diff --git a/src/openfermion/utils/pauli_term_grouping.py b/src/openfermion/utils/pauli_term_grouping.py new file mode 100644 index 000000000..4e9ecfbac --- /dev/null +++ b/src/openfermion/utils/pauli_term_grouping.py @@ -0,0 +1,195 @@ +""" +Optimized Pauli term grouping strategies for measurement reduction in fermionic simulations. +Based on research showing up to 50% measurement reduction compared to traditional techniques. +""" + +import numpy as np +from openfermion.ops import QubitOperator +from openfermion.utils import commutator +from typing import List, Dict, Set, Tuple +import networkx as nx +from collections import defaultdict + +class OptimizedPauliGrouper: + """ + Advanced Pauli term grouping with overlapping strategy for simultaneous measurements. + + This implementation reduces measurement requirements by leveraging commuting Pauli terms + and introduces overlapping groupings for enhanced parallelization. + """ + + def __init__(self, hamiltonian: QubitOperator, overlap_threshold: float = 0.7): + """ + Initialize the optimized Pauli grouper. + + Args: + hamiltonian: QubitOperator representing the molecular Hamiltonian + overlap_threshold: Threshold for determining overlapping groups (0.0-1.0) + """ + self.hamiltonian = hamiltonian + self.overlap_threshold = overlap_threshold + self.pauli_terms = list(hamiltonian.terms.keys()) + self.coefficients = list(hamiltonian.terms.values()) + + def create_overlapping_groups(self) -> List[List[int]]: + """ + Create overlapping groups of commuting Pauli terms for parallel measurement. + + Returns: + List of groups, where each group contains indices of commuting Pauli terms + """ + # Build commutation graph + commutation_graph = self._build_commutation_graph() + + # Find maximal cliques (groups of mutually commuting terms) + cliques = list(nx.find_cliques(commutation_graph)) + + # Sort cliques by size (prioritize larger groups) + cliques.sort(key=len, reverse=True) + + # Create overlapping groups based on threshold + overlapping_groups = self._create_overlaps(cliques) + + return overlapping_groups + + def _build_commutation_graph(self) -> nx.Graph: + """Build graph where edges connect commuting Pauli terms.""" + graph = nx.Graph() + n_terms = len(self.pauli_terms) + + # Add all terms as nodes + graph.add_nodes_from(range(n_terms)) + + # Add edges between commuting terms + for i in range(n_terms): + for j in range(i + 1, n_terms): + if self._pauli_terms_commute(self.pauli_terms[i], self.pauli_terms[j]): + graph.add_edge(i, j) + + return graph + + def _pauli_terms_commute(self, term1: Tuple, term2: Tuple) -> bool: + """Check if two Pauli terms commute.""" + if not term1 or not term2: # Identity terms always commute + return True + + # Count anti-commuting pairs + anti_commuting_count = 0 + + # Get all qubits involved in both terms + qubits1 = {qubit for qubit, _ in term1} + qubits2 = {qubit for qubit, _ in term2} + common_qubits = qubits1.intersection(qubits2) + + # Check anti-commutation for each common qubit + for qubit in common_qubits: + pauli1 = dict(term1)[qubit] + pauli2 = dict(term2)[qubit] + + # X and Y anti-commute, Y and Z anti-commute, X and Z anti-commute + if (pauli1, pauli2) in [('X', 'Y'), ('Y', 'X'), ('Y', 'Z'), + ('Z', 'Y'), ('X', 'Z'), ('Z', 'X')]: + anti_commuting_count += 1 + + # Terms commute if even number of anti-commuting pairs + return anti_commuting_count % 2 == 0 + + def _create_overlaps(self, cliques: List[List[int]]) -> List[List[int]]: + """Create overlapping groups based on similarity threshold.""" + overlapping_groups = [] + used_terms = set() + + for clique in cliques: + if len(clique) >= 2: # Only consider non-trivial cliques + # Check overlap with existing groups + overlap_found = False + for existing_group in overlapping_groups: + overlap_ratio = len(set(clique) & set(existing_group)) / len(set(clique) | set(existing_group)) + if overlap_ratio >= self.overlap_threshold: + # Merge with existing group + existing_group.extend([term for term in clique if term not in existing_group]) + overlap_found = True + break + + if not overlap_found: + overlapping_groups.append(clique) + used_terms.update(clique) + + # Add remaining terms as individual groups + for i, term in enumerate(self.pauli_terms): + if i not in used_terms: + overlapping_groups.append([i]) + + return overlapping_groups + + def estimate_measurement_reduction(self) -> Dict[str, float]: + """ + Estimate measurement reduction compared to individual term measurement. + + Returns: + Dictionary with reduction metrics + """ + groups = self.create_overlapping_groups() + individual_measurements = len(self.pauli_terms) + grouped_measurements = len(groups) + + # Calculate average group size + avg_group_size = sum(len(group) for group in groups) / len(groups) + + # Estimate reduction based on group efficiency + measurement_reduction = 1 - (grouped_measurements / individual_measurements) + + return { + 'individual_measurements': individual_measurements, + 'grouped_measurements': grouped_measurements, + 'measurement_reduction_ratio': measurement_reduction, + 'average_group_size': avg_group_size, + 'largest_group_size': max(len(group) for group in groups), + 'estimated_speedup': individual_measurements / grouped_measurements + } + +def optimized_pauli_grouping(hamiltonian: QubitOperator, + overlap_threshold: float = 0.7) -> Tuple[List[List[int]], Dict]: + """ + Convenience function for optimized Pauli term grouping. + + Args: + hamiltonian: QubitOperator representing the molecular Hamiltonian + overlap_threshold: Threshold for overlapping groups + + Returns: + Tuple of (groups, metrics) where groups contains indices of commuting terms + """ + grouper = OptimizedPauliGrouper(hamiltonian, overlap_threshold) + groups = grouper.create_overlapping_groups() + metrics = grouper.estimate_measurement_reduction() + + return groups, metrics + +# Example usage for testing +def demo_pauli_grouping(): + """Demonstrate the improved Pauli grouping on a molecular system.""" + from openfermion.chem import MolecularData + from openfermion.transforms import get_fermion_operator, jordan_wigner + + # Create a simple molecular system (H2) + geometry = [('H', (0., 0., 0.)), ('H', (0., 0., 0.7414))] + molecule = MolecularData(geometry, 'sto-3g', 1, 0) + + # Get the Hamiltonian + molecular_hamiltonian = molecule.get_molecular_hamiltonian() + fermion_hamiltonian = get_fermion_operator(molecular_hamiltonian) + qubit_hamiltonian = jordan_wigner(fermion_hamiltonian) + + # Apply optimized grouping + groups, metrics = optimized_pauli_grouping(qubit_hamiltonian) + + print(f"Original terms: {metrics['individual_measurements']}") + print(f"Grouped measurements: {metrics['grouped_measurements']}") + print(f"Measurement reduction: {metrics['measurement_reduction_ratio']:.2%}") + print(f"Estimated speedup: {metrics['estimated_speedup']:.2f}x") + + return groups, metrics + +if __name__ == "__main__": + demo_pauli_grouping()