backend/core/quantum_search.py

# --- Real Quantum Circuit Simulation (Qiskit, Cirq) ---
try:
    from qiskit import QuantumCircuit, Aer, transpile, assemble, execute
    from qiskit.visualization import plot_histogram
    from qiskit.providers.ibmq import least_busy, IBMQ
except Exception:
    # Provide lightweight fallbacks for environments without qiskit
    QuantumCircuit = None
    Aer = None
    transpile = None
    assemble = None
    execute = None
    def plot_histogram(counts):
        print('plot_histogram:', counts)
    least_busy = None
    IBMQ = None

try:
    import cirq
except Exception:
    cirq = None

from typing import List, Dict, Any, Optional, Callable

try:
    import numpy as np
except Exception:
    class _np_stub:
        def array(self, *a, **k):
            return []
        def ones(self, *a, **k):
            return []
        def zeros(self, *a, **k):
            return []
        def identity(self, n):
            return [[1 if i==j else 0 for j in range(n)] for i in range(n)]
        def mean(self, *a, **k):
            return 0
        def argmax(self, *a, **k):
            return 0
        def abs(self, x):
            return x
        def random(self):
            import random
            return random

    np = _np_stub()

def simulate_qiskit_circuit(num_qubits: int, shots: int = 1024):
    qc = QuantumCircuit(num_qubits, num_qubits)
    for i in range(num_qubits):
        qc.h(i)
    qc.measure(range(num_qubits), range(num_qubits))
    backend = Aer.get_backend('qasm_simulator')
    job = execute(qc, backend, shots=shots)
    result = job.result()
    counts = result.get_counts()
    plot_histogram(counts)
    return counts

def simulate_cirq_circuit(num_qubits: int, shots: int = 1024):
    qubits = [cirq.LineQubit(i) for i in range(num_qubits)]
    circuit = cirq.Circuit()
    circuit.append([cirq.H(q) for q in qubits])
    circuit.append([cirq.measure(q) for q in qubits])
    simulator = cirq.Simulator()
    result = simulator.run(circuit, repetitions=shots)
    print("Cirq result:", result)
    return result

# --- Real Hardware Execution (IBM Q) ---
def run_on_ibmq(qc: QuantumCircuit, shots: int = 1024):
    IBMQ.load_account()
    provider = IBMQ.get_provider(hub='ibm-q')
    backend = least_busy(provider.backends(filters=lambda b: b.configuration().n_qubits >= qc.num_qubits and not b.configuration().simulator and b.status().operational==True))
    transpiled = transpile(qc, backend, optimization_level=3)
    job = backend.run(transpiled, shots=shots)
    result = job.result()
    counts = result.get_counts()
    plot_histogram(counts)
    return counts

# --- Advanced Quantum Algorithms ---
def quantum_phase_estimation(num_qubits: int):
    qc = QuantumCircuit(num_qubits+1, num_qubits)
    for q in range(num_qubits):
        qc.h(q)
    qc.x(num_qubits)
    # Placeholder: add controlled-U operations
    qc.measure(range(num_qubits), range(num_qubits))
    backend = Aer.get_backend('qasm_simulator')
    job = execute(qc, backend, shots=1024)
    result = job.result()
    counts = result.get_counts()
    plot_histogram(counts)
    return counts

def quantum_counting(num_qubits: int):
    # Placeholder: quantum counting circuit
    qc = QuantumCircuit(num_qubits, num_qubits)
    for i in range(num_qubits):
        qc.h(i)
    qc.measure(range(num_qubits), range(num_qubits))
    backend = Aer.get_backend('qasm_simulator')
    job = execute(qc, backend, shots=1024)
    result = job.result()
    counts = result.get_counts()
    plot_histogram(counts)
    return counts

def quantum_machine_learning_example(num_qubits: int):
    # Placeholder: QML circuit (e.g., variational classifier)
    qc = QuantumCircuit(num_qubits, 1)
    for i in range(num_qubits):
        qc.ry(np.pi/4, i)
    qc.measure(0, 0)
    backend = Aer.get_backend('qasm_simulator')
    job = execute(qc, backend, shots=1024)
    result = job.result()
    counts = result.get_counts()
    plot_histogram(counts)
    return counts

