Further optimize, and debug:

```
import chess
import chess.polyglot
import random
import sys
import math
import multiprocessing as mp
import time
import logging
from quantum_features import QuantumBoard, QuantumMove, generate_quantum_moves, apply_entanglement, collapse_superpositions

def evaluate(self, board: QuantumBoard):
    """
    Evaluates the board state, accounting for both classical and quantum pieces.
    """
    if board.board.is_checkmate():
        if board.board.turn:
            return -100000  # White is checkmated
        else:
            return 100000   # Black is checkmated
    if board.board.is_stalemate() or board.board.is_insufficient_material():
        return 0  # Draw

    material = self.evaluate_material(board)
    mobility = self.evaluate_mobility(board)
    king_safety = self.evaluate_king_safety(board)
    control_center = self.evaluate_control_center(board)
    pawn_structure = self.evaluate_pawn_structure(board)
    positional = self.evaluate_positional(board)

    total_evaluation = material + mobility + king_safety + control_center + pawn_structure + positional
    logging.debug(f"Board Evaluation: Material={material}, Mobility={mobility}, "
                  f"KingSafety={king_safety}, ControlCenter={control_center}, "
                  f"PawnStructure={pawn_structure}, Positional={positional} => "
                  f"Total={total_evaluation}")
    return total_evaluation

def maybe_collapse_superpositions(self):
    """
    Determines whether to collapse superpositions based on game conditions.
    """
    # Example condition: collapse superpositions with a probability of 20% each move
    if random.random() < 0.2:
        collapse_superpositions(self.board)
        logging.info("Superpositions collapsed based on probabilistic trigger.")

def initialize_quantum_pieces(self):
    """
    Initializes quantum pieces at the start of the game.
    """
    # Example: Make both knights quantum pieces
    for square in [chess.E2, chess.B1, chess.G8, chess.B8]:
        piece = self.board.board.piece_at(square)
        if piece and piece.piece_type == chess.KNIGHT:
            piece_id = self.board.add_quantum_piece(piece, square)
            # Optionally entangle knights
            if square in [chess.G8, chess.B8]:
                self.board.entangle_pieces(piece_id, 1)  # Assuming piece_id 1 is already assigned

def choose_move(self):
    """
    Chooses the best move using quantum search.
    """
    best_move = self.get_best_move_iterative_deepening(
        self.board.board, time_limit=5.0, multi_pv=1
    )
    if best_move:
        move = best_move[0][0]
        if isinstance(move, QuantumMove):
            piece_id = self.get_quantum_piece_id(move.from_square)
            self.handle_quantum_move(move, piece_id)
        else:
            self.board.push_move(move)
        logging.info(f"Best move selected: {move}")



def handle_quantum_move(self, move: QuantumMove, piece_id: int):
    """
    Executes a quantum move and handles entanglement effects.
    """
    self.make_move(move, piece_id=piece_id, quantum=True, num_superpositions=2)
    # Apply entanglement effects if the piece is entangled
    self.board.apply_entanglement_effects(piece_id, move)

def maybe_collapse_superpositions(self):
    """
    Decides whether to collapse superpositions based on game conditions.
    """
    # Example condition: collapse after every 5 moves
    if self.board.board.fullmove_number % 5 == 0:
        collapse_superpositions(self.board)
        logging.info("Superpositions collapsed based on move count.")

def generate_moves(self):
    """
    Generates a list of possible moves, including quantum moves.
    """
    quantum_moves = generate_quantum_moves(self.board, depth=1)
    classical_moves = list(self.board.board.legal_moves)
    return classical_moves + quantum_moves

def handle_entanglements(self, piece_id: int, move: chess.Move):
    """
    Applies the effects of entanglement for the moved piece.
    """
    entangled_ids = self.board.get_entangled_piece_ids(piece_id)
    for ent_id in entangled_ids:
        # For simplicity, mirror the move of the entangled piece
        mirrored_move = chess.Move(move.to_square, move.from_square)
        if mirrored_move in self.board.board.legal_moves:
            self.board.board.push(mirrored_move)
            logging.info(f"Entangled QuantumPiece ID {ent_id} mirrored move: {mirrored_move}")
        else:
            logging.warning(f"Mirrored move {mirrored_move} for entangled QuantumPiece ID {ent_id} is illegal.")

def make_move(self, move, piece_id=None, quantum=False, num_superpositions=2):
    """
    Executes a move, which can be classical or quantum.
