Optimize qubit order for better data locality

[totikom]

(This may be completely unnecessary/inapplicable, so feel free to just close it)

The performance of simulating gates on big states drastically depends on its position (i.e. it is much faster to apply H to 0th qubit of the 30-qubit state that to the 29th)

So, for "unbalanced" circuits it is very beneficial to move "the most used" qubits to lower indices.

[smu160]

Hi @totikom,

Thank you for your insight! This would be a great initial start to a "circuit optimizer" that can be run prior to executing the actual circuit. If you're interested in implementing your suggestion, you are more than welcome to submit a PR.

For the sake of completeness and posterity, I will include some other findings/insights:

In my recent tests, I found that the single-threaded performance difference is negligible whether applying H to the 0th qubit, or to the 29th qubit; however, once you throw more threads at the problem, the story changes. Applying H to the 0th qubit is 2x faster than applying H to the 29th qubit. In fact, applying H to the 29th qubit with more than a single thread degrades performance. Hence, your suggestion may be a way to fix this issue in the case where we only apply a gate to a subset of the qubits.

Note that applying a gate to the kth qubit has the same exact memory access pattern as the kth stage in the decimation-in-time FFT. I've been looking into leveraging strategies from high performance FFT implementations in order to improve data locality. In principle, we can bring all pairs right next to each-other by looking at how the FFT interleaves data-points at each stage.

This may be a way to tackle the implementation of your suggestion.

Best, Saveliy

[totikom]

Note that applying a gate to the kth qubit has the same exact memory access pattern as the kth stage in the decimation-in-time FFT. I've been looking into leveraging strategies from high performance FFT implementations in order to improve data locality. In principle, we can bring all pairs right next to each-other by looking at how the FFT interleaves data-points at each stage.

Yes! I've also though about it (I was doing a toy QC simulator for my curriculum two years ago), but I haven't found a data structure, which will "remain local" for all qubits, so I decided that it would be beneficial to reorder circuits.

Unfortunately, that course has ended and I was busy working on my Master's, so that project was abandoned.

I'll try to implement a naive optimizer for circuits and will make a PR.)

[totikom]

The optimizer can be based on a cost model, which will justify, whenever transformations are beneficial. I'm going to use LLVM VPlan as an example.

(Well, it is going to be not so naive optimizer)

[smu160]

@totikom Thank you!

I found a great resource that discusses the same data locality issue, but in the context of FFT. Please see chapter 7 in Construction of a High-Performance FFT.

Best, Saveliy