# --- Quantum State Tomography, Fidelity, Error Mitigation ---
def quantum_state_tomography(qc: QuantumCircuit):
    # Placeholder: state tomography
    print("Quantum state tomography (stub)")

def quantum_fidelity(state1: np.ndarray, state2: np.ndarray) -> float:
    return np.abs(np.dot(state1.conj(), state2))**2

def error_mitigation(counts: Dict[str, int]) -> Dict[str, int]:
    # Placeholder: error mitigation
    print("Error mitigation (stub)")
    return counts

# --- Quantum Dataset Management, Async/Batch Execution ---
class QuantumDatasetManager:
    def __init__(self):
        self.datasets = {}
    def add_dataset(self, name: str, data):
        self.datasets[name] = data
    def get_dataset(self, name: str):
        return self.datasets.get(name, None)

import asyncio
async def async_quantum_search(search_fn: Callable, *args, **kwargs):
    await asyncio.sleep(0.1)
    return search_fn(*args, **kwargs)

# --- Expanded Test Harness with Real Quantum Circuits ---
def test_real_quantum_search():
    logging.basicConfig(level=logging.INFO)
    # Qiskit simulation
    print("Qiskit simulation:")
    simulate_qiskit_circuit(3)
    # Cirq simulation
    print("Cirq simulation:")
    simulate_cirq_circuit(3)
    # Quantum phase estimation
    print("Quantum phase estimation:")
    quantum_phase_estimation(3)
    # Quantum counting
    print("Quantum counting:")
    quantum_counting(3)
    # QML example
    print("Quantum machine learning example:")
    quantum_machine_learning_example(3)
    # State tomography
    qc = QuantumCircuit(2,2)
    quantum_state_tomography(qc)
    # Fidelity
    s1 = np.array([1,0])
    s2 = np.array([1,0])
    print("Fidelity:", quantum_fidelity(s1, s2))
    # Error mitigation
    print("Error mitigation:", error_mitigation({'00': 500, '11': 524}))
    # Dataset manager
    qdm = QuantumDatasetManager()
    qdm.add_dataset("test", [1,2,3])
    print("Quantum dataset:", qdm.get_dataset("test"))
    # Async quantum search
    async def run_async():
        result = await async_quantum_search(lambda: 42)
        print("Async quantum search result:", result)
    asyncio.run(run_async())

if __name__ == "__main__":
    test_real_quantum_search()

import numpy as np
import logging
from typing import List, Dict, Any, Optional, Callable

class GroverSearch:
    """
    Simulates Grover's quantum search algorithm for unstructured search problems.
    Extensible for integration with quantum backends and theorem proving.
    """
    def __init__(self, database_size: int, logger: Optional[logging.Logger] = None):
        self.N = database_size
        self.state = np.ones(self.N) / self.N
        self.logger = logger or logging.getLogger("GroverSearch")
        self.logger.info(f"GroverSearch initialized with database size {self.N}")

    def oracle(self, target_idx: int):
        """Flip the sign of the target state."""
        oracle_matrix = np.identity(self.N)
        oracle_matrix[target_idx, target_idx] = -1
        self.state = np.dot(oracle_matrix, self.state)
        self.logger.debug(f"Oracle applied at index {target_idx}")

    def diffusion(self):
        """Invert about the mean."""
        mean = np.mean(self.state)
        self.state = 2 * mean - self.state
        self.logger.debug("Diffusion operator applied")

    def run(self, target_idx: int, iterations: Optional[int] = None) -> int:
        if iterations is None:
            iterations = int(np.pi/4 * np.sqrt(self.N))
        for i in range(iterations):
            self.oracle(target_idx)
            self.diffusion()
            self.logger.debug(f"Iteration {i+1}/{iterations}")
        result = int(np.argmax(self.state))
        self.logger.info(f"GroverSearch result: {result}")
        return result

    def explain_search(self) -> Dict[str, Any]:
        return {"explanation": "Grover's algorithm amplifies the probability of the target state."}

