How can I use the quantum volume to design the scale of my experiment?

Question

I am designing an experiment which involves solving a linear system of equations of the form $Ax=b$. To do this, I am using the HHL algorithm on the IBMQ system. My experiment is scalable such that the size of matrix $A$ can be as large or small as I choose it to be. I would like to tailor the size of my matrix $A$ to be as large as possible but still within the computation limit of the quantum computer that I use. My suspicion is that to determine this I need to account for the quantum volume of the IBMQ machine that I use, but I do not understand exactly how.

Here is a little more information that may be useful. My experiment is adapted from the code in this HHL tutorial describing the general method to run the algorithm (section 4A). This means that I have not optimized the algorithm in any way. That being said, an example of the resource requirements for a modestly sized matrix $A$ for my experiment are as follows:

circuit_width:   11
circuit_depth:   101
CNOT gates:      54

My question is, how can I use these numbers to determine the quantum volume required to run my experiment?

Answer 1

You can't. The quantum volume is supposed to be an average measure of the quality of the quantum computer - it doesn't tell you anything on how good it will perform on solving a certain problem. (It is even questionable whether it is telling you anything meaningful, see also Is the "Quantum Volume" a fair metric for future, elaborate, high value quantum computations?) A quantum volume of 64 tells you that circuits of random 2-qubit gates of width and depth 6 can be done more or less reliably on that device. Compare that to your depth of 101. Running any kind of half-way realistic algorithm on a quantum computer these days is basically an expensive way of rolling dice.