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In his inaugural lecture, Ronald de Wolf states

People are working with quantum objects, but trying to make them behave as classical as possible. (...) Instead of suppressing them to make systems behave as classically as possible, why not try to benefit from them?

While he goes on to state that looking at fully exploiting the quantum effects is more interesting, I do wonder if and how the 'naturally occurring' quantum effects on extremely small transistors could be used to get better classical (or perhaps some classical/quantum hybrid) computation.

Obviously, the design of those transistors needs to use quantum mechanics, but not necessarily quantum information or quantum computation theory.

Has there been any promising research or results in this direction? Or are the good reasons why this wouldn't work?

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It may or may not be exactly what you're looking for, but there is research done on coherent charge oscillations in a silicon field-effect transistor (paper by Gonzalez-Zalba et. al. at Hitatchi labs).

In the above paper, they coherently control a double quantum dot in a silicon-on-insulator nanowire CMOS transistor, with a $T_2$ coherence time of $\approx 100$ ps. While this is a small coherence time, as already existing CMOS technology was used, putting this (or something similar) on a classical chip would be relatively easy. Although it's probably not going to perform any advanced quantum computations in the near future, it arguably demonstrates some potential for a limited classical/quantum hybrid chip. Regardless, this is a clear example of a field-effect transistor having the potential to be used for quantum computation.

The same labs also created a Spin Hall effect transistor, where they use spin-orbit coupling to manipulate spin to implement an AND gate. While spin-orbit coupling is a quantum mechanical process (that doesn't particularly involve quantum information or computing), manipulating spin is something that's required in various different types of quantum computer and so, I wouldn't be all that surprised if talking about such processes in terms of quantum computing/information were possible to some extent.

Overall, while you may or may not count the above as definitive evidence of what you want, they are at least small steps in that direction

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In order to benefit from the use of quantum objects to perform classical computation, one possibility is proposed by Spintronics.

Since the discovery of the giant magnetorresistence by Fert et al. (in Giant Magnetoresistance of (001)Fe/(001)Cr Magnetic Superlattices) a new field has been developed in which the spin has been used instead of the classical charge. This new electronics relies on the use of the quantum properties of the spin to to encode information, an approach that permits the manipulation (write/read) of information using lower energies compared to those involved in conventional electronics. Spintronics proposes new materials to the data storage and data processing industries but also aims at offering novel possibilities to quantum technologies. See: Spintronics, A Spin-Based Electronics Vision for the Future.

Molecular spintronics, developed in the past decade,deals with the possibility of transferring the spintronic properties displayed by the purely inorganic compounds to systems made out of discrete molecules. Motivated by the fact that organic molecules are mostly formed by light atoms, which bear weak spin−orbit coupling and present low-contact nuclear hyperfine interaction, molecular spintronics hold promises for enhanced quantum coherence and the preservation of the spin during the operation time.

Regarding classical/quantum hybrid computation, recently the group of W. Wernsdorfer et al have reported the fist quantum algorithm implemented in a single-molecule device by means of spintronics in Operating Quantum States in Single Magnetic Molecules: Implementation of Grover’s Quantum Algorithm. I am not aware that any advance in this approach has been performed by the inorganic (non-molecular) counterpart in Spintronics.

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Miniaturizing switching or transistor technology needs to go hand in hand with quantum (transport and computing) theory. I think that many challenging aspects (like for instance isotopically purifying silicon and donor implementation for single atom transistors) are classical material science problems. There is a recent review article on the strategies to develop beyond current CMOS transistor technology:

Beyond CMOS computing with spin and polarization

Moreover, there is a lot of research on building qubits transistor-like:

A CMOS spin qubit

And a comment on recent advances in silicon quantum technology which is important for quantum computing applications (CNOT gate, strong coupling) from this year 2018:

Toward a silicon-based quantum computer

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  • $\begingroup$ Because of the possibility of link rot, could you add the critical information from the links to your answer? I.e., author/abstract of papers, or quotes of the key points from other articles. $\endgroup$ – heather Apr 22 '18 at 16:58

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