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Exponential rise of dynamical complexity in quantum computing through projections.

Burgarth DK, Facchi P, Giovannetti V, Nakazato H, Pascazio S, Yuasa K - Nat Commun (2014)

Bottom Line: After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above.Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions.We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

View Article: PubMed Central - PubMed

Affiliation: Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK.

ABSTRACT
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

No MeSH data available.


Related in: MedlinePlus

Schematics of the full versus projected system algebras.The arrows are tangents (generators) on a manifold of unitary transformations. In the larger space (upper), the operations commute, so no matter which way we go, we end up at the same point. It is not the case for the projected system (lower): the projected operations do not commute, and the gap represents the non-commutativity. Even though the projected system is embedded in a smaller space, its dynamics is more complex, because of the curvature induced by the projection: new directions can be explored.
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f2: Schematics of the full versus projected system algebras.The arrows are tangents (generators) on a manifold of unitary transformations. In the larger space (upper), the operations commute, so no matter which way we go, we end up at the same point. It is not the case for the projected system (lower): the projected operations do not commute, and the gap represents the non-commutativity. Even though the projected system is embedded in a smaller space, its dynamics is more complex, because of the curvature induced by the projection: new directions can be explored.

Mentions: exhibit a non-trivial commutator , which makes the dimension of equal to 3 (the situation is schematically illustrated in Fig. 2). This in particular implies that can now be used to fully control the system in the subspace (which is isomorphic to the Hilbert space of qubit 2), a task that could not be fulfilled with the original .


Exponential rise of dynamical complexity in quantum computing through projections.

Burgarth DK, Facchi P, Giovannetti V, Nakazato H, Pascazio S, Yuasa K - Nat Commun (2014)

Schematics of the full versus projected system algebras.The arrows are tangents (generators) on a manifold of unitary transformations. In the larger space (upper), the operations commute, so no matter which way we go, we end up at the same point. It is not the case for the projected system (lower): the projected operations do not commute, and the gap represents the non-commutativity. Even though the projected system is embedded in a smaller space, its dynamics is more complex, because of the curvature induced by the projection: new directions can be explored.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4214416&req=5

f2: Schematics of the full versus projected system algebras.The arrows are tangents (generators) on a manifold of unitary transformations. In the larger space (upper), the operations commute, so no matter which way we go, we end up at the same point. It is not the case for the projected system (lower): the projected operations do not commute, and the gap represents the non-commutativity. Even though the projected system is embedded in a smaller space, its dynamics is more complex, because of the curvature induced by the projection: new directions can be explored.
Mentions: exhibit a non-trivial commutator , which makes the dimension of equal to 3 (the situation is schematically illustrated in Fig. 2). This in particular implies that can now be used to fully control the system in the subspace (which is isomorphic to the Hilbert space of qubit 2), a task that could not be fulfilled with the original .

Bottom Line: After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above.Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions.We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

View Article: PubMed Central - PubMed

Affiliation: Institute of Mathematics, Physics and Computer Science, Aberystwyth University, Aberystwyth SY23 3BZ, UK.

ABSTRACT
The ability of quantum systems to host exponentially complex dynamics has the potential to revolutionize science and technology. Therefore, much effort has been devoted to developing of protocols for computation, communication and metrology, which exploit this scaling, despite formidable technical difficulties. Here we show that the mere frequent observation of a small part of a quantum system can turn its dynamics from a very simple one into an exponentially complex one, capable of universal quantum computation. After discussing examples, we go on to show that this effect is generally to be expected: almost any quantum dynamics becomes universal once 'observed' as outlined above. Conversely, we show that any complex quantum dynamics can be 'purified' into a simpler one in larger dimensions. We conclude by demonstrating that even local noise can lead to an exponentially complex dynamics.

No MeSH data available.