    """
    if quantum and piece_id:
        # Create a QuantumMove instance
        quantum_move = QuantumMove(
            from_square=move.from_square,
            to_square=move.to_square,
            promotion=move.promotion,
            quantum=True
        )
        success = self.board.make_quantum_move(quantum_move, piece_id, num_superpositions)
        if success:
            self.handle_entanglements(piece_id, move)
        return success
    else:
        # Execute classical move
        self.board.push_move(move)
        return True

class TranspositionTableEntry:
    def __init__(self, depth, score, flag, best_move):
        self.depth = depth
        self.score = score
        self.flag = flag  # 'EXACT', 'LOWERBOUND', 'UPPERBOUND'
        self.best_move = best_move

class QuantumZobrist:
    def __init__(self):
        self.zobrist_table = {}
        for piece in chess.PIECE_TYPES:
            for color in [chess.WHITE, chess.BLACK]:
                for square in chess.SQUARES:
                    self.zobrist_table[(piece, color, square)] = random.getrandbits(64)
        self.side_to_move = random.getrandbits(64)
        self.castling_rights_table = {}
        for cr in range(16):
            self.castling_rights_table[cr] = random.getrandbits(64)
        self.en_passant_table = {}
        for square in chess.SQUARES:
            self.en_passant_table[square] = random.getrandbits(64)

    def hash_board(self, board):
        h = 0
        for square in chess.SQUARES:
            piece = board.piece_at(square)
            if piece:
                h ^= self.zobrist_table[(piece.piece_type, piece.color, square)]
        if board.turn:
            h ^= self.side_to_move
        h ^= self.castling_rights_table[board.castling_rights]
        if board.ep_square:
            h ^= self.en_passant_table[board.ep_square]
        return h

class MCTSNode:
    def __init__(self, board, parent=None, move=None):
        self.board = board.copy()
        self.parent = parent
        self.move = move
        self.children = {}
        self.visits = 0
        self.wins = 0

    def is_fully_expanded(self):
        return len(self.children) == len(list(self.board.legal_moves))

    def best_child(self, exploration_constant=1.414):
        best_score = -float('inf')
        best_moves = []
        for child in self.children.values():
            if child.visits == 0:
                score = float('inf')
            else:
                exploitation = child.wins / child.visits
                exploration = exploration_constant * math.sqrt(math.log(self.visits) / child.visits)
                score = exploitation + exploration
            if score > best_score:
                best_score = score
                best_moves = [child]
            elif score == best_score:
                best_moves.append(child)
        return random.choice(best_moves) if best_moves else None

    def expand(self):
        moves = list(self.board.legal_moves)
        for move in moves:
            if move not in self.children:
                new_board = self.board.copy()
                new_board.push(move)
                self.children[move] = MCTSNode(new_board, parent=self, move=move)
                return self.children[move]
        return None

    def rollout_policy(self):
        return random.choice(list(self.board.legal_moves)) if list(self.board.legal_moves) else None

    def simulate(self):
        current_board = self.board.copy()
        while not current_board.is_game_over():
            move = self.rollout_policy()
            current_board.push(move)
        result = current_board.result()
        if result == '1-0':
            return 1
        elif result == '0-1':
            return -1
        else:
            return 0

class QuantumChessEngine:
    PIECE_SQUARE_TABLE = {
        chess.PAWN: [
            0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
            5.0, 5.0, 5.0, -5.0, -5.0, 5.0, 5.0, 5.0,
            1.0, 1.0, 2.0, 3.0, 3.0, 2.0, 1.0, 1.0,
            0.5, 0.5, 1.0, 2.5, 2.5, 1.0, 0.5, 0.5,
            0.0, 0.0, 0.0, 2.0, 2.0, 0.0, 0.0, 0.0,
            0.5, -0.5, -1.0, 0.0, 0.0, -1.0, -0.5, 0.5,
            0.5, 1.0, 1.0, -2.0, -2.0, 1.0, 1.0, 0.5,
            0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
        ],
        chess.KNIGHT: [
            -5.0, -4.0, -3.0, -3.0, -3.0, -3.0, -4.0, -5.0,
            -4.0, -2.0, 0.0, 0.0, 0.0, 0.0, -2.0, -4.0,
            -3.0, 0.0, 1.0, 1.5, 1.5, 1.0, 0.0, -3.0,
            -3.0, 0.5, 1.5, 2.0, 2.0, 1.5, 0.5, -3.0,
            -3.0, 0.0, 1.5, 2.0, 2.0, 1.5, 0.0, -3.0,
            -3.0, 0.5, 1.0, 1.5, 1.5, 1.0, 0.5, -3.0,
            -4.0, -2.0, 0.0, 0.5, 0.5, 0.0, -2.0, -4.0,
            -5.0, -4.0, -3.0, -3.0, -3.0, -3.0, -4.0, -5.0
        ],
        chess.BISHOP: [
            -2.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -2.0,
            -1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, -1.0,
            -1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 0.5, -1.0,
            -1.0, 0.5, 1.0, 1.5, 1.5, 1.0, 0.5, -1.0,
            -1.0, 0.5, 1.0, 1.5, 1.5, 1.0, 0.5, -1.0,
            -1.0, 0.5, 1.0, 1.0, 1.0, 1.0, 0.5, -1.0,
            -1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.5, -1.0,
            -2.0, -1.0, -1.0, -1.0, -1.0, -1.0, -1.0, -2.0
        ],
        chess.ROOK: [
            0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
            0.5, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.5,
            -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5,
            -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5,
            -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5,
            -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5,
            -0.5, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -0.5,
            0.0, 0.0, 0.0, 0.5, 0.5, 0.0, 0.0, 0.0
        ],
        chess.QUEEN: [
            -2.0, -1.0, -1.0, -0.5, -0.5, -1.0, -1.0, -2.0,
            -1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, -1.0,
            -1.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, -1.0,
            -0.5, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, -0.5,
            0.0, 0.0, 0.5, 0.5, 0.5, 0.5, 0.0, -0.5,
            -1.0, 0.5, 0.5, 0.5, 0.5, 0.5, 0.0, -1.0,
            -1.0, 0.0, 0.5, 0.0, 0.0, 0.0, 0.0, -1.0,
            -2.0, -1.0, -1.0, -0.5, -0.5, -1.0, -1.0, -2.0
        ],
        chess.KING: [
            -3.0, -4.0, -4.0, -5.0, -5.0, -4.0, -4.0, -3.0,
            -3.0, -4.0, -4.0, -5.0, -5.0, -4.0, -4.0, -3.0,
            -3.0, -4.0, -4.0, -5.0, -5.0, -4.0, -4.0, -3.0,
            -3.0, -4.0, -4.0, -5.0, -5.0, -4.0, -4.0, -3.0,
            -2.0, -3.0, -3.0, -4.0, -4.0, -3.0, -3.0, -2.0,
            -1.0, -2.0, -2.0, -2.0, -2.0, -2.0, -2.0, -1.0,
            2.0, 2.0, 0.0, 0.0, 0.0, 0.0, 2.0, 2.0,
            2.0, 3.0, 1.0, 0.0, 0.0, 1.0, 3.0, 2.0
        ]
    }

    class QuantumChessEngine:
        def __init__(self):
            self.board = QuantumBoard()
            self.zobrist = QuantumZobrist()
            self.transposition_table = {}
            self.opening_book = self.load_opening_book()
            self.depth_limit = 3  # Initial search depth
            self.max_depth_setting = 10  # Maximum allowed depth
            self.start_time = None
            self.time_limit = None

            # Set up logging
            logging.basicConfig(
                filename='quantum_gambit_engine.log',
                filemode='w',
                level=logging.DEBUG,
                format='%(asctime)s - %(levelname)s - %(message)s'
            )
            logging.info("Quantum Gambit Chess Engine initialized.")

