diff --git a/doc/GeneralizedStabilizer.py b/doc/GeneralizedStabilizer.py new file mode 100644 index 0000000..92010dc --- /dev/null +++ b/doc/GeneralizedStabilizer.py @@ -0,0 +1,134 @@ +class GraphState: + def __init__(self, num_qubits): + self.num_qubits = num_qubits + self.stabilizers = [self._initial_stabilizer(i) for i in range(num_qubits)] + self.destabilizers = [self._initial_destabilizer(i) for i in range(num_qubits)] + self.active_stabilizers = {i: True for i in range(num_qubits)} + self.active_destabilizers = {i: True for i in range(num_qubits)} + + def _initial_stabilizer(self, i): + """Create initial stabilizer for qubit i: Z_i (all Zs except for an X at position i).""" + return ['I'] * i + ['Z'] + ['I'] * (self.num_qubits - i - 1) + + def _initial_destabilizer(self, i): + """Create initial destabilizer for qubit i: X_i (all Is except for an X at position i).""" + return ['I'] * i + ['X'] + ['I'] * (self.num_qubits - i - 1) + + def apply_gate(self, gate, *args): + if gate == 'H': + qubit_index = args[0] + self._apply_hadamard(qubit_index) + elif gate == 'S': + qubit_index = args[0] + self._apply_phase(qubit_index) + elif gate == 'CZ': + qubit_index1, qubit_index2 = args + self._apply_controlled_z(qubit_index1, qubit_index2) + elif gate == 'CNOT': + control, target = args + self._apply_cnot(control, target) + else: + raise ValueError(f"Unsupported gate: {gate}") + + def _apply_hadamard(self, qubit_index): + for stabilizer in self.stabilizers: + if stabilizer[qubit_index] == 'X': + stabilizer[qubit_index] = 'Z' + elif stabilizer[qubit_index] == 'Z': + stabilizer[qubit_index] = 'X' + for destabilizer in self.destabilizers: + if destabilizer[qubit_index] == 'X': + destabilizer[qubit_index] = 'Z' + elif destabilizer[qubit_index] == 'Z': + destabilizer[qubit_index] = 'X' + + def _apply_phase(self, qubit_index): + for stabilizer in self.stabilizers: + if stabilizer[qubit_index] == 'X': + stabilizer[qubit_index] = 'Y' + elif stabilizer[qubit_index] == 'Y': + stabilizer[qubit_index] = 'X' + for destabilizer in self.destabilizers: + if destabilizer[qubit_index] == 'X': + destabilizer[qubit_index] = 'Y' + elif destabilizer[qubit_index] == 'Y': + destabilizer[qubit_index] = 'X' + + def _apply_controlled_z(self, qubit_index1, qubit_index2): + for stabilizer in self.stabilizers: + if stabilizer[qubit_index1] == 'X' and stabilizer[qubit_index2] == 'X': + stabilizer[qubit_index2] = 'Z' + elif stabilizer[qubit_index1] == 'Z' and stabilizer[qubit_index2] == 'Z': + stabilizer[qubit_index1] = 'X' + for destabilizer in self.destabilizers: + if destabilizer[qubit_index1] == 'X' and destabilizer[qubit_index2] == 'X': + destabilizer[qubit_index2] = 'Z' + elif destabilizer[qubit_index1] == 'Z' and destabilizer[qubit_index2] == 'Z': + destabilizer[qubit_index1] = 'X' + + def _apply_cnot(self, control, target): + for stabilizer in self.stabilizers: + if stabilizer[control] == 'X': + if stabilizer[target] == 'I': + stabilizer[target] = 'X' + elif stabilizer[target] == 'X': + stabilizer[target] = 'I' + elif stabilizer[target] == 'Z': + stabilizer[target] = 'Y' + elif stabilizer[target] == 'Y': + stabilizer[target] = 'Z' + elif stabilizer[control] == 'Z': + if stabilizer[target] == 'I': + stabilizer[target] = 'Z' + elif stabilizer[target] == 'Z': + stabilizer[target] = 'I' + elif stabilizer[target] == 'X': + stabilizer[target] = 'Y' + elif stabilizer[target] == 'Y': + stabilizer[target] = 'X' + for destabilizer in self.destabilizers: + if destabilizer[control] == 'X': + if destabilizer[target] == 'I': + destabilizer[target] = 'X' + elif destabilizer[target] == 'X': + destabilizer[target] = 'I' + elif destabilizer[target] == 'Z': + destabilizer[target] = 'Y' + elif destabilizer[target] == 'Y': + destabilizer[target] = 'Z' + elif destabilizer[control] == 'Z': + if destabilizer[target] == 'I': + destabilizer[target] = 'Z' + elif destabilizer[target] == 'Z': + destabilizer[target] = 'I' + elif destabilizer[target] == 'X': + destabilizer[target] = 'Y' + elif destabilizer[target] == 'Y': + destabilizer[target] = 