Grover, Qiskit, general definition of "good state"

Question

Trying to implement Grover under Qiskit I found an example with good_state = ['110','101'] For a given $n$ it possible to define good_state as "any string of $n$ bits whose last bit is 1"? And if so, how?

Answer 1

Yes, there's two options:

1. Define the good state as "1" and use only the last bit as objective qubit:

from qiskit.algorithms import EstimationProblem

stateprep = # your state preparation, or "A" operator
n = # index of your target qubit
problem = EstimationProblem(stateprep, objective_qubits=[n])  
# the good state default is 1, so you don't need to specify it, but if you want to:
# problem = EstimationProblem(stateprep, objective_qubits=[n], is_good_state="1") 

2. Define the is_good_state via a function

from qiskit.algorithms import EstimationProblem

stateprep = # your state preparation, or "A" operator
n = # index of your target qubit

def is_good_state(bitstring):
    return bitstring[n] == "1"  # note: maybe the bitstring needs to be reverted

problem = EstimationProblem(stateprep, objective_qubits=list(range(n)), is_good_state=is_good_state) 

I would strongly suggest option 1, that'll generate the more efficient circuits.