        def load_opening_book(self):
            try:
                book = chess.polyglot.open_reader("book.bin")
                logging.info("Opening book 'book.bin' loaded successfully.")
                return book
            except FileNotFoundError:
                logging.warning("Opening book 'book.bin' not found. Proceeding without it.")
                return None

        def piece_value(self, piece_type):
            values = {
                chess.PAWN: 100,
                chess.KNIGHT: 320,
                chess.BISHOP: 330,
                chess.ROOK: 500,
                chess.QUEEN: 900,
                chess.KING: 0
            }
            return values.get(piece_type, 0)

def evaluate_material(self, board: QuantumBoard):
    material = 0
    for square in chess.SQUARES:
        piece = board.board.piece_at(square)
        if piece:
            material += self.piece_value(piece.piece_type) if piece.color == chess.WHITE else -self.piece_value(piece.piece_type)
    # Account for quantum pieces
    for qp in board.quantum_pieces.values():
        for sq, prob in qp.superpositions.items():
            value = self.piece_value(qp.piece_type)
            material += value * prob if qp.color else -value * prob
    return material

        def evaluate_mobility(self, board):
            # Mobility: number of legal moves
            white_moves = len(list(board.legal_moves)) if board.turn else 0
            board.push(chess.Move.null())
            black_moves = len(list(board.legal_moves))
            board.pop()
            return (white_moves - black_moves) * 10  # Weight adjustment

        def evaluate_king_safety(self, board):
            safety = 0
            for color in [chess.WHITE, chess.BLACK]:
                king_square = board.king(color)
                if king_square:
                    # Count attackers and defenders
                    attackers = len(board.attackers(not color, king_square))
                    defenders = len(board.attackers(color, king_square))
                    safety += (defenders - attackers) * 20
            return safety

        def evaluate_control_center(self, board):
            center_squares = [chess.D4, chess.E4, chess.D5, chess.E5]
            white_control = sum([1 for square in center_squares if board.is_attacked_by(chess.WHITE, square)])
            black_control = sum([1 for square in center_squares if board.is_attacked_by(chess.BLACK, square)])
            return (white_control - black_control) * 30  # Weight adjustment

        def count_doubled_pawns(self, pawns, board):
            """
            Counts the number of doubled pawns for a given side.
            """
            files = [chess.square_file(pawn) for pawn in pawns]
            doubled = 0
            for file in set(files):
                count = files.count(file)
                if count > 1:
                    doubled += count - 1
            return doubled

        def evaluate_pawn_structure(self, board):
            white_pawns = board.pieces(chess.PAWN, chess.WHITE)
            black_pawns = board.pieces(chess.PAWN, chess.BLACK)
            white_doubled = self.count_doubled_pawns(white_pawns, board)
            black_doubled = self.count_doubled_pawns(black_pawns, board)
            return (-(white_doubled - black_doubled)) * 20  # Weight adjustment

        def evaluate_piece_activity(self, board):
            activity = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                for rook in white_pieces:
                    if not board.is_pinned(chess.WHITE, rook):
                        activity += 0.1 * len(board.attacks(rook))
                for rook in black_pieces:
                    if not board.is_pinned(chess.BLACK, rook):
                        activity -= 0.1 * len(board.attacks(rook))
            return activity

        def evaluate_bishop_pairs(self, board):
            white_bishops = len(board.pieces(chess.BISHOP, chess.WHITE))
            black_bishops = len(board.pieces(chess.BISHOP, chess.BLACK))
            bonus = 30
            return (white_bishops - black_bishops) * bonus

        def evaluate_positional(self, board):
            positional = 0
            for piece_type, table in self.PIECE_SQUARE_TABLE.items():
                for square in board.pieces(piece_type, chess.WHITE):
                    positional += table[square]
                for square in board.pieces(piece_type, chess.BLACK):
                    positional -= table[chess.square_mirror(square)]
            # Additional positional factors
            positional += self.evaluate_piece_activity(board)
            positional += self.evaluate_bishop_pairs(board)
            return positional

        def evaluate(self, board):
            if board.is_checkmate():
                if board.turn:
                    return -100000  # White is checkmated
                else:
                    return 100000   # Black is checkmated
            if board.is_stalemate() or board.is_insufficient_material():
                return 0  # Draw

            material = self.evaluate_material(board)
            mobility = self.evaluate_mobility(board)
            king_safety = self.evaluate_king_safety(board)
            control_center = self.evaluate_control_center(board)
            pawn_structure = self.evaluate_pawn_structure(board)
            positional = self.evaluate_positional(board)

            total_evaluation = material + mobility + king_safety + control_center + pawn_structure + positional
            logging.debug(f"Board Evaluation: Material={material}, Mobility={mobility}, "
                          f"KingSafety={king_safety}, ControlCenter={control_center}, "
                          f"PawnStructure={pawn_structure}, Positional={positional} => "
                          f"Total={total_evaluation}")
            return total_evaluation

        def is_simple_endgame(self, board):
            """
            Checks for simple endgames such as King and Pawn vs. King.
            """
            if board.is_checkmate() or board.is_stalemate():
                return True
            if len(board.piece_map()) <= 3:
                return True
            return False

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

def quantum_search(self, board: QuantumBoard, depth: int):
    if self.is_simple_endgame(board):
        endgame_move = self.get_endgame_move(board)
        if endgame_move:
            logging.info(f"Endgame move determined: {endgame_move}")
            return self.evaluate(board)

    # Check transposition table
    hash_key = self.zobrist.hash_board(board.board)
    if hash_key in self.transposition_table:
        entry = self.transposition_table[hash_key]
        if entry.depth >= depth:
            if entry.flag == "EXACT":
                logging.debug(f"Transposition table hit for exact score: {entry.score}")
                return entry.score
            elif entry.flag == "LOWERBOUND":
                logging.debug(f"Transposition table hit for lower bound: {entry.score}")
                return max(entry.score, self.evaluate(board))
            elif entry.flag == "UPPERBOUND":
                logging.debug(f"Transposition table hit for upper bound: {entry.score}")
                return min(entry.score, self.evaluate(board))

    legal_moves = self.generate_moves()
    if not legal_moves:
        eval_score = self.evaluate(board)
        return eval_score

    # Schrödinger’s Opening Book: Probabilistic selection in early game
    if board.board.fullmove_number < 10:
        opening_move = self.quantum_schrödinger_opening(board)
        if opening_move:
            board.make_move(opening_move, piece_id=None, quantum=False)
            score = self.quantum_search(board, depth - 1)
            # Store in transposition table
            self.transposition_table[hash_key] = TranspositionTableEntry(depth, score, "EXACT", opening_move)
            return score

    move_scores = {}
    for move in legal_moves:
        if isinstance(move, QuantumMove) and move.quantum:
            piece_id = self.get_quantum_piece_id(move.from_square)
            if piece_id is None:
                continue  # Cannot perform quantum move without a quantum piece
            self.board.make_move(move, piece_id=piece_id, quantum=True)
            score = self.quantum_search(board, depth - 1)
            move_scores[move] = score
            # Undo the move
            self.board.board.pop()
        else:
            self.board.make_move(move)
            score = self.quantum_search(board, depth - 1)
            move_scores[move] = score
            # Undo the move
            self.board.board.pop()

    # Select the best move
    best_move = max(move_scores, key=move_scores.get)
    best_score = move_scores[best_move]
    # Store in transposition table
    self.transposition_table[hash_key] = TranspositionTableEntry(depth, best_score, "EXACT", best_move)

    return best_score

def get_quantum_piece_id(self, square: chess.Square) -> int:
    """
    Retrieves the QuantumPiece ID at the given square, if any.
