Quantum Computers – Secrets and Promises

Much interest is attracted nowadays towards quantum computers. Both academy and industry wish to develop the right hardware and software which could benefit the most from the principles of quantum mechanics. However, many questions are still open, namely, why is it that only special problems have, at the moment, efficient quantum algorithms to solve them? Why is the advantage that quantum algorithms provide, compared to classical ones, vary so much from problem to problem? What are the most fundamental ingredients that make a quantum algorithm successful and what is the optimal balance between them? How can we systematically devise new quantum algorithms?

These are hard problems, which I cannot fully solve at the moment, but 1) I think that they are interesting and important. 2) I feel that we should discuss them more often these days. 3) I would like to present in my talk some suitable background and then our first attempts at solving them.

After a general overview I will present some unique quantum features underlying quantum algorithms, e.g. quantum nonlocality [1,2], uncertainty and non-commutativity [3], quantum discord [4], and mostly, irrealism [5]. I will then address our more recent approach which attempts to analyze quantum algorithms as communications channels via the mutual information between the output of the computer and the parameter it wished to find or estimate.

[1] Carmi A., Cohen E.,"Relativistic independence bounds nonlocality", Sci. Adv. 5, eaav8370 (2019).
[2] Cohen E., Carmi A., "In praise of quantum uncertainty", Entropy 22, 302 (2020).
[3] Carmi A., Herasymenko Y., Cohen E., Snizhko K., "Bounds on nonlocal correlations in the presence of signaling and their application to topological zero modes", New J. Phys. 21, 073032 (2019).
[4] Peled B.Y., Te'eni A., Carmi A., Cohen E., "Correlation Minor Norm as a Detector and Quantifier of Entanglement", Sci. Rep. 11, 2849 (2021).
[5] Paiva I. L., Dieguez P. R., Angelo R. M., Cohen E., "Coherence and realism in the Aharonov-Bohm effect", under review in Phys. Rev. A, arXiv:2209.00480.