The error "Qubits cannot become global efficiently in this stage."

[fxfxfxfxfxfxfxfx]

When using Quartz for quantum circuit simulation compilation, I encountered the message: "1 qubit cannot become global efficiently in this stage." The issue occurs at [this line](

quartz/src/quartz/simulator/schedule.cpp

Line 2812 in cac0d3a

if (num_global_qubits_not_global > 0) {

). I don't fully understand under what circumstances this problem arises. Will this affect the correctness of the final circuit partitioning result? In other words, if this error appears, does it mean that the final partitioning result is incorrect?

[xumingkuan]

Hi @fxfxfxfxfxfxfxfx , thanks for your interest in Quartz and Atlas. This is an implementation artifact. The short answer is it won't affect the correctness.

In the Atlas paper, we partition the qubits into three sets, local/regional/global, for each stage using the ILP algorithm. However, we cannot permute the qubits arbitrarily; the cuQuantum API only supports a list of qubit pairs to be swapped. In the Atlas repo, we implement a heuristic to perform local-regional swaps and local-global swaps greedily. Ideally, we won't need any regional-global swaps after that. However, we may still need regional-global swaps (which could be viewed as simply relabeling GPUs), which need some extra handling.

In Quartz here, after the ILP, we implement the same heuristic to print out the concrete qubit order in C++, to reduce the effort Atlas has to implement in CUDA. Whenever we need regional-global swaps, the message x qubits cannot become global efficiently in this stage. is printed. This message shows that the qubit schedule should be used with extra care because regional-global swaps are present, and also signals room for improvement because theoretically we only need local-regional swaps and local-global swaps.

[fxfxfxfxfxfxfxfx]

First of all, I’d like to express my appreciation for the excellent work on Atlas. The design and implementation are truly impressive!

The conclusion that "when only regional qubits swap with global qubits while local qubits remain unchanged, no actual communication is needed—only GPU relabeling is required" is particularly insightful. I suspect that this optimization could be implemented by modifying [this line](https://github.com/quantum-compiler/atlas/blob/main/src/base/simulator.cu#L493) in simulator.cu to handle GPU relabeling.

It also seems like this might have been intentionally left as a future optimization. If that's the case, it actually resolves another question I had—why the seemingly redundant line devices[i] = i; was set. If this was indeed meant to facilitate relabeling in the future, it makes perfect sense!

Thanks again for your great work, and I’d love to hear your thoughts on this!

[xumingkuan]

I'm glad that you like our work and take the time to look into the details!

It also seems like this might have been intentionally left as a future optimization. If that's the case, it actually resolves another question I had—why the seemingly redundant line devices[i] = i; was set. If this was indeed meant to facilitate relabeling in the future, it makes perfect sense!

Yes, we were debating whether to implement this optimization or not, but we ended up not doing this because the message x qubits cannot become global efficiently in this stage. is rarely printed on the benchmarks we evaluated.

If I remember correctly, devices[i] is always i in the current implementation. @caoshiyi wrote this part of the code and maybe she can either confirm or point out something I forgot.

[fxfxfxfxfxfxfxfx]

Thanks for your response!

You remember correctly—devices[i] is indeed always i in the current implementation. I had also explored this optimization before, and my conclusions aligned with yours. This situation does seem to be quite rare in commonly used benchmarks.

Looking forward to more great work from you！