    """
    for pid, qp in self.board.quantum_pieces.items():
        if square in qp.superpositions:
            return pid
    return None

            def evaluate_move_process(move, move_scores_dict):
                board.push(move)
                hash_key_move = self.zobrist.hash_board(board)
                if hash_key_move in self.transposition_table:
                    score = self.transposition_table[hash_key_move].score
                    logging.debug(f"Transposition table hit for move {move}: {score}")
                else:
                    score = self.quantum_search(board, depth - 1)
                    with self.lock:
                        self.transposition_table[hash_key_move] = TranspositionTableEntry(depth -1, score, "EXACT", move)
                    logging.debug(f"Evaluated move {move}: {score}")
                board.pop()
                move_scores_dict[move.uci()] = score

            pool = mp.Pool(processes=mp.cpu_count())
            for move in legal_moves:
                pool.apply_async(evaluate_move_process, args=(move, move_scores))
            pool.close()
            pool.join()

            # Convert move_scores keys back to Move objects
            move_scores_converted = {chess.Move.from_uci(k): v for k, v in move_scores.items()}

            # Entanglement Heuristics
            move_scores_coordinated = self.entanglement_heuristic(move_scores_converted, board)

            # Quantum-Zobrist Hybrid
            move_scores_adjusted = self.quantum_zobrist_adjust(move_scores_coordinated)

            # Store in transposition table
            best_move, best_score = max(move_scores_adjusted.items(), key=lambda item: item[1])
            self.transposition_table[hash_key] = TranspositionTableEntry(depth, best_score, "EXACT", best_move)

            return best_score

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def get_dynamic_depth(self, board):
            # Determine search depth based on game phase
            if board.fullmove_number < 10:
                return 5  # Deeper search in the opening
            elif board.fullmove_number < 30:
                return 4  # Standard search in the middlegame
            else:
                return 3  # Shallower search in the endgame

        def get_best_move_iterative_deepening(self, board, time_limit=None, multi_pv=1):
            """
            Performs iterative deepening to find the best move within the time limit.
            """
            self.start_time = time.time()
            self.time_limit = time_limit
            best_moves = []
            depth = 1
            while True:
                if self.time_limit and (time.time() - self.start_time) >= self.time_limit:
                    logging.info("Time limit reached during iterative deepening.")
                    break
                logging.info(f"Starting search at depth {depth}")
                try:
                    move_scores = self.quantum_search(board, depth)
                    sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
                    best_moves = sorted_moves[:multi_pv]
                    logging.info(f"Depth {depth} search completed. Best moves: {best_moves}")
                    depth += 1
                    if depth > self.max_depth_setting:
                        logging.info("Maximum depth setting reached.")
                        break
                except Exception as e:
                    logging.error(f"Error during iterative deepening at depth {depth}: {e}")
                    break
            return best_moves

        def get_best_move_multi_pv(self, board, max_depth=3, multi_pv=3):
            """
            Retrieves multiple best moves based on the search.
            """
            move_scores = self.quantum_search(board, max_depth)
            sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
            best_moves = sorted_moves[:multi_pv]
            return best_moves

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def quantum_schrödinger_opening(self, board):
            openings = []
            if self.opening_book:
                try:
                    with self.opening_book as book:
                        for entry in book.find_all(board):
                            openings.append(entry.move)
                except Exception as e:
                    logging.error(f"Error reading opening book: {e}")
            if openings:
                # Assign equal probability to all available opening moves
                probabilities = [1/len(openings)] * len(openings)
                selected_move = random.choices(openings, weights=probabilities, k=1)[0]
                logging.info(f"Selected opening move from Schrödinger's Opening Book: {selected_move}")
                return selected_move
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def get_dynamic_depth(self, board):
            # Determine search depth based on game phase
            if board.fullmove_number < 10:
                return 5  # Deeper search in the opening
            elif board.fullmove_number < 30:
                return 4  # Standard search in the middlegame
            else:
                return 3  # Shallower search in the endgame

        def get_best_move_iterative_deepening(self, board, time_limit=None, multi_pv=1):
            """
            Performs iterative deepening to find the best move within the time limit.
            """
            self.start_time = time.time()
            self.time_limit = time_limit
            best_moves = []
            depth = 1
            while True:
                if self.time_limit and (time.time() - self.start_time) >= self.time_limit:
                    logging.info("Time limit reached during iterative deepening.")
                    break
                logging.info(f"Starting search at depth {depth}")
                try:
                    move_scores = self.quantum_search(board, depth)
                    sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
                    best_moves = sorted_moves[:multi_pv]
                    logging.info(f"Depth {depth} search completed. Best moves: {best_moves}")
                    depth += 1
                    if depth > self.max_depth_setting:
                        logging.info("Maximum depth setting reached.")
                        break
                except Exception as e:
                    logging.error(f"Error during iterative deepening at depth {depth}: {e}")
                    break
            return best_moves

        def get_best_move_multi_pv(self, board, max_depth=3, multi_pv=3):
            """
            Retrieves multiple best moves based on the search.
