Has any research been done on quantum Zeno machines?

Question

Zeno machines (abbreviated ZM, and also called accelerated Turing machine, ATM) are a hypothetical computational model related to Turing machines that allows a countably infinite number of algorithmic steps to be performed in finite time. -Wikipedia

The quantum Zeno effect (also known as the Turing paradox) is a feature of quantum-mechanical systems allowing a particle's time evolution to be arrested by measuring it frequently enough with respect to some chosen measurement setting. -Wikipedia

This seems fitting for a continuous-variable environment (eg. photonics). Has any research been done on quantum Zeno machines? (Google: No results found for "quantum zeno machine".)

David Bar Moshe · Accepted Answer

There are two notions of Zeno topics related to quantum computation. The first, which is controversial is usually called hypercomputation, which deals with the possibility of surpassing the limitations of the Church-Turing thesis by means of quantum computation. It is related to the Zeno effect through the fact that if it could be realized, it may solve the halting problem.  Contogo refers to this option as a "Quantum Zeno machine". In this context, please see also:Nielsen  exploring this possibility.

The second topic which goes by the name Quantum Zeno effect (as referred to in the Wikipedia page in the question) is well established and experimentally verified, (please see Kwiat, White, Mitchell, Nairz, Weihs, Weinfurter, and Zeilinger ).

Kwiat et al. were motivated by one of the most striking examples of this effect: the Elitzur-Vaidman bomb testing problem, (please see the following review by Vaidman).

This problem deals with bombs which can only interact with the outside world by means of their trigger, classically, testing the bomb would cause every good bomb to explode, but quantum mechanically, one can reach, using the Zeno effect, almost 100% detection probability without exploding the bomb.  This is an example of a non-demolition measurement which is not accompanied by state reduction.

Translated to quantum computation terminology, this effect is called by Jozsa counterfactual quantum computation, according to which a quantum computer, programmed to solve a problem, can give the result even without running.

A detailed account of the Elitzur-Vaidman bomb testing problem is given by Penrose in his popular book: Shadows of the mind.

One of the most important application of the quantum Zeno effect is its exploitation to keep a system inside a decoherence free subspace (by performing repeated measurements) as proposed by: Beige, Braun, Tregenna, and Knigh. Very recently, this proposal was adapted to holonomic quantum computation by Mousolou and Sjöqvist .

Mark S · Answer

Suppose we are given the ($ntimes n$ adjacency matrix $M_0$ of graph $G_0$ and $M_1$ of graph $G_1$, and we wish to know whether $G_0simeq G_1$.  It is a folklore result that if we can prepare states:
$$vertalpha_Grangle=sumlimits_{sigmain S_n}vert sigma (G)rangle,$$
with $S_n$ being the symmetric group on $n$ elements, we can prepare such a state for $G=G_0$ and another for $G=G_1$, and run the $mathsf{SWAP}$ test between them, to answer the graph isomorphism problem.
Following the ideas of Aharonov and Ta-Shma we can propose a "quantum Zeno effect" preparation for such a state $vert alpha_Grangle$.
That is, Aharanov and Ta-Shma speak of adiabatic state preparation in terms of this "quantum Zeno effect."
Of course, although the quantum Zeno effect was discussed/envisioned by Turing, there is no other relation between the quantum Zeno effect and "Zeno" hypercomputation, as mentioned above.

Has any research been done on quantum Zeno machines?

2 Answers

Add your own answers!

Ask a Question