How to generate statevector evolution?

Question

I have created the following 2-qubit circuit in qiskit:

import numpy as np
import matplotlib.pyplot as plt
import warnings
warnings.filterwarnings('ignore')

from qiskit import QuantumCircuit, QuantumRegister, Aer, transpile, assemble
from qiskit.providers.aer import AerSimulator
from qiskit.providers.aer.library import save_statevector

# XX(t) subcircuit
def XX(target_time):
    XX_qr = QuantumRegister(2)
    XX_qc = QuantumCircuit(XX_qr, name='XX')

    XX_qc.ry(np.pi/2,[0,1])
    XX_qc.cnot(0,1)
    XX_qc.rz(2*target_time,1)
    XX_qc.cnot(0,1)
    XX_qc.ry(-np.pi/2,[0,1])
    return XX_qc

# YY(t) subcircuit
def YY(target_time):
    YY_qr = QuantumRegister(2)
    YY_qc = QuantumCircuit(YY_qr, name='YY')

    YY_qc.rx(np.pi/2,[0,1])
    YY_qc.cnot(0,1)
    YY_qc.rz(2*target_time,1)
    YY_qc.cnot(0,1)
    YY_qc.rx(-np.pi/2,[0,1])
    return YY_qc

# ZZ(t) subcircuit
def ZZ(target_time):
    ZZ_qr = QuantumRegister(2)
    ZZ_qc = QuantumCircuit(ZZ_qr, name='ZZ')

    ZZ_qc.cnot(0,1)
    ZZ_qc.rz(2*target_time,1)
    ZZ_qc.cnot(0,1)
    return ZZ_qc

# create ZZ(t)YY(t)XX(t) circuit and prepare in initial state
def quantum_circuit(target_time, num_qubits, initial_state):
    # initialize quantum circuit for 2 qubits
    qr = QuantumRegister(num_qubits)
    qc = QuantumCircuit(qr)
    # initialize circuit
    qc.initialize(initial_state)
    # construct circuit from ZZ(t), YY(t), and XX(t) subcircuits
    for i in range(0, num_qubits - 1):
        qc.append(ZZ(target_time), [qr[i], qr[i+1]])
        qc.append(YY(target_time), [qr[i], qr[i+1]])
        qc.append(XX(target_time), [qr[i], qr[i+1]])
    # measure qubits
    qc.measure_all()
    return qc

# create circuit
qc = quantum_circuit(target_time=0.0, num_qubits=2, initial_state='10')
print(qc)

I transpile, assemble, and pass this to the Aer statevector_simulator:

backend = Aer.get_backend('statevector_simulator')
qobj = transpile(qc,backend)
job = assemble(qobj)
run_job = backend.run(job)

When I do this, I get the following error: ERROR: Failed to load qobj: Unable to cast Python instance to C++ type (compile in debug mode for details).

In this particular circuit, I am initializing it in the |10> state. In the code that I have provided here, I am initializing the state using the QuantumCircuit.initialize() method. However, when I initialize the state to |10> by just adding an x gate to the second qubit, there is no problem. It runs fine.

Ultimately, I am trying to find a way to initialize the circuit in some state, run it at time=0, extract the final state, and then run it at some later time, where the final state is now the initial state. Where I am stuck is initializing the circuit evaluated at t=t0+dt with the final state of the circuit evaluated at t (for example). In essence, I am trying to evaluate unitary time evolution of the state: |psi(t+dt)>=U|psi(t)>.

So... my question is two fold: 1.) Why am I getting this Failed to load qobj: Unable to cast Python instance to C++ type (compile in debug mode for details) error? How can I fix this? 2.) How can I generate this state evolution?

Answer 1

1.) Why am I getting this Failed to load qobj: Unable to cast Python instance to C++ type (compile in debug mode for details) error? How can I fix this?

Initializing a circuit via circuit.initialize() with labels makes the simulation fail. See here.

2.) How can I generate this state evolution?

Just replace this line

qc = quantum_circuit(target_time=0.0, num_qubits=2, initial_state='10')

with

qc = quantum_circuit(target_time=0.0, num_qubits=2, initial_state=[0, 0, 1, 0])

or,

from qiskit.quantum_info import Statevector
qc = quantum_circuit(target_time=0.0, num_qubits=2, initial_state=Statevector.from_label('10'))