            """
            move_scores = self.quantum_search(board, max_depth)
            sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
            best_moves = sorted_moves[:multi_pv]
            return best_moves

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def quantum_schrödinger_opening(self, board):
            openings = []
            if self.opening_book:
                try:
                    with self.opening_book as book:
                        for entry in book.find_all(board):
                            openings.append(entry.move)
                except Exception as e:
                    logging.error(f"Error reading opening book: {e}")
            if openings:
                # Assign equal probability to all available opening moves
                probabilities = [1/len(openings)] * len(openings)
                selected_move = random.choices(openings, weights=probabilities, k=1)[0]
                logging.info(f"Selected opening move from Schrödinger's Opening Book: {selected_move}")
                return selected_move
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def get_dynamic_depth(self, board):
            # Determine search depth based on game phase
            if board.fullmove_number < 10:
                return 5  # Deeper search in the opening
            elif board.fullmove_number < 30:
                return 4  # Standard search in the middlegame
            else:
                return 3  # Shallower search in the endgame

        def get_best_move_iterative_deepening(self, board, time_limit=None, multi_pv=1):
            """
            Performs iterative deepening to find the best move within the time limit.
            """
            self.start_time = time.time()
            self.time_limit = time_limit
            best_moves = []
            depth = 1
            while True:
                if self.time_limit and (time.time() - self.start_time) >= self.time_limit:
                    logging.info("Time limit reached during iterative deepening.")
                    break
                logging.info(f"Starting search at depth {depth}")
                try:
                    move_scores = self.quantum_search(board, depth)
                    sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
                    best_moves = sorted_moves[:multi_pv]
                    logging.info(f"Depth {depth} search completed. Best moves: {best_moves}")
                    depth += 1
                    if depth > self.max_depth_setting:
                        logging.info("Maximum depth setting reached.")
                        break
                except Exception as e:
                    logging.error(f"Error during iterative deepening at depth {depth}: {e}")
                    break
            return best_moves

        def get_best_move_multi_pv(self, board, max_depth=3, multi_pv=3):
            """
            Retrieves multiple best moves based on the search.
            """
            move_scores = self.quantum_search(board, max_depth)
            sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
            best_moves = sorted_moves[:multi_pv]
            return best_moves

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def quantum_schrödinger_opening(self, board):
            openings = []
            if self.opening_book:
                try:
                    with self.opening_book as book:
                        for entry in book.find_all(board):
                            openings.append(entry.move)
                except Exception as e:
                    logging.error(f"Error reading opening book: {e}")
            if openings:
                # Assign equal probability to all available opening moves
                probabilities = [1/len(openings)] * len(openings)
                selected_move = random.choices(openings, weights=probabilities, k=1)[0]
                logging.info(f"Selected opening move from Schrödinger's Opening Book: {selected_move}")
                return selected_move
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def get_dynamic_depth(self, board):
            # Determine search depth based on game phase
            if board.fullmove_number < 10:
                return 5  # Deeper search in the opening
            elif board.fullmove_number < 30:
                return 4  # Standard search in the middlegame
            else:
                return 3  # Shallower search in the endgame

        def get_best_move_iterative_deepening(self, board, time_limit=None, multi_pv=1):
            """
            Performs iterative deepening to find the best move within the time limit.
            """
            self.start_time = time.time()
            self.time_limit = time_limit
            best_moves = []
            depth = 1
            while True:
                if self.time_limit and (time.time() - self.start_time) >= self.time_limit:
                    logging.info("Time limit reached during iterative deepening.")
                    break
                logging.info(f"Starting search at depth {depth}")
                try:
                    move_scores = self.quantum_search(board, depth)
                    sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
                    best_moves = sorted_moves[:multi_pv]
                    logging.info(f"Depth {depth} search completed. Best moves: {best_moves}")
                    depth += 1
                    if depth > self.max_depth_setting:
                        logging.info("Maximum depth setting reached.")
                        break
                except Exception as e:
                    logging.error(f"Error during iterative deepening at depth {depth}: {e}")
                    break
            return best_moves

        def get_best_move_multi_pv(self, board, max_depth=3, multi_pv=3):
            """
            Retrieves multiple best moves based on the search.
            """
            move_scores = self.quantum_search(board, max_depth)
            sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
            best_moves = sorted_moves[:multi_pv]
            return best_moves

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def quantum_schrödinger_opening(self, board):
            openings = []
            if self.opening_book:
                try:
                    with self.opening_book as book:
                        for entry in book.find_all(board):
                            openings.append(entry.move)
                except Exception as e:
                    logging.error(f"Error reading opening book: {e}")
            if openings:
                # Assign equal probability to all available opening moves
                probabilities = [1/len(openings)] * len(openings)
                selected_move = random.choices(openings, weights=probabilities, k=1)[0]
                logging.info(f"Selected opening move from Schrödinger's Opening Book: {selected_move}")
                return selected_move
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def get_dynamic_depth(self, board):
            # Determine search depth based on game phase
            if board.fullmove_number < 10:
                return 5  # Deeper search in the opening
            elif board.fullmove_number < 30:
                return 4  # Standard search in the middlegame
            else:
                return 3  # Shallower search in the endgame

        def get_best_move_iterative_deepening(self, board, time_limit=None, multi_pv=1):
            """
            Performs iterative deepening to find the best move within the time limit.
            """
            self.start_time = time.time()
            self.time_limit = time_limit
            best_moves = []
            depth = 1
            while True:
                if self.time_limit and (time.time() - self.start_time) >= self.time_limit:
                    logging.info("Time limit reached during iterative deepening.")
                    break
                logging.info(f"Starting search at depth {depth}")
                try:
                    move_scores = self.quantum_search(board, depth)
                    sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
                    best_moves = sorted_moves[:multi_pv]
                    logging.info(f"Depth {depth} search completed. Best moves: {best_moves}")
                    depth += 1
                    if depth > self.max_depth_setting:
                        logging.info("Maximum depth setting reached.")
                        break
                except Exception as e:
                    logging.error(f"Error during iterative deepening at depth {depth}: {e}")
                    break
            return best_moves

        def get_best_move_multi_pv(self, board, max_depth=3, multi_pv=3):
            """
            Retrieves multiple best moves based on the search.
