code: def generate_equivalent_ids(gate_seq, return_as_muls=False):
      """Returns a set of equivalent gate identities.
  
      A gate identity is a quantum circuit such that the product
      of the gates in the circuit is equal to a scalar value.
      For example, XYZ = i, where X, Y, Z are the Pauli gates and
      i is the imaginary value, is considered a gate identity.
  
      This function uses the four operations (LL, LR, RL, RR)
      to generate the gate rules and, subsequently, to locate equivalent
      gate identities.
  
      Note that all equivalent identities are reachable in n operations
      from the starting gate identity, where n is the number of gates
      in the sequence.
  
      The max number of gate identities is 2n, 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 as Muls; False to return as tuples
  
      Examples
      ========
  
      Find equivalent gate identities from the current circuit with tuples:
  
      >>> from sympy.physics.quantum.identitysearch import generate_equivalent_ids
      >>> from sympy.physics.quantum.gate import X, Y, Z
      >>> x = X(0); y = Y(0); z = Z(0)
      >>> generate_equivalent_ids((x, x))
      {(X(0), X(0))}
  
      >>> generate_equivalent_ids((x, y, z))
      {(X(0), Y(0), Z(0)), (X(0), Z(0), Y(0)), (Y(0), X(0), Z(0)),
       (Y(0), Z(0), X(0)), (Z(0), X(0), Y(0)), (Z(0), Y(0), X(0))}
  
      Find equivalent gate identities from the current circuit with Muls:
  
      >>> generate_equivalent_ids(x*x, return_as_muls=True)
      {1}
  
      >>> generate_equivalent_ids(x*y*z, return_as_muls=True)
      {X(0)*Y(0)*Z(0), X(0)*Z(0)*Y(0), Y(0)*X(0)*Z(0),
       Y(0)*Z(0)*X(0), Z(0)*X(0)*Y(0), Z(0)*Y(0)*X(0)}
      """
  
      if isinstance(gate_seq, Number):
          return {S.One}
      elif isinstance(gate_seq, Mul):
          gate_seq = gate_seq.args
  
      # Filter through the gate rules and keep the rules
      # with an empty tuple either on the left or right side
  
      # A set of equivalent gate identities
      eq_ids = set()
  
      gate_rules = generate_gate_rules(gate_seq)
      for rule in gate_rules:
          l, r = rule
          if l == ():
              eq_ids.add(r)
          elif r == ():
              eq_ids.add(l)
  
      if return_as_muls:
          convert_to_mul = lambda id_seq: Mul(*id_seq)
          eq_ids = set(map(convert_to_mul, eq_ids))
  
      return eq_ids
  
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 9 for calling a global function with example usage: generate_equivalent_ids(gate_seq, return_as_muls) and returns: eq_ids, unknown