class QuantumProofSearchEngine:
    """
    Quantum-inspired engine for proof search and axiom selection.
    Extensible for integration with neuro-symbolic, external provers, and quantum backends.
    """
    def __init__(self, config: Optional[Dict[str, Any]] = None, logger: Optional[logging.Logger] = None):
        self.config = config or {}
        self.logger = logger or logging.getLogger("QuantumProofSearchEngine")
        self.logger.info("QuantumProofSearchEngine initialized with config: %s", self.config)

    def search(self, universe: Any, axioms: List[Any], theorems: List[Any], context: Optional[Dict[str, Any]] = None) -> Dict[str, Any]:
        """
        Perform quantum-inspired search for proofs or axiom selection.
        In production, use quantum algorithms, simulators, or hybrid approaches.
        """
        self.logger.info("Starting quantum proof search in universe %s", getattr(universe, 'id', None))
        # Example: Use GroverSearch to select an axiom
        if not axioms:
            self.logger.warning("No axioms provided for quantum search.")
            return {"result": None, "reason": "No axioms provided"}
        grover = GroverSearch(database_size=len(axioms), logger=self.logger)
        target_idx = 0  # Placeholder: in production, use a scoring function
        selected_idx = grover.run(target_idx)
        self.logger.info(f"Quantum search selected axiom index: {selected_idx}")
        return {"selected_axiom": axioms[selected_idx]}

    def batch_search(self, universes: List[Any], axiom_batches: List[List[Any]], theorem_batches: List[List[Any]], context: Optional[Dict[str, Any]] = None) -> List[Dict[str, Any]]:
        results = []
        for u, a, t in zip(universes, axiom_batches, theorem_batches):
            result = self.search(u, a, t, context)
            results.append(result)
        return results

    def integrate_with_neuro_symbolic(self, *args, **kwargs):
        # Hook for neuro-symbolic integration
        self.logger.info("Integrating with neuro-symbolic module.")
        pass

    def integrate_with_external_prover(self, *args, **kwargs):
        # Hook for AlphaGeometry, Lean, Coq, etc.
        self.logger.info("Integrating with external prover.")
        pass

    def explain_search(self, *args, **kwargs):
        # Placeholder for quantum search explainability
        return {"explanation": "Quantum search amplifies the probability of promising proof paths."}

class QuantumAxiomSelector:
    """
    Quantum-inspired axiom selector for theorem proving.
    """
    def __init__(self, logger: Optional[logging.Logger] = None):
        self.logger = logger or logging.getLogger("QuantumAxiomSelector")

    def select(self, axioms: List[Any], scoring_fn: Optional[Callable[[Any], float]] = None) -> Any:
        if not axioms:
            self.logger.warning("No axioms provided for selection.")
            return None
        if scoring_fn:
            scores = [scoring_fn(ax) for ax in axioms]
            idx = int(np.argmax(scores))
        else:
            idx = 0  # Placeholder
        self.logger.info(f"Axiom selected at index {idx}")
        return axioms[idx]

class QuantumSimulator:
    """
    Simulates quantum circuits and algorithms for mathematical objects.
    """
    def __init__(self, logger: Optional[logging.Logger] = None):
        self.logger = logger or logging.getLogger("QuantumSimulator")

    def simulate_circuit(self, circuit: Any) -> Dict[str, Any]:
        # Placeholder for quantum circuit simulation
        self.logger.info("Simulating quantum circuit.")
        return {"result": "Simulation not implemented"}

    def encode_math_object(self, obj: Any) -> np.ndarray:
        # Placeholder for encoding mathematical objects as quantum states
        self.logger.info("Encoding mathematical object as quantum state.")
        return np.zeros(8)

class QAOAStub:
    """
    Stub for Quantum Approximate Optimization Algorithm (QAOA).
    """
    def __init__(self, logger: Optional[logging.Logger] = None):
        self.logger = logger or logging.getLogger("QAOAStub")

    def optimize(self, problem: Any) -> Dict[str, Any]:
        self.logger.info("QAOA optimization stub called.")
        return {"result": "QAOA optimization not implemented"}

class VQEStub:
    """
    Stub for Variational Quantum Eigensolver (VQE).
    """
    def __init__(self, logger: Optional[logging.Logger] = None):
        self.logger = logger or logging.getLogger("VQEStub")

    def solve(self, hamiltonian: Any) -> Dict[str, Any]:
        self.logger.info("VQE solve stub called.")
        return {"result": "VQE not implemented"}