            """
            move_scores = self.quantum_search(board, max_depth)
            sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
            best_moves = sorted_moves[:multi_pv]
            return best_moves

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def quantum_schrödinger_opening(self, board):
            openings = []
            if self.opening_book:
                try:
                    with self.opening_book as book:
                        for entry in book.find_all(board):
                            openings.append(entry.move)
                except Exception as e:
                    logging.error(f"Error reading opening book: {e}")
            if openings:
                # Assign equal probability to all available opening moves
                probabilities = [1/len(openings)] * len(openings)
                selected_move = random.choices(openings, weights=probabilities, k=1)[0]
                logging.info(f"Selected opening move from Schrödinger's Opening Book: {selected_move}")
                return selected_move
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def get_dynamic_depth(self, board):
            # Determine search depth based on game phase
            if board.fullmove_number < 10:
                return 5  # Deeper search in the opening
            elif board.fullmove_number < 30:
                return 4  # Standard search in the middlegame
            else:
                return 3  # Shallower search in the endgame

        def get_best_move_iterative_deepening(self, board, time_limit=None, multi_pv=1):
            """
            Performs iterative deepening to find the best move within the time limit.
            """
            self.start_time = time.time()
            self.time_limit = time_limit
            best_moves = []
            depth = 1
            while True:
                if self.time_limit and (time.time() - self.start_time) >= self.time_limit:
                    logging.info("Time limit reached during iterative deepening.")
                    break
                logging.info(f"Starting search at depth {depth}")
                try:
                    move_scores = self.quantum_search(board, depth)
                    sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
                    best_moves = sorted_moves[:multi_pv]
                    logging.info(f"Depth {depth} search completed. Best moves: {best_moves}")
                    depth += 1
                    if depth > self.max_depth_setting:
                        logging.info("Maximum depth setting reached.")
                        break
                except Exception as e:
                    logging.error(f"Error during iterative deepening at depth {depth}: {e}")
                    break
            return best_moves

        def get_best_move_multi_pv(self, board, max_depth=3, multi_pv=3):
            """
            Retrieves multiple best moves based on the search.
            """
            move_scores = self.quantum_search(board, max_depth)
            sorted_moves = sorted(move_scores.items(), key=lambda item: item[1], reverse=True)
            best_moves = sorted_moves[:multi_pv]
            return best_moves

        def get_endgame_move(self, board):
            """
            Provides the best move for simple endgames like King and Pawn vs. King.
            This is a simplified implementation and doesn't cover all scenarios.
            """
            white_pawns = list(board.pieces(chess.PAWN, chess.WHITE))
            black_pawns = list(board.pieces(chess.PAWN, chess.BLACK))
            if white_pawns and not black_pawns:
                pawn = white_pawns[0]
                promotion_square = chess.square_rank(pawn) == 6
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 7:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            elif black_pawns and not white_pawns:
                pawn = black_pawns[0]
                promotion_square = chess.square_rank(pawn) == 1
                for move in board.pseudo_legal_moves:
                    if move.from_square == pawn:
                        if chess.square_rank(move.to_square) == 0:
                            if promotion_square:
                                return chess.Move(pawn, move.to_square, promotion=chess.QUEEN)
            return None

        def quantum_schrödinger_opening(self, board):
            openings = []
            if self.opening_book:
                try:
                    with self.opening_book as book:
                        for entry in book.find_all(board):
                            openings.append(entry.move)
                except Exception as e:
                    logging.error(f"Error reading opening book: {e}")
            if openings:
                # Assign equal probability to all available opening moves
                probabilities = [1/len(openings)] * len(openings)
                selected_move = random.choices(openings, weights=probabilities, k=1)[0]
                logging.info(f"Selected opening move from Schrödinger's Opening Book: {selected_move}")
                return selected_move
            return None

        def evaluate_piece_coordination(self, board):
            # Evaluate coordination based on piece support and control
            coordination = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                coordination += self.count_coordinated_pairs(white_pieces, board, chess.WHITE)
                coordination -= self.count_coordinated_pairs(black_pieces, board, chess.BLACK)
            return coordination

        def count_coordinated_pairs(self, pieces, board, color):
            count = 0
            piece_list = list(pieces)
            for i in range(len(piece_list)):
                for j in range(i + 1, len(piece_list)):
                    piece1 = piece_list[i]
                    piece2 = piece_list[j]
                    # Check if pieces are supporting each other
                    piece1_attacks = board.attacks(piece1)
                    piece2_attacks = board.attacks(piece2)
                    shared_controls = piece1_attacks & piece2_attacks
                    count += len(shared_controls)
            return count

        def entanglement_heuristic(self, move_scores, board):
            # Reward moves that contribute to piece coordination and control
            bonus = 20
            for move in move_scores:
                board.push(move)
                coordinated_pieces = self.evaluate_piece_coordination(board)
                move_scores[move] += coordinated_pieces * bonus
                board.pop()
            return move_scores

        def quantum_zobrist_adjust(self, move_scores):
            # Introduce randomness to simulate quantum uncertainty
            for move in move_scores:
                adjustment = random.uniform(-50, 50)
                move_scores[move] += adjustment
                logging.debug(f"Quantum-Zobrist adjustment for move {move}: {adjustment}")
            return move_scores

        def collapse_superposition(self, move_scores):
            # Convert move scores to probabilities using softmax
            move_list = list(move_scores.keys())
            scores = list(move_scores.values())
