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"Fig. 2 shows the circuit that was designed to fit the ibmqx4 quantum computer. The circuit consists of state
preparation (first two time slots), a Toffoli gate (the next 13 time slots), followed by the
2
|
ψ
〉〈
ψ
|−
I
operator (7 time
slots), and measurement (the final 2 time slots). We use
q
[0]
(in the register notation from Fig. 2) as the ancillary bit,
q
, and
q
[1]
and
q
[2]
as
x
1
and
x
2
. Note that the quantum computer imposes constraints on the possible source and
target of CNOT gates. Some care must be taken to choose the appropriate qubits to represent each variable so that
the necessary CNOT gates can be implemented. It is possible to circumvent some of the limitations in the source and
target of the CNOT gates (i.e., the source and target can be reversed), but this requires increasing the depth of the
circuit. Our initial implementation utilized a Toffoli gate that used such an approach, but the circuit was significantly
deeper and the results were inferior to the results with the circuit in Fig. 2.
"Using the simulator, this circuit produces the correct answer
x
= (1
,
1)
every time. We executed 1,024 shots using
the ibmqx4 and
x
= (1
,
1)
was obtained 662 times with
(0
,
0)
,
(0
,
1)
, and
(1
,
0)
occurring 119, 101, and 142 times
respectively. This indicates that the probability of obtaining the correct answer is approximately 65%. The deviation
between the simulator and the quantum computer is apparently due to the depth of the circuit combined with the
approximate nature of the quantum computer. We note that our first implementation of this algorithm which used a
Toffoli gate with a depth of 23 (compared to a depth of 13 here) obtained the correct answer 48% of the time."
"We designed a circuit that implements an instance of Grover’s algorithm for an IBM 5-qubit quantum computer. The
outcome was successful in the sense that the quantum computer successfully completed the search with a probability
that is appreciably greater than 50%. However, the 65% success rate that was obtained is much lower than the 100%
that is obtained by the simulator. Deeper and more complex oracles would likely produce less satisfactory results, and
this is in line with our experience implementing the oracle with a deeper implementation of the Toffoli gate."
I'm still not sure how measurement of quantum computing results works, and this isn't helping.