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As far as I understood from a series of papers, minimizing the T-count in Clifford+T circuits is essential for fault-tolerant quantum computing:

While techniques such as magic state distillation and injection allow for fault-tolerant implementation of T gates, they typically require an order of magnitude more resources than Clifford gates

For example see here and here.

But do I understand correctly that while minimizing T-count (incl. in Clifford+T circuits) does not give a significant gain for the current IBM open quantum systems (real hardware, not simulations!), in particular, due to the fact that at the moment T gate (like T†, U1/P and RZ gates)

can be implemented virtually in hardware via framechanges (i.e. at zero error and duration)

See the documentation

luciano
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Psanfi
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2 Answers2

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No, it doesn't make sense to minimize T count on NISQ hardware. As you note, T gates don't even have a cost because they are done virtually by updating the rotation frame of later operations. No reason to minimize things that are free! If anything, you should be maximizing their use.

Craig Gidney
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Every gate has a cost because each gate of NISQ computers are noisy so each one introduces a little bit of error. This means that if you use fewer gates to do the same task, you'll end up with less error. Also, coherence time is limited so one can only perform so many gates...meaning that if you reduce your gate-count, you are able to do more meaningful computation than if you didn't minimize the gate count.

ComputerNerd
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