            max_score = max(scores)
            exp_scores = [math.exp(score - max_score) for score in scores]
            total = sum(exp_scores)
            probabilities = [score / total for score in exp_scores]

            # Select move based on probabilities
            selected_move = random.choices(move_list, weights=probabilities, k=1)[0]
            logging.info(f"Superposition collapsed to move: {selected_move} with probability {probabilities[move_list.index(selected_move)]:.4f}")
            return selected_move

        def quantum_search(self, board, depth):
            if self.is_simple_endgame(board):
                endgame_move = self.get_endgame_move(board)
                if endgame_move:
                    logging.info(f"Endgame move determined: {endgame_move}")
                    # Evaluate the board after the endgame move
                    board.push(endgame_move)
                    score = self.evaluate(board)
                    board.pop()
                    return score

            # Check transposition table
            hash_key = self.zobrist.hash_board(board)
            if hash_key in self.transposition_table:
                entry = self.transposition_table[hash_key]
                if entry.depth >= depth:
                    if entry.flag == "EXACT":
                        logging.debug(f"Transposition table hit for exact score: {entry.score}")
                        return entry.score
                    elif entry.flag == "LOWERBOUND":
                        logging.debug(f"Transposition table hit for lower bound: {entry.score}")
                        return max(entry.score, self.evaluate(board))
                    elif entry.flag == "UPPERBOUND":
                        logging.debug(f"Transposition table hit for upper bound: {entry.score}")
                        return min(entry.score, self.evaluate(board))

            legal_moves = list(board.legal_moves)
            if not legal_moves:
                eval_score = self.evaluate(board)
                return eval_score

            # Schrödinger’s Opening Book: Probabilistic selection in early game
            if board.fullmove_number < 10:
                opening_move = self.quantum_schrödinger_opening(board)
                if opening_move:
                    board.push(opening_move)
                    score = self.quantum_search(board, depth - 1)
                    board.pop()
                    # Store in transposition table
                    self.transposition_table[hash_key] = TranspositionTableEntry(depth, score, "EXACT", opening_move)
                    return score

            manager = mp.Manager()
            move_scores = manager.dict()
            jobs = []

            def evaluate_move_process(move, move_scores_dict):
                board.push(move)
                hash_key_move = self.zobrist.hash_board(board)
                if hash_key_move in self.transposition_table:
                    score = self.transposition_table[hash_key_move].score
                    logging.debug(f"Transposition table hit for move {move}: {score}")
                else:
                    score = self.quantum_search(board, depth - 1)
                    with self.lock:
                        self.transposition_table[hash_key_move] = TranspositionTableEntry(depth -1, score, "EXACT", move)
                    logging.debug(f"Evaluated move {move}: {score}")
                board.pop()
                move_scores_dict[move.uci()] = score

            pool = mp.Pool(processes=mp.cpu_count())
            for move in legal_moves:
                pool.apply_async(evaluate_move_process, args=(move, move_scores))
            pool.close()
            pool.join()

            # Convert move_scores keys back to Move objects
            move_scores_converted = {chess.Move.from_uci(k): v for k, v in move_scores.items()}

            # Entanglement Heuristics
            move_scores_coordinated = self.entanglement_heuristic(move_scores_converted, board)

            # Quantum-Zobrist Hybrid
            move_scores_adjusted = self.quantum_zobrist_adjust(move_scores_coordinated)

            # Store in transposition table
            best_move, best_score = max(move_scores_adjusted.items(), key=lambda item: item[1])
            self.transposition_table[hash_key] = TranspositionTableEntry(depth, best_score, "EXACT", best_move)

            return best_score

        def evaluate_piece_activity(self, board):
            activity = 0
            for piece_type in [chess.ROOK, chess.BISHOP, chess.QUEEN]:
                white_pieces = board.pieces(piece_type, chess.WHITE)
                black_pieces = board.pieces(piece_type, chess.BLACK)
                for piece in white_pieces:
                    if not board.is_pinned(chess.WHITE, piece):
                        activity += 0.1 * len(board.attacks(piece))
                for piece in black_pieces:
                    if not board.is_pinned(chess.BLACK, piece):
                        activity -= 0.1 * len(board.attacks(piece))
            return activity

        def evaluate_bishop_pairs(self, board):
            white_bishops = len(board.pieces(chess.BISHOP, chess.WHITE))
            black_bishops = len(board.pieces(chess.BISHOP, chess.BLACK))
            bonus = 30
            return (white_bishops - black_bishops) * bonus

        def evaluate_positional(self, board):
            positional = 0
            for piece_type, table in self.PIECE_SQUARE_TABLE.items():
                for square in board.pieces(piece_type, chess.WHITE):
                    positional += table[square]
                for square in board.pieces(piece_type, chess.BLACK):
                    positional -= table[chess.square_mirror(square)]
            # Additional positional factors
            positional += self.evaluate_piece_activity(board)
            positional += self.evaluate_bishop_pairs(board)
            return positional

        def evaluate(self, board):
            if board.is_checkmate():
                if board.turn:
                    return -100000  # White is checkmated
                else:
                    return 100000   # Black is checkmated
            if board.is_stalemate() or board.is_insufficient_material():
                return 0  # Draw

            material = self.evaluate_material(board)
            mobility = self.evaluate_mobility(board)
            king_safety = self.evaluate_king_safety(board)
            control_center = self.evaluate_control_center(board)
            pawn_structure = self.evaluate_pawn_structure(board)
            positional = self.evaluate_positional(board)

            total_evaluation = material + mobility + king_safety + control_center + pawn_structure + positional
            logging.debug(f"Board Evaluation: Material={material}, Mobility={mobility}, "
                          f"KingSafety={king_safety}, ControlCenter={control_center}, "
                          f"PawnStructure={pawn_structure}, Positional={positional} => "
                          f"Total={total_evaluation}")
            return total_evaluation

        def is_simple_endgame(self, board):
            """
            Checks for simple endgames such as King and Pawn vs. King.
