code: def generate_gate_rules(gate_seq, return_as_muls=False):
      """Returns a set of gate rules.  Each gate rules is represented
      as a 2-tuple of tuples or Muls.  An empty tuple represents an arbitrary
      scalar value.
  
      This function uses the four operations (LL, LR, RL, RR)
      to generate the gate rules.
  
      A gate rule is an expression such as ABC = D or AB = CD, where
      A, B, C, and D are gates.  Each value on either side of the
      equal sign represents a circuit.  The four operations allow
      one to find a set of equivalent circuits from a gate identity.
      The letters denoting the operation tell the user what
      activities to perform on each expression.  The first letter
      indicates which side of the equal sign to focus on.  The
      second letter indicates which gate to focus on given the
      side.  Once this information is determined, the inverse
      of the gate is multiplied on both circuits to create a new
      gate rule.
  
      For example, given the identity, ABCD = 1, a LL operation
      means look at the left value and multiply both left sides by the
      inverse of the leftmost gate A.  If A is Hermitian, the inverse
      of A is still A.  The resulting new rule is BCD = A.
  
      The following is a summary of the four operations.  Assume
      that in the examples, all gates are Hermitian.
  
          LL : left circuit, left multiply
               ABCD = E -> AABCD = AE -> BCD = AE
          LR : left circuit, right multiply
               ABCD = E -> ABCDD = ED -> ABC = ED
          RL : right circuit, left multiply
               ABC = ED -> EABC = EED -> EABC = D
          RR : right circuit, right multiply
               AB = CD -> ABD = CDD -> ABD = C
  
      The number of gate rules generated is n*(n+1), where n
      is the number of gates in the sequence (unproven).
  
      Parameters
      ==========
  
      gate_seq : Gate tuple, Mul, or Number
          A variable length tuple or Mul of Gates whose product is equal to
          a scalar matrix
      return_as_muls : bool
          True to return a set of Muls; False to return a set of tuples
  
      Examples
      ========
  
      Find the gate rules of the current circuit using tuples:
  
      >>> from sympy.physics.quantum.identitysearch import generate_gate_rules
      >>> from sympy.physics.quantum.gate import X, Y, Z
      >>> x = X(0); y = Y(0); z = Z(0)
      >>> generate_gate_rules((x, x))
      {((X(0),), (X(0),)), ((X(0), X(0)), ())}
  
      >>> generate_gate_rules((x, y, z))
      {((), (X(0), Z(0), Y(0))), ((), (Y(0), X(0), Z(0))),
       ((), (Z(0), Y(0), X(0))), ((X(0),), (Z(0), Y(0))),
       ((Y(0),), (X(0), Z(0))), ((Z(0),), (Y(0), X(0))),
       ((X(0), Y(0)), (Z(0),)), ((Y(0), Z(0)), (X(0),)),
       ((Z(0), X(0)), (Y(0),)), ((X(0), Y(0), Z(0)), ()),
       ((Y(0), Z(0), X(0)), ()), ((Z(0), X(0), Y(0)), ())}
  
      Find the gate rules of the current circuit using Muls:
  
      >>> generate_gate_rules(x*x, return_as_muls=True)
      {(1, 1)}
  
      >>> generate_gate_rules(x*y*z, return_as_muls=True)
      {(1, X(0)*Z(0)*Y(0)), (1, Y(0)*X(0)*Z(0)),
       (1, Z(0)*Y(0)*X(0)), (X(0)*Y(0), Z(0)),
       (Y(0)*Z(0), X(0)), (Z(0)*X(0), Y(0)),
       (X(0)*Y(0)*Z(0), 1), (Y(0)*Z(0)*X(0), 1),
       (Z(0)*X(0)*Y(0), 1), (X(0), Z(0)*Y(0)),
       (Y(0), X(0)*Z(0)), (Z(0), Y(0)*X(0))}
      """
  
      if isinstance(gate_seq, Number):
          if return_as_muls:
              return {(S.One, S.One)}
          else:
              return {((), ())}
  
      elif isinstance(gate_seq, Mul):
          gate_seq = gate_seq.args
  
      # Each item in queue is a 3-tuple:
      #     i)   first item is the left side of an equality
      #    ii)   second item is the right side of an equality
      #   iii)   third item is the number of operations performed
      # The argument, gate_seq, will start on the left side, and
      # the right side will be empty, implying the presence of an
      # identity.
      queue = deque()
      # A set of gate rules
      rules = set()
      # Maximum number of operations to perform
      max_ops = len(gate_seq)
  
      def process_new_rule(new_rule, ops):
          if new_rule is not None:
              new_left, new_right = new_rule
  
              if (
                  new_rule not in rules
                  and (new_right, new_left) not in rules
              ):
                  rules.add(new_rule)
              # If haven't reached the max limit on operations
              if ops + 1 < max_ops:
                  queue.append(new_rule + (ops + 1,))
  
      queue.append((gate_seq, (), 0))
      rules.add((gate_seq, ()))
  
      while len(queue) > 0:
          left, right, ops = queue.popleft()
  
          # Do a LL
          new_rule = ll_op(left, right)
          process_new_rule(new_rule, ops)
          # Do a LR
          new_rule = lr_op(left, right)
          process_new_rule(new_rule, ops)
          # Do a RL
          new_rule = rl_op(left, right)
          process_new_rule(new_rule, ops)
          # Do a RR
          new_rule = rr_op(left, right)
          process_new_rule(new_rule, ops)
  
      if return_as_muls:
          # Convert each rule as tuples into a rule as muls
          mul_rules = set()
          for rule in rules:
              left, right = rule
              mul_rules.add((Mul(*left), Mul(*right)))
  
          rules = mul_rules
  
      return rules
  
imports: from collections import deque
  from sympy.core.random import randint
  from sympy.external import import_module
  from sympy.core.basic import Basic
  from sympy.core.mul import Mul
  from sympy.core.numbers import Number, equal_valued
  from sympy.core.power import Pow
  from sympy.core.singleton import S
  from sympy.physics.quantum.represent import represent
  from sympy.physics.quantum.dagger import Dagger
label_desc: Use image node_id 8 for calling a global function with example usage: generate_gate_rules(gate_seq, return_as_muls) and returns: rules, unknown, unknown