'X' + + def measure(self, qubit_index): + stabilizer = self.stabilizers[qubit_index] + return '0' if stabilizer[qubit_index] == 'Z' else '1' + + def __str__(self): + stabs = '\n'.join([' '.join(stabilizer) for stabilizer in self.stabilizers]) + destabs = '\n'.join([' '.join(destabilizer) for destabilizer in self.destabilizers]) + return f'Stabilizers:\n{stabs}\n\nDestabilizers:\n{destabs}' + +# Usage +gs_state = GraphState(3) +print("Initial stabilizers and destabilizers:") +print(gs_state) + +# Apply Clifford gates +gs_state.apply_gate('H', 0) +gs_state.apply_gate('S', 1) +gs_state.apply_gate('CZ', 1, 2) +print("\nState after applying Clifford gates:") +print(gs_state) + +# Apply non-Clifford gates +gs_state.apply_gate('H', 0) +gs_state.apply_gate('CNOT', 1, 2) +print("\nState after applying non-Clifford gates:") +print(gs_state) diff --git a/generalized_stabilizer_state.py b/generalized_stabilizer_state.py new file mode 100644 index 0000000..3578631 --- /dev/null +++ b/generalized_stabilizer_state.py @@ -0,0 +1,221 @@ +# Define the Pauli matrices +Pauli_I = np.array([[1, 0], [0, 1]]) +Pauli_X = np.array([[0, 1], [1, 0]]) +Pauli_Y = np.array([[0, -1j], [1j, 0]]) +Pauli_Z = np.array([[1, 0], [0, -1]]) + +# Define the single-qubit Clifford gates +Clifford_gates = { + 'I': Pauli_I, + 'X': Pauli_X, + 'Y': Pauli_Y, + 'Z': Pauli_Z, + 'H': 1/np.sqrt(2) * (Pauli_X + Pauli_Z), + 'S': Pauli_Z, + 'T': np.array([[1, 0], [0, np.exp(1j * np.pi / 4)]]) +} + + +class GeneralizedStabilizerState: + """ + Class representing a generalized stabilizer state in a quantum system. + + Attributes: + num_qubits (int): Number of qubits in the state. + stabilizers (list): List of stabilizer generators (strings of Pauli operators). + phase (list): List of phase indicators (0 or 1). + + Methods: + __init__(self, num_qubits): + Initializes a GeneralizedStabilizerState object with given number of qubits. + + apply_clifford_map(self, clifford_map): + Applies a Clifford map to the stabilizer state. + + apply_gate(self, gate, *args): + Applies a single-qubit or two-qubit gate to the stabilizer state. + + measure(self, qubit_index): + Measures a qubit and updates the stabilizers and phases accordingly. + + __str__(self): + Returns a string representation of the GeneralizedStabilizerState object. + """ + + def __init__(self, num_qubits): + """ + Initialize a GeneralizedStabilizerState object. + + Args: + num_qubits (int): Number of qubits in the state. + """ + self.num_qubits = num_qubits + self.stabilizers = ['I' * num_qubits] # Initialize with the identity stabilizer + self.phase = [0] * num_qubits # Initialize with all phases set to 0 + + def apply_clifford_map(self, clifford_map): + """ + Apply a Clifford map to the stabilizer state. + + Args: + clifford_map (dict): Dictionary specifying the Clifford operations to apply. + + Returns: + GeneralizedStabilizerState: Updated state after applying the Clifford map. + """ + new_stabilizers = [] + new_phase = self.phase[:] # Copy current phase + + for g, p in zip(self.stabilizers, self.phase): + new_g, _ = self.apply_single_clifford(g, p, clifford_map) + new_stabilizers.append(new_g) + + return GeneralizedStabilizerState(self.num_qubits)._from_stabilizers(new_stabilizers, new_phase) + + def apply_single_clifford(self, g, p, clifford_map): + """ + Apply a single Clifford operation to a stabilizer generator. + + Args: + g (str): Stabilizer generator (string of Pauli operators). + p (int): Phase indicator (0 or 1). + clifford_map (dict): Dictionary specifying the Clifford operations to apply. + + Returns: + str: Updated stabilizer generator after applying the Clifford operation. + int: Updated phase after applying the Clifford operation. + """ + new_g = [] + for char in g: + if char == 'I': + new_g.append('I') + elif len(char) >= 2: + qubit_index = int(char[1]) + if char[0] in clifford_map: + new_g.append(clifford_map[char[0]][qubit_index]) + else: + new_g.append('I') # If the character doesn't match known patterns, default to 'I' + else: + new_g.append('I') # If