Quantum ZX-Calculus MCP Server

""" Layers 2-3: ZX-Calculus Core Implementation Layer 2 (Structure): Deterministic circuit analysis and optimization selection Layer 3 (Relational): Circuit composition rules, rewrite sequence planning Provides deterministic mapping from quantum circuits to ZX-diagrams with simplification strategies. Zero LLM cost for these layers. """ from typing import Dict, List, Tuple, Optional, Set from dataclasses import dataclass from enum import Enum import re from collections import defaultdict from quantum_zx_ologs import ( QUANTUM_GATE_TAXONOMY, SPIDER_FUSION_RULES, lookup_gate, SpiderType, QuantumGate ) class CircuitFormat(Enum): """Supported quantum circuit formats.""" QASM = "qasm" QISKIT = "qiskit" QUIPPER = "quipper" ZX_DIAGRAM = "zx_diagram" class OptimizationStrategy(Enum): """Strategies for circuit simplification.""" CLIFFORD_SIMPLIFICATION = "clifford" T_COUNT_REDUCTION = "t_count" MEASUREMENT_BASED = "mbqc" ERROR_CORRECTION = "error_correction" FULL_REDUCTION = "full" EDUCATIONAL = "educational" @dataclass class QuantumCircuit: """Parsed quantum circuit.""" num_qubits: int gates: List[Tuple[str, List[int]]] # (gate_name, [qubit_indices]) classical_bits: int = 0 measurements: List[Tuple[int, int]] = None # (qubit, classical_bit) def __post_init__(self): if self.measurements is None: self.measurements = [] @dataclass class ZXDiagram: """ZX-diagram representation of a quantum circuit.""" spiders: List[Dict] # List of spider definitions wires: List[Tuple[int, int]] # Connections between spiders phases: Dict[int, float] # Phase values for each spider bounding_box: Optional[Tuple[int, int]] = None def to_dict(self) -> Dict: """Convert to dictionary for JSON serialization.""" return { "spiders": self.spiders, "wires": self.wires, "phases": self.phases, "bounding_box": self.bounding_box } @dataclass class CircuitAnalysis: """Analysis of circuit properties and optimization potential.""" total_gates: int clifford_gates: int t_gates: int two_qubit_gates: int measurements: int entanglement_score: float # 0-1 estimate of entanglement clifford_depth: int estimated_t_count: int has_measurements: bool is_clifford_only: bool recommended_strategies: List[OptimizationStrategy] potential_optimizations: Dict[str, str] # ============================================================================ # LAYER 2: CIRCUIT PARSING (Deterministic) # ============================================================================ def parse_qasm_circuit(qasm_code: str) -> Optional[QuantumCircuit]: """ Parse OpenQASM 2.0 circuit (deterministic, 0 tokens). Extracts gate sequence and qubit mapping. """ lines = qasm_code.strip().split('\n') num_qubits = 0 gates = [] for line in lines: line = line.strip() # Extract qubit count if line.startswith('qreg'): match = re.search(r'qreg\s+\w+\[(\d+)\]', line) if match: num_qubits = max(num_qubits, int(match.group(1))) # Parse gate operations elif line and not line.startswith('//') and not line.startswith('OPENQASM'): # Handle parametric gates if '(' in line: match = re.match(r'(\w+)\([^)]*\)\s+(q\[\d+\](?:,\s*q\[\d+\])*)', line) else: match = re.match(r'(\w+)\s+(q\[\d+\](?:,\s*q\[\d+\])*)', line) if match: gate_name = match.group(1) qubits_str = match.group(2) # Extract qubit indices qubit_indices = [int(m) for m in re.findall(r'\[(\d+)\]', qubits_str)] gates.append((gate_name.lower(), qubit_indices)) if num_qubits == 0 and gates: num_qubits = max(max(q for _, qs in gates for q in qs), 0) + 1 return QuantumCircuit(num_qubits=num_qubits, gates=gates) if gates else None # ============================================================================ # LAYER 2: CIRCUIT ANALYSIS (Deterministic) # ============================================================================ def analyze_circuit(circuit: QuantumCircuit) -> CircuitAnalysis: """ Analyze circuit properties and determine optimization strategy (deterministic, 0 tokens). """ clifford_gates = 0 t_gates = 0 two_qubit_gates = 0 measurements = 0 entangling_ops = 0 for gate_name, qubits in circuit.gates: gate_def = lookup_gate(gate_name) if not gate_def: continue if gate_def.is_clifford: clifford_gates += 1 if not gate_def.is_clifford and gate_def.is_clifford_t: t_gates += 1 if len(qubits) >= 2: two_qubit_gates += 1 entangling_ops += 1 if gate_name in ['measure_z', 'measure_x']: measurements += 1 total_gates = len(circuit.gates) is_clifford_only = t_gates == 0 # Estimate entanglement (simple heuristic) entanglement_score = min(1.0, entangling_ops / max(1, total_gates)) # Estimate clifford depth (simplified) clifford_depth = total_gates - t_gates # Estimate T-count (critical for fault tolerance) estimated_t_count = t_gates * 4 # Rough estimate # Recommend optimization strategies recommended_strategies = [] if is_clifford_only: recommended_strategies.append(OptimizationStrategy.CLIFFORD_SIMPLIFICATION) if t_gates > 0: recommended_strategies.append(OptimizationStrategy.T_COUNT_REDUCTION) if measurements > 0: recommended_strategies.append(OptimizationStrategy.MEASUREMENT_BASED) if entanglement_score > 0.5: recommended_strategies.append(OptimizationStrategy.ERROR_CORRECTION) recommended_strategies.append(OptimizationStrategy.EDUCATIONAL) # Potential optimizations potential_optimizations = {} if clifford_gates > 3: potential_optimizations["clifford_simplification"] = "Multiple Clifford gates detected - can be simplified" if t_gates > 2: potential_optimizations["t_count_reduction"] = f"Circuit has {t_gates} T gates - T-count reduction applicable" if two_qubit_gates > 3: potential_optimizations["entanglement_routing"] = "Multiple entangling gates - routing optimization possible" return CircuitAnalysis( total_gates=total_gates, clifford_gates=clifford_gates, t_gates=t_gates, two_qubit_gates=two_qubit_gates, measurements=measurements, entanglement_score=entanglement_score, clifford_depth=clifford_depth, estimated_t_count=estimated_t_count, has_measurements=measurements > 0, is_clifford_only=is_clifford_only, recommended_strategies=recommended_strategies, potential_optimizations=potential_optimizations ) # ============================================================================ # LAYER 2: ZX-DIAGRAM CONVERSION (Deterministic) # ============================================================================ def circuit_to_zx_diagram(circuit: QuantumCircuit) -> ZXDiagram: """ Convert quantum circuit to ZX-diagram representation (deterministic, 0 tokens). Maps gates to spiders and builds wire connectivity. """ spiders = [] wires = [] phases = {} spider_id = 0 qubit_to_spider: Dict[int, int] = {} # Create initial state spiders (one per qubit) for qubit in range(circuit.num_qubits): spiders.append({ "id": spider_id, "type": "Z", "inputs": 0, "outputs": 1, "label": f"q{qubit}_init" }) phases[spider_id] = 0.0 qubit_to_spider[qubit] = spider_id spider_id += 1 # Process gates for gate_name, qubits in circuit.gates: gate_def = lookup_gate(gate_name) if not gate_def: continue spider_type = gate_def.primary_spider.value phase = gate_def.phase if len(qubits) == 1: # Single-qubit gate input_spider = qubit_to_spider[qubits[0]] spiders.append({ "id": spider_id, "type": spider_type, "inputs": 1, "outputs": 1, "label": gate_name }) phases[spider_id] = phase wires.append((input_spider, spider_id)) qubit_to_spider[qubits[0]] = spider_id spider_id += 1 elif len(qubits) == 2: # Two-qubit gate (CNOT, CZ, SWAP) input1 = qubit_to_spider[qubits[0]] input2 = qubit_to_spider[qubits[1]] # Create gate spider spiders.append({ "id": spider_id, "type": spider_type, "inputs": 2, "outputs": 2, "label": gate_name }) phases[spider_id] = phase wires.append((input1, spider_id)) wires.append((input2, spider_id)) current_spider = spider_id spider_id += 1 # Update qubit mappings qubit_to_spider[qubits[0]] = current_spider qubit_to_spider[qubits[1]] = current_spider return ZXDiagram( spiders=spiders, wires=wires, phases=phases, bounding_box=(circuit.num_qubits, len(circuit.gates)) ) # ============================================================================ # LAYER 2: REWRITE STRATEGY SELECTION (Deterministic) # ============================================================================ def select_simplification_strategy(analysis: CircuitAnalysis, desired_outcome: str = "balanced") -> Dict: """ Select ZX-calculus rewrite strategy based on circuit analysis (deterministic, 0 tokens). """ strategy = { "primary_goal": desired_outcome, "rewrite_rules": [], "expected_gate_reduction": 0.0, "expected_t_reduction": 0, "implementation_notes": [] } if desired_outcome == "clifford_simplification": strategy["rewrite_rules"] = [ "spider_fusion", "phase_cancellation", "hadamard_removal" ] strategy["expected_gate_reduction"] = min(0.3, analysis.clifford_gates / max(1, analysis.total_gates)) strategy["implementation_notes"] = [ "Apply fusion rules to connected spiders of same type", "Cancel phases that sum to 2π", "Remove Hadamard pairs" ] elif desired_outcome == "t_count_reduction": strategy["rewrite_rules"] = [ "phase_teleportation", "color_change", "local_complementation" ] strategy["expected_t_reduction"] = int(analysis.estimated_t_count * 0.3) strategy["implementation_notes"] = [ "Identify T gates (π/4 phases)", "Apply phase teleportation to reduce T-count", "Use color change to reposition expensive operations" ] elif desired_outcome == "measurement_based": strategy["rewrite_rules"] = [ "measurement_spider", "byproduct_correction", "flow_verification" ] strategy["implementation_notes"] = [ "Represent measurements as X-spiders with parameters", "Verify flow structure for measurement-based computation", "Compute byproduct corrections" ] elif desired_outcome == "educational": strategy["rewrite_rules"] = [ "step_by_step_fusion", "visualization_friendly", "explanation_generation" ] strategy["expected_gate_reduction"] = 0.2 strategy["implementation_notes"] = [ "Generate step-by-step transformations", "Create SVG visualizations at each step", "Generate natural language explanations" ] return strategy # ============================================================================ # LAYER 2-3: CIRCUIT STATISTICS # ============================================================================ def get_circuit_statistics(circuit: QuantumCircuit) -> Dict: """Get comprehensive circuit statistics (deterministic).""" analysis = analyze_circuit(circuit) return { "basic_info": { "num_qubits": circuit.num_qubits, "num_gates": analysis.total_gates, "num_classical_bits": circuit.classical_bits, "num_measurements": analysis.measurements }, "gate_composition": { "clifford_gates": analysis.clifford_gates, "t_gates": analysis.t_gates, "two_qubit_gates": analysis.two_qubit_gates, "single_qubit_gates": analysis.total_gates - analysis.two_qubit_gates }, "complexity_metrics": { "clifford_depth": analysis.clifford_depth, "estimated_t_count": analysis.estimated_t_count, "entanglement_score": round(analysis.entanglement_score, 3), "is_clifford_only": analysis.is_clifford_only }, "optimization_potential": { "recommended_strategies": [s.value for s in analysis.recommended_strategies], "potential_optimizations": analysis.potential_optimizations } }