eg.left.run_protocol(eg.left_protocol, (n,)))
+                ts.append(eg.right.run_protocol(eg.right_protocol, (n,)))
+            for t in ts:
+                t.join()
+
+            # Perform the swap synchronously from the left-most repeater. This
+            # creates a sequence like:
+            #    Alice <-> Polly_0 <-> Polly_1 <-> Bob
+            #    Alice <-------------> Polly_1 <-> Bob
+            #    Alice <-------------------------> Bob
+            for k in range(self.num_repeaters):
+                a, p, b = self[0], self[k+1], self[k+2]
+
+                # 2. Encoded Connection
+                t1 = p.run_protocol(encoded_connection, (a, b, n, code_length))
+
+                # 3. Establish Pauli Frame
+                t2 = a.run_protocol(pauli_frame_left, (p, n, code_length))
+                t3 = b.run_protocol(pauli_frame_right, (p, n, code_length))
+
+                t1.join()
+                t2.join()
+                t3.join()
+
+
+def main():
+    logical_qubits = 5
+    code_length = 3
+    repeater_nodes = 2
+
+    with LinearRelayNetwork(repeater_nodes) as network:
+        network.run_with_repetition_code(logical_qubits=logical_qubits,
+                                         code_length=code_length)
+        check_correlations(network.hosts, logical_qubits, code_length)
+
+
+if __name__ == "__main__":
+    main()