How to run on NISQ

Since current quantum hardware lacks support for repeat-until-success protocols, this example demonstrates how to implement block encodings on NISQ devices using post-selection.

Define a block encoding for a Heisenberg Hamiltonian and apply it to an initial system state.

from qrisp import *
from qrisp.block_encodings import BlockEncoding
from qrisp.operators import X, Y, Z

H = sum(X(i)*X(i+1) + Y(i)*Y(i+1) + Z(i)*Z(i+1) for i in range(3))
BE = BlockEncoding.from_operator(H)

# Prepare initial system state
operand = QuantumFloat(4)
h(operand[0])

# Apply the operator to an initial system state
ancillas = BE.apply(operand)

Utilize the Qrisp Backend Interface to define a backend. While this example uses the Qiskit Aer simulator, the interface also supports physical quantum backends.

from qrisp.interface import QiskitBackend
from qiskit_aer import AerSimulator
example_backend = QiskitBackend(backend = AerSimulator())

# Use backend keyword to specify quantum backend
res_dict = multi_measurement([operand] + ancillas,
                            shots=1000,
                            backend=example_backend)

# Post-selection on ancillas being in |0> state
filtered_dict = {k[0]: p for k, p in res_dict.items() \
                if all(x == 0 for x in k[1:])}
success_prob = sum(filtered_dict.values())
filtered_dict = {k: p / success_prob for k, p in filtered_dict.items()}
filtered_dict

Note that the limited number of shots leads to significant statistical variance in the output distribution.