# Utility functions for quantum search
def encode_axioms_as_states(axioms: List[Any]) -> np.ndarray:
    """
    Encode a list of axioms as quantum states (feature vectors).
    In production, use embeddings, graph encodings, or symbolic representations.
    """
    if not axioms:
        return np.array([])
    return np.ones(len(axioms)) / len(axioms)

def quantum_log(message: str, level: int = logging.INFO):
    logger = logging.getLogger("QuantumSearch")
    logger.log(level, message)

# --- Advanced Quantum Algorithms ---
class QuantumWalkSearch:
    """
    Quantum walk-based search for graph-structured theorem spaces.
    """
    def __init__(self, graph: Any, logger: Optional[logging.Logger] = None):
        self.graph = graph
        self.logger = logger or logging.getLogger("QuantumWalkSearch")
        self.logger.info("QuantumWalkSearch initialized.")

    def run(self, start_node: Any, target_node: Any, steps: int = 10) -> List[Any]:
        # Placeholder for quantum walk simulation
        self.logger.info(f"Running quantum walk from {start_node} to {target_node} for {steps} steps.")
        path = [start_node]
        for _ in range(steps):
            # In production, use quantum walk transition rules
            neighbors = list(self.graph.get(start_node, []))
            if not neighbors:
                break
            start_node = neighbors[0]  # Placeholder: pick first neighbor
            path.append(start_node)
            if start_node == target_node:
                break
        self.logger.info(f"Quantum walk path: {path}")
        return path

class AmplitudeAmplification:
    """
    Generalized amplitude amplification for quantum search.
    """
    def __init__(self, N: int, logger: Optional[logging.Logger] = None):
        self.N = N
        self.state = np.ones(self.N) / self.N
        self.logger = logger or logging.getLogger("AmplitudeAmplification")

    def amplify(self, oracle_fn: Callable[[int], bool], iterations: Optional[int] = None) -> int:
        if iterations is None:
            iterations = int(np.pi/4 * np.sqrt(self.N))
        for i in range(iterations):
            # Oracle: flip sign of marked states
            for idx in range(self.N):
                if oracle_fn(idx):
                    self.state[idx] *= -1
            # Diffusion
            mean = np.mean(self.state)
            self.state = 2 * mean - self.state
            self.logger.debug(f"Iteration {i+1}/{iterations}")
        result = int(np.argmax(np.abs(self.state)))
        self.logger.info(f"Amplitude amplification result: {result}")
        return result

class QuantumAnnealing:
    """
    Quantum annealing for combinatorial optimization in theorem search.
    """
    def __init__(self, problem_size: int, logger: Optional[logging.Logger] = None):
        self.problem_size = problem_size
        self.logger = logger or logging.getLogger("QuantumAnnealing")

    def solve(self, cost_fn: Callable[[List[int]], float], steps: int = 1000) -> List[int]:
        # Placeholder for quantum annealing simulation
        self.logger.info(f"Quantum annealing for problem size {self.problem_size}")
        state = np.random.randint(0, 2, self.problem_size).tolist()
        best_state = state[:]
        best_cost = cost_fn(state)
        for step in range(steps):
            idx = np.random.randint(0, self.problem_size)
            state[idx] ^= 1  # Flip bit
            cost = cost_fn(state)
            if cost < best_cost:
                best_cost = cost
                best_state = state[:]
            else:
                state[idx] ^= 1  # Revert
        self.logger.info(f"Quantum annealing best state: {best_state}, cost: {best_cost}")
        return best_state

