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I was pointed to this very nice paper On the CNOT-cost of TOFFOLI gates . The issue appears to be much more complicated than I thought. Apparently there are theses yet to be written on the decomposition of Toffoli into $CNOT$s. First, due to identity $HXH=Z$ decompositions into $CNOT$s and $CZ$s can be translated into each others. Similarly, decomposing $n$-...

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As detailed in The simplified Toffoli gate implementation by Margolus is optimal, a construction of the simplified Toffoli (which introduces for some relative phase) cannot be constructed with fewer than $3$ controlled-not operations. Also mentioned in that paper, it is conjectured that the Toffoli gate cannot be implemented with less than six controlled-...

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The lack of positive semidefiniteness is very easy to see. Suppose your quantum state is $|0\rangle\langle 0|$, and you do tomography by measuring in the $X, Y,$ and $Z$ bases. Furthermore, assume there is no experimental error whatsoever. Then after $n$ measurement rounds in each basis, the estimate for $\operatorname{tr}(\rho X)$ will be $2k/n-1$ with ...

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If you are looking for implementations of quantum memories, you can find a few in this QRAM library for Q#. I am not quite sure what you mean by the bucket brigade protocol is not able to readout entangled data, but as far as I understand you can do that with bucket brigade (we used it in this example that implements Grover's algorithm with a bucket brigade ...

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The progress in DIQKD security proofs has been quite rapid in recent years. In particular, the approach of Vazirani and Vidick is no longer what the community uses. The two major approaches that I know of are using the entropy accumulation theorem or quantum probability estimation. These two approaches are quite similar in spirit but the entropy accumulation ...

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It largely depends on the technology you're interested in. If you want to learn about photonic quantum computing you can check out this video which summarizes very well how it works. If you want to learn more then I would suggest going to the Strawberry Fields website, specially this page. Also going through the demos and tutorials is a great way to get a ...

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Here are some useful materials with respect to superconducting qubits that I found to be helpful: A Quantum Engineer’s Guide to Superconducting Qubits, P. Krantz, M. Kjaergaard, F. Yan, T.P. Orlando, S. Gustavsson, and W. D. Oliver Tutorial: Gate-based superconducting quantum computing, Sangil Kwon, Akiyoshi Tomonaga, Gopika Lakshmi Bhai, Simon J. Devitt, ...

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