Meyer-Wallach measure

PennyLane Help
1

How can we correctly implement the standard Meyer-Wallach measure using PennyLane? We’ve been encountering difficulties in accurately calculating the final Q value. Would it be possible to provide a reference implementation of the standard Meyer-Wallach measure for guidance? Thank you. For your reference, the Meyer-Wallach measure is detailed in the following paper: https://arxiv.org/pdf/quant-ph/0305094.pdf.

2

Hey @zj-lucky!

I’m not aware of any implementations of this measure that you can reference. Maybe I can still give you a hand, though. Can you be a bit more specific / detailed here? Seeing some code would help alongside a specific equation(s) from the paper you attached.

3

Hey, use this

def entangling_capability(circuit_template, num_qubits, num_params, num_samples=1000):
    #Compute entangling capability (Q) of a parameterized quantum circuit using PennyLane.
    dev = qml.device("default.qubit", wires=num_qubits)

    @qml.qnode(dev)
    def run_circuit(params):
        circuit_template(params, wires=range(num_qubits))
        return qml.state()

    q_values = []

    for _ in range(num_samples):
        params = np.random.uniform(0, 2 * np.pi, num_params) #Generate random parameters

        
        state = run_circuit(params)#  statevector

        # Meyer-Wallach Q
        sum_purities = 0.0
        for qubit in range(num_qubits):
            
            psi = state.reshape([2] * num_qubits) #compute reduced density matrix
            psi = np.moveaxis(psi, qubit, 0).reshape(2, -1)

           
            rho = psi @ psi.conj().T #purity
            purity = np.trace(rho @ rho).real
            sum_purities += purity

        Q = 2 * (1 - sum_purities / num_qubits)
        q_values.append(Q)

    return np.mean(q_values)
4

Thanks for sharing @mitul3737! :raised_hands:

And welcome to the Forum! :waving_hand: