Average execution time for T gate

Using the Q# resource estimator, I found out that my program, meant to do graph coloring using Grover's algorithm, could be decomposed into ~500-1000*x T gates, where x in the number of iterations, often ranging between 5 and 10. This means I am considering thousands of T gates.

I am considering T gates because they can be a universal gate when paired with the Clifford group which is easy to simulate.

I am interested to know the average time it would take for a quantum computer (any type) to execute one of these T gates, time which I would then multiply to estimate the runtime of my program.

• Even though there is a T-count, this often isn't necessarily a good approximation of runtime cost - notably, if you have a multiply controlled NOT gate, Q# will incur T-costs, but your architecture may be able to apply the CCNOT natively Oct 25 '20 at 23:53
• Is the question here more about just framing the time cost of your program? Because if so, it's safe to say the runtime will likely be within hours/minutes (rather than days/weeks) Oct 25 '20 at 23:54
• @C.Kang I was more interested about the difference between a simulation and a real quantum computer in 10 node graph situation Oct 26 '20 at 13:01
• Ah, in that case the quantum computer will run almost certainly much faster than your simulation. Gates typically take on the order of ms / ns to apply Oct 26 '20 at 15:55
• @C.Kang what would a good runtime cost approximation be then ? I have to do this for a paper, since I tested graphs from size 1-8, I would like to generalize my results. I saw that there was a resource estimator built in, and I thought I was made for this kind thing. However, I have troubles evaluating what every character means (I am referring to the first comment) Oct 26 '20 at 18:42