            """
            if board.is_checkmate() or board.is_stalemate():
                return True
            minor_pieces = sum(1 for p in board.piece_map().values() if p.piece_type in [chess.KNIGHT, chess.BISHOP])
            pawns = len(list(board.pieces(chess.PAWN, chess.WHITE))) + len(list(board.pieces(chess.PAWN, chess.BLACK)))
            queens = len(list(board.pieces(chess.QUEEN, chess.WHITE))) + len(list(board.pieces(chess.QUEEN, chess.BLACK)))
            if queens == 0 and pawns <= 1 and minor_pieces <= 1:
                return True
            return False

        def quantum_search(self, board, depth):
            if self.is_simple_endgame(board):
                endgame_move = self.get_endgame_move(board)
                if endgame_move:
                    logging.info(f"Endgame move determined: {endgame_move}")
                    # Evaluate the board after the endgame move
                    board.push(endgame_move)
                    score = self.evaluate(board)
                    board.pop()
                    return score

            # Check transposition table
            hash_key = self.zobrist.hash_board(board)
            if hash_key in self.transposition_table:
                entry = self.transposition_table[hash_key]
                if entry.depth >= depth:
                    if entry.flag == "EXACT":
                        logging.debug(f"Transposition table hit for exact score: {entry.score}")
                        return entry.score
                    elif entry.flag == "LOWERBOUND":
                        logging.debug(f"Transposition table hit for lower bound: {entry.score}")
                        return max(entry.score, self.evaluate(board))
                    elif entry.flag == "UPPERBOUND":
                        logging.debug(f"Transposition table hit for upper bound: {entry.score}")
                        return min(entry.score, self.evaluate(board))

            legal_moves = list(board.legal_moves)
            if not legal_moves:
                eval_score = self.evaluate(board)
                return eval_score

            # Schrödinger’s Opening Book: Probabilistic selection in early game
            if board.fullmove_number < 10:
                opening_move = self.quantum_schrödinger_opening(board)
                if opening_move:
                    board.push(opening_move)
                    score = self.quantum_search(board, depth - 1)
                    board.pop()
                    # Store in transposition table
                    self.transposition_table[hash_key] = TranspositionTableEntry(depth, score, "EXACT", opening_move)
                    return score

            manager = mp.Manager()
            move_scores = manager.dict()
            jobs = []

            def evaluate_move_process(move, move_scores_dict):
                board.push(move)
                hash_key_move = self.zobrist.hash_board(board)
                if hash_key_move in self.transposition_table:
                    score = self.transposition_table[hash_key_move].score
                    logging.debug(f"Transposition table hit for move {move}: {score}")
                else:
                    score = self.quantum_search(board, depth - 1)
                    with self.lock:
                        self.transposition_table[hash_key_move] = TranspositionTableEntry(depth -1, score, "EXACT", move)
                    logging.debug(f"Evaluated move {move}: {score}")
                board.pop()
                move_scores_dict[move.uci()] = score

            pool = mp.Pool(processes=mp.cpu_count())
            for move in legal_moves:
                pool.apply_async(evaluate_move_process, args=(move, move_scores))
            pool.close()
            pool.join()

            # Convert move_scores keys back to Move objects
            move_scores_converted = {chess.Move.from_uci(k): v for k, v in move_scores.items()}

            # Entanglement Heuristics
            move_scores_coordinated = self.entanglement_heuristic(move_scores_converted, board)

            # Quantum-Zobrist Hybrid
            move_scores_adjusted = self.quantum_zobrist_adjust(move_scores_coordinated)

            # Store in transposition table
            best_move, best_score = max(move_scores_adjusted.items(), key=lambda item: item[1])
            self.transposition_table[hash_key] = TranspositionTableEntry(depth, best_score, "EXACT", best_move)

            return best_score

        def uci(self):
            print("id name QuantumGambitEngine")
            print("id author OpenAI")
            print("uciok")

        def isready(self):
            print("readyok")

        def setoption(self, args):
            # Placeholder for setting options
            pass

        def go(self, args):
            # Parse 'go' command arguments for search parameters
            depth = self.depth_limit
            movetime = None
            ponder = False
            multi_pv = 1
            for i, arg in enumerate(args):
                if arg == "depth" and i + 1 < len(args):
                    try:
                        depth = int(args[i + 1])
                    except ValueError:
                        pass
                elif arg == "movetime" and i + 1 < len(args):
                    try:
                        movetime = int(args[i + 1])
                    except ValueError:
                        pass
                elif arg == "ponder":
                    ponder = True
                elif arg == "multipv" and i + 1 < len(args):
                    try:
                        multi_pv = int(args[i + 1])
                    except ValueError:
                        pass

            if movetime:
                best_moves = self.get_best_move_iterative_deepening(
                    self.board, time_limit=movetime / 1000.0, multi_pv=multi_pv
                )
                for idx, move in enumerate(best_moves):
                    print(f"info depth {self.depth_limit} multipv {idx+1} score cp {int(move[1])} pv {move[0]}")
                if best_moves:
                    print(f"bestmove {best_moves[0][0]} ponder {best_moves[0][0]}")
                else:
                    print("bestmove (none)")
                return

            # Standard search without movetime
            best_move = self.get_best_move_multi_pv(self.board, max_depth=depth, multi_pv=multi_pv)
            for idx, (move, score) in enumerate(best_move):
                print(f"info depth {depth} multipv {idx+1} score cp {int(score)} pv {move}")
            if best_move:
                print(f"bestmove {best_move[0][0]}")
            else:
                print("bestmove (none)")

        def handle_command(self, command):
            tokens = command.strip().split()
            if len(tokens) == 0:
                return
            cmd = tokens[0]
            if cmd == "uci":
                self.uci()
            elif cmd == "isready":
                self.isready()
            elif cmd == "setoption":
                self.setoption(tokens[1:])
            elif cmd == "position":
                self.set_position(tokens)
            elif cmd == "go":
                self.go(tokens[1:])
            elif cmd == "quit":
                sys.exit(0)

        def set_position(self, tokens):
            # Parses the 'position' command to set up the board
            if tokens[1] == "startpos":
                self.board.reset()
                move_start_index = 2
            elif tokens[1] == "fen":
                fen = ' '.join(tokens[2:7])
                self.board.set_fen(fen)
                move_start_index = 7
            else:
                logging.warning(f"Unsupported position command: {' '.join(tokens)}")
                return  # Unsupported position command
            if "moves" in tokens:
                moves_idx = tokens.index("moves")
                for move_uci in tokens[moves_idx + 1:]:
                    move = chess.Move.from_uci(move_uci)
                    if move in self.board.legal_moves:
                        self.board.push(move)
                        logging.info(f"Pushed move from position command: {move}")
                    else:
                        logging.warning(f"Illegal move attempted: {move_uci}")
                        break

def run(self):
    # Main loop to handle UCI commands
    while True:
        try:
            command = sys.stdin.readline().strip()
            if command:
                logging.info(f"Received command: {command}")
                self.handle_command(command)
                # Optionally collapse superpositions after handling a command
                self.maybe_collapse_superpositions()
        except EOFError:
            break
        except Exception as e:
            logging.error(f"Error handling command: {e}", exc_info=True)

if __name__ == "__main__":
    engine = QuantumChessEngine()
    engine.initialize_quantum_pieces()  # Initialize quantum pieces as per game rules

    while not engine.board.board.is_game_over():
        engine.play_turn()
        engine.maybe_collapse_superpositions()

    print("Game Over")
    print(engine.board.board.result())