# Grover's algorithm outputting random/incorrect results

I am sorry if this question is trivial, I am relatively new to QC. Here is my grover's circuit, as you can see it is displaying that it has a 100% probability of measuring 100

however when placed into the quantum simulator (IBMQ statevector) here is the result:

I am stumped as to why this is the case. it clearly displays 100% output probability which means the algorithm is working right? Or am I missing something fundamental?

Edit:

OKAY? I fixed it somehow? by getting rid of the bottom H gate? I am even more confused than I was before. Why is this working, how does this work?

• This link might be helpful, I think. Jun 20 at 12:00

## 1 Answer

As @narip already mentioned in the comments, the statevector simulator of the IQX (your top picture) shows that one state has 100% measure probability since you added measurements and thus the state collapses. You should only add measurements for shot-based readouts, not if you do statevector simulations.

Regarding your question about the Hadamard gate: I think there are actually some Hadamards missing! Based on your circuit I assume the oracle/boolean function you want to implement is $$f(x_1, x_2) = x_1 \text{ and } x_2$$. The Toffoli gate with surrounding X gates you implemented indeed flips a target qubit if both qubit 1 and 2 are 0. But keep in mind that Grover's oracle must do phaseflip and not a bitflip! To convert your oracle you should add two Hadamards around the target qubit, to be

        ┌───┐     ┌───┐
x_1: ┤ X ├──■──┤ X ├
├───┤  │  ├───┤
x_2: ┤ X ├──■──┤ X ├
├───┤┌─┴─┐├───┤
target: ┤ H ├┤ X ├┤ H ├
└───┘└───┘└───┘


And on top of that, you should have an initial layer of Hadamards, to initialize in an equal superposition. In total your circuit would be something like

        ┌───┐┌───┐     ┌───┐┌───┐┌───┐     ┌───┐┌───┐
x_1: ┤ H ├┤ X ├──■──┤ X ├┤ H ├┤ X ├──■──┤ X ├┤ H ├────
├───┤├───┤  │  ├───┤├───┤├───┤  │  ├───┤├───┤
x_2: ┤ H ├┤ X ├──■──┤ X ├┤ H ├┤ X ├──■──┤ X ├┤ H ├────
├───┤├───┤┌─┴─┐├───┤└───┘└───┘     └───┘└───┘
target: ┤ H ├┤ H ├┤ X ├┤ H ├─────────────────────────────
└───┘└───┘└───┘└───┘