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arXiv · 2408.10093

IQP computations with intermediate measurements

Richard Jozsa·Soumik Ghosh·Sergii Strelchuk
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Abstract

We consider the computational model of IQP circuits (in which all computational steps are $X$ basis diagonal gates), supplemented by intermediate $X$ or $Z$ basis measurements. We show that if we allow non-adaptive or adaptive $X$ basis measurements, or allow non-adaptive $Z$ basis measurements, then the computational power remains the same as that of the original IQP model; and with adaptive $Z$ basis measurements the model becomes quantum universal. Furthermore we show that the computational model having circuits of only $CZ$ gates and adaptive $X$ basis measurements, with input states that are tensor products of 1-qubit states from the set $\{ |+\rangle, |1\rangle,\frac{1}{\sqrt{2}}(|0\rangle+i|1\rangle), \frac{1}{\sqrt{2}}(|0\rangle+e^{i\pi/4}|1\rangle) \} $, is quantum universal. In contrast to the relation of IQP to PH collapse, all our results here are manifestly stable under small additive implementational errors.

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Richard Jozsa, Soumik Ghosh, Sergii Strelchuk. 2024-08-19. IQP computations with intermediate measurements. https://arxiv.org/abs/2408.10093

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