I recently read papers about optimizing circuits for specific quantum devices and for optimizing quantum circuits against decoherence. The first paper is about how qubits are connected differently within each quantum computer, and how you can optimize circuits by using connected qubits. The second paper is about minimizing the time between performing operations on qubits and measuring them.

I decided to run some tests to see what effects these strategies might actually have.

CAPTION: this is a screenshot from Practical Period Finding on IBM Q — Quantum Speedups in the Presence of Errors.

I ran all of these tests on my favorite quantum computer, the 14-qubit ibmq_16_melbourne, available via the cloud thanks to IBM Q Experience. I created the circuits using OpenQASM.

This first circuit was the control. This is a generic, non-device-specific circuit using qubits in order and with all measurements at the end.

This is a GHZ state controlled by qubit5. The z measurements are immediately following each CNOT gate.

This is also a GHZ state controlled by qubit5, but with all measurements at the end. The histograms are virtually identical.

This is a GHZ state controlled by qubit11 and with z measurements immediately following each CNOT gate.

This is also a GHZ state controlled by qubit11, but with all measurements at the end. The histograms are very similar, but slightly different.

The main takeaways from these tests:

1. Qubit choice matters, because using connected qubits minimizes the number of operations that need to be performed.

2. Connected qubit choice matters; the qubit5-controlled GHZ state and the qubit11-controlled GHZ state performed quite differently.

3. Although measurement placement seems to have a slight effect on the qubit11-controlled GHZ state, it shouldn’t; to my knowledge, all IBMQ measurements are performed at the end regardless of placement.

In conclusion, the first paper appears to be on to something. Controlling GHZ states with different qubits produces noticeably different results. However, the second paper seems irrelevant, at least in regard to short-length circuits on IBMQ. Perhaps a difference might be noticeable with longer circuits; although measurements cannot be moved to the left with any effect, operations can sometimes be delayed and, consequently, moved to the right, closer to the measurements. But, that’s an experiment for another day….