the character doesn't match known patterns, default to 'I' + + return ''.join(new_g), p + + def apply_gate(self, gate, *args): + """ + Apply a gate (single-qubit or two-qubit) to the stabilizer state. + + Args: + gate (str): Gate to apply ('H', 'X', 'Y', 'Z', 'S', 'T', 'CNOT'). + *args: Qubit index/indices for single-qubit/two-qubit gates. + + Raises: + ValueError: If an unsupported gate is provided. + """ + if gate in Clifford_gates: + gate_matrix = Clifford_gates[gate] + + if len(args) == 1: # Single-qubit gate + qubit_index = args[0] + for i in range(len(self.stabilizers)): + if self.stabilizers[i][qubit_index] == 'X': + self.stabilizers[i] = self.stabilizers[i][:qubit_index] + gate + self.stabilizers[i][qubit_index + 1:] + elif self.stabilizers[i][qubit_index] == 'Y': + self.stabilizers[i] = self.stabilizers[i][:qubit_index] + gate + self.stabilizers[i][qubit_index + 1:] + self.phase[i] = (self.phase[i] + 1) % 2 + elif self.stabilizers[i][qubit_index] == 'Z': + self.phase[i] = (self.phase[i] + 1) % 2 + + elif len(args) == 2 and gate == 'CNOT': # Two-qubit CNOT gate + control_qubit = args[0] + target_qubit = args[1] + for i in range(len(self.stabilizers)): + if self.stabilizers[i][control_qubit] == 'X': + self.stabilizers[i] = self.stabilizers[i][:control_qubit] + 'X' + self.stabilizers[i][control_qubit + 1:] + self.stabilizers[i] = self.stabilizers[i][:target_qubit] + 'X' + self.stabilizers[i][target_qubit + 1:] + elif self.stabilizers[i][control_qubit] == 'Y': + self.stabilizers[i] = self.stabilizers[i][:control_qubit] + 'Y' + self.stabilizers[i][control_qubit + 1:] + self.stabilizers[i] = self.stabilizers[i][:target_qubit] + 'Y' + self.stabilizers[i][target_qubit + 1:] + self.phase[i] = (self.phase[i] + 1) % 2 + elif self.stabilizers[i][control_qubit] == 'Z': + self.stabilizers[i] = self.stabilizers[i][:target_qubit] + 'Z' + self.stabilizers[i][target_qubit + 1:] + + else: + raise ValueError(f"Unsupported gate: {gate}") + + else: + raise ValueError(f"Unsupported gate: {gate}") + + def measure(self, qubit_index): + """ + Measure a qubit and update the stabilizers and phase accordingly. + + Args: + qubit_index (int): Index of the qubit to measure. + """ + for i in range(len(self.stabilizers)): + if self.stabilizers[i][qubit_index] == 'X' or self.stabilizers[i][qubit_index] == 'Y': + self.phase[i] = (self.phase[i] + 1) % 2 + self.stabilizers[i] = self.stabilizers[i][:qubit_index] + 'I' + self.stabilizers[i][qubit_index + 1:] + + def _from_stabilizers(self, stabilizers, phase): + """ + Internal method to create a new GeneralizedStabilizerState from stabilizers and phase. + + Args: + stabilizers (list): List of stabilizer generators. + phase (list): List of phase indicators. + + Returns: + GeneralizedStabilizerState: New instance of GeneralizedStabilizerState. + """ + state = GeneralizedStabilizerState(self.num_qubits) + state.stabilizers = stabilizers + state.phase = phase + return state + + def __str__(self): + """ + Return a string representation of the GeneralizedStabilizerState object. + + Returns: + str: String representation of the state. + """ + output = [] + for g in self.stabilizers: + output.append(f" +{g}") + return "\n".join(output) + + +if __name__ == "__main__": + # Example usage + num_qubits = 3 + + # Create an initial state + gs_state = GeneralizedStabilizerState(num_qubits) + gs_state.stabilizers = ['XIZ', 'ZXX', 'YIZ'] + gs_state.phase = [0, 1, 0] + + print("Initial state:") + print(gs_state) + + # Apply a Clifford map + clifford_map = { + 'X0': '+IIXI', 'Y0': '+IIYI', 'Z0': '+IIZI', + 'X1': '+IXII', 'Y1': '+IYII', 'Z1': '+IIZI', + 'X2': '+IXII', 'Y2': '+IYII', 'Z2': '+IIZI' + } + + gs_state.apply_clifford_map(clifford_map) + print("\nState after applying Clifford map:") + print(gs_state) + + # Apply non-Clifford gates + gs_state.apply_gate('H', 0) + gs_state.apply_gate('CNOT', 1, 2) + print("\nState after applying non-Clifford gates:") + print(gs_state) + + # Measure qubit 0 + gs_state.measure(0) + print("\nState after measuring qubit 0:") + print(gs_state)