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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.10093 |
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Table of Contents:
- 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^{iπ/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.