Asynchronous quantum distributed computing framework implementing atomic quantum global operations. Based on Chandy-Lamport snapshot algorithm adapted for quantum systems with causality preservation. Activation: quantum distributed computing, quantum snapshots, asynchronous quantum systems, quantum global operations.
This skill provides methodologies for implementing asynchronous quantum distributed systems, focusing on atomic quantum global operations that can be decomposed into local operations on system components. Based on the classical Chandy-Lamport snapshot algorithm, the QGO (Quantum Global Operations) Algorithm enables quantum snapshots where the whole system is instantaneously measured while preserving quantum causality.
import numpy as np
from typing import List, Dict, Tuple
from dataclasses import dataclass
@dataclass
class QuantumComponent:
"""Represents a component in a quantum distributed system."""
id: str
state: np.ndarray # Local quantum state
entangled_with: List[str] # IDs of entangled components
class QuantumSnapshotAlgorithm:
"""
QGO Algorithm for asynchronous quantum distributed computing.
Implements atomic quantum global operations using the
Chandy-Lamport snapshot approach adapted for quantum systems.
"""
def __init__(self, components: List[QuantumComponent]):
self.components = {c.id: c for c in components}
self.channels = self._build_channel_map()
self.marker_received = {c.id: False for c in components}
self.local_snapshots = {}
def _build_channel_map(self) -> Dict[Tuple[str, str], List]:
"""Build mapping of communication channels between components."""
channels = {}
for c1 in self.components.values():
for c2_id in c1.entangled_with:
channels[(c1.id, c2_id)] = []
channels[(c2_id, c1.id)] = []
return channels
def initiate_snapshot(self, initiator_id: str):
"""
Initiate a quantum snapshot from a specific component.
Args:
initiator_id: ID of the component initiating the snapshot
"""
# Record local state
self.local_snapshots[initiator_id] = {
'state': self.components[initiator_id].state.copy(),
'timestamp': self._get_timestamp()
}
self.marker_received[initiator_id] = True
# Send markers to all neighbors
for neighbor_id in self.components[initiator_id].entangled_with:
self._send_marker(initiator_id, neighbor_id)
def _send_marker(self, from_id: str, to_id: str):
"""Send a marker message to a neighboring component."""
marker = {
'type': 'MARKER',
'from': from_id,
'timestamp': self._get_timestamp()
}
self._process_marker(to_id, marker)
def _process_marker(self, component_id: str, marker: Dict):
"""Process a received marker message."""
if not self.marker_received[component_id]:
# First marker - record state and forward
self.local_snapshots[component_id] = {
'state': self.components[component_id].state.copy(),
'timestamp': marker['timestamp']
}
self.marker_received[component_id] = True
# Forward to all other neighbors
for neighbor_id in self.components[component_id].entangled_with:
if neighbor_id != marker['from']:
self._send_marker(component_id, neighbor_id)
# Record channel state
self._record_channel_state(marker['from'], component_id)
def _record_channel_state(self, from_id: str, to_id: str):
"""Record the state of a communication channel."""
channel_key = (from_id, to_id)
if channel_key in self.channels:
self.channels[channel_key] = {
'entanglement_strength': self._calculate_entanglement(from_id, to_id),
'recorded': True
}
def _calculate_entanglement(self, id1: str, id2: str) -> float:
"""Calculate entanglement strength between two components."""
c1 = self.components[id1]
c2 = self.components[id2]
if id2 in c1.entangled_with and id1 in c2.entangled_with:
return self._von_neumann_entropy(c1.state, c2.state)
return 0.0
def _von_neumann_entropy(self, state1: np.ndarray, state2: np.ndarray) -> float:
"""Calculate von Neumann entropy as entanglement measure."""
rho = np.outer(state1, state1.conj())
eigenvalues = np.linalg.eigvalsh(rho)
eigenvalues = eigenvalues[eigenvalues > 1e-10]
return -np.sum(eigenvalues * np.log2(eigenvalues))
def _get_timestamp(self) -> int:
"""Get current logical timestamp."""
return len(self.local_snapshots)
def get_global_snapshot(self) -> Dict:
"""
Retrieve the complete global snapshot.
Returns:
Dictionary containing all local snapshots and channel states
"""
if not all(self.marker_received.values()):
raise RuntimeError("Snapshot not yet complete")
return {
'local_snapshots': self.local_snapshots,
'channel_states': self.channels,
'causal_consistent': self._verify_causal_consistency()
}
def _verify_causal_consistency(self) -> bool:
"""Verify that the snapshot is causally consistent."""
for (from_id, to_id), state in self.channels.items():
if not state.get('recorded', False):
return False
return True
def execute_global_operation(self, operation: str) -> np.ndarray:
"""
Execute a decomposable global quantum operation.
Args:
operation: Type of global operation ('measure', 'snapshot', etc.)
Returns:
Result of the global operation
"""
if operation == 'snapshot':
first_component = list(self.components.keys())[0]
self.initiate_snapshot(first_component)
return self.get_global_snapshot()
elif operation == 'measure':
results = {}
for comp_id, comp in self.components.items():
results[comp_id] = self._measure_component(comp)
return results
else:
raise ValueError(f"Unknown operation: {operation}")
def _measure_component(self, component: QuantumComponent) -> Dict:
"""Perform measurement on a single component."""
probabilities = np.abs(component.state) ** 2
outcome = np.random.choice(len(probabilities), p=probabilities)
return {
'outcome': outcome,
'probability': probabilities[outcome],
'post_measurement_state': self._collapse_state(component.state, outcome)
}
def _collapse_state(self, state: np.ndarray, outcome: int) -> np.ndarray:
"""Collapse quantum state after measurement."""
new_state = np.zeros_like(state)
new_state[outcome] = 1.0
return new_state
class DistributedQuantumSystem:
"""High-level interface for distributed quantum systems."""
def __init__(self):
self.components = []
self.algorithm = None
def add_component(self, component_id: str, initial_state: np.ndarray):
"""Add a quantum component to the system."""
component = QuantumComponent(
id=component_id,
state=initial_state,
entangled_with=[]
)
self.components.append(component)
def establish_entanglement(self, id1: str, id2: str):
"""Establish entanglement between two components."""
c1 = next(c for c in self.components if c.id == id1)
c2 = next(c for c in self.components if c.id == id2)
c1.entangled_with.append(id2)
c2.entangled_with.append(id1)
def initialize_algorithm(self):
"""Initialize the QGO algorithm."""
self.algorithm = QuantumSnapshotAlgorithm(self.components)
def take_snapshot(self) -> Dict:
"""Take a global snapshot of the quantum system."""
if self.algorithm is None:
self.initialize_algorithm()
return self.algorithm.execute_global_operation('snapshot')