Inverse of Statevector.from_label in Qiskit

Question

In Qiskit I can construct a computational basis statevector in the following fashion

from qiskit.quantum_info import Statevector
sv = Statevector.from_label('10')
print(sv.data)

which gives [0.+0.j 0.+0.j 1.+0.j 0.+0.j] . If I have the data for a statevector in the computation basis, is there a built-in way to return a corresponding string? For [0.+0.j 0.+0.j 1.+0.j 0.+0.j] I should get back '10'. More generally, if the state is not in the computational basis it would be nice to get a linear combination of the basis states.

Answer 1

You can just use the constructor of the Statevector class.

sv1 = Statevector.from_label('1010')  # construct Statevector from string label

sv2 = Statevector(sv1.data)   # construct Statevector from numpy array

sv1 == sv2

returns True

Answer 2

The output is a bit ugly but I think basically does what you want:

import numpy as np
from qiskit.quantum_info import random_statevector
sv = random_statevector(4)


s = ""
for state, amp in enumerate(sv.data):
    if not np.isclose(amp, 0):
        s += f"+ ({amp:.2f})|{state:0{sv.num_qubits}b}⟩ "
print(s)

output:

+ (0.34-0.22j)|00⟩ + (-0.53-0.34j)|01⟩ + (0.43-0.24j)|10⟩ + (-0.12-0.42j)|11⟩ 

You can make this smarter and neater if you need.