# --- Distributed and Batch Quantum Search ---
class DistributedQuantumSearch:
    """
    Distributed quantum search for large-scale theorem spaces.
    """
    def __init__(self, num_workers: int = 4, logger: Optional[logging.Logger] = None):
        self.num_workers = num_workers
        self.logger = logger or logging.getLogger("DistributedQuantumSearch")

    def run(self, search_fn: Callable, *args, **kwargs) -> List[Any]:
        # Placeholder for distributed execution
        self.logger.info(f"Running distributed quantum search with {self.num_workers} workers.")
        results = []
        for i in range(self.num_workers):
            result = search_fn(*args, **kwargs)
            results.append(result)
        self.logger.info(f"Distributed quantum search results: {results}")
        return results

# --- Research Utilities ---
def benchmark_quantum_search(search_fn: Callable, *args, repeats: int = 10, **kwargs) -> Dict[str, Any]:
    import time
    times = []
    for _ in range(repeats):
        start = time.time()
        search_fn(*args, **kwargs)
        times.append(time.time() - start)
    return {"mean_time": np.mean(times), "std_time": np.std(times), "runs": repeats}

def visualize_state(state: np.ndarray, title: str = "Quantum State"):
    import matplotlib.pyplot as plt
    plt.figure(figsize=(10, 4))
    plt.bar(range(len(state)), np.abs(state))
    plt.title(title)
    plt.xlabel("Index")
    plt.ylabel("Amplitude")
    plt.show()

def simulate_quantum_noise(state: np.ndarray, noise_level: float = 0.01) -> np.ndarray:
    noise = np.random.normal(0, noise_level, size=state.shape)
    return state + noise

# --- Integration Hooks ---
def integrate_with_theorem_engine(engine: Any, quantum_module: Any):
    # Hook for integrating quantum search with theorem engine
    quantum_log("Integrating quantum search with theorem engine.")
    pass

def integrate_with_neuro_symbolic(neuro_module: Any, quantum_module: Any):
    # Hook for integrating quantum search with neuro-symbolic module
    quantum_log("Integrating quantum search with neuro-symbolic module.")
    pass

def integrate_with_external_provers(prover_modules: List[Any], quantum_module: Any):
    # Hook for integrating quantum search with external provers
    quantum_log("Integrating quantum search with external provers.")
    pass

# --- Example/Test Harnesses ---
if __name__ == "__main__":
    import sys
    logging.basicConfig(level=logging.INFO)
    # Grover's Search Example
    search = GroverSearch(database_size=16)
    result = search.run(target_idx=5)
    print(f"Found target at index: {result}")
    visualize_state(search.state, title="Grover Final State")

    # Quantum Walk Example
    graph = {0: [1, 2], 1: [2, 3], 2: [3], 3: []}
    qwalk = QuantumWalkSearch(graph)
    path = qwalk.run(start_node=0, target_node=3, steps=5)
    print(f"Quantum walk path: {path}")

    # Amplitude Amplification Example
    amp = AmplitudeAmplification(N=8)
    oracle_fn = lambda idx: idx == 3
    amp_result = amp.amplify(oracle_fn)
    print(f"Amplitude amplification found index: {amp_result}")

    # Quantum Annealing Example
    annealer = QuantumAnnealing(problem_size=8)
    cost_fn = lambda state: sum(state)  # Minimize number of 1s
    best_state = annealer.solve(cost_fn, steps=100)
    print(f"Quantum annealing best state: {best_state}")

    # Distributed Quantum Search Example
    dqs = DistributedQuantumSearch(num_workers=3)
    dqs_results = dqs.run(lambda: np.random.randint(0, 100))
    print(f"Distributed quantum search results: {dqs_results}")

    # Benchmarking Example
    bench = benchmark_quantum_search(search.run, target_idx=5, repeats=5)
    print(f"Benchmark: {bench}")

    # Simulate Quantum Noise
    noisy_state = simulate_quantum_noise(search.state, noise_level=0.05)
    visualize_state(noisy_state, title="Noisy Quantum State")

    # Integration Hooks Example
    integrate_with_theorem_engine(None, search)
    integrate_with_neuro_symbolic(None, search)
    integrate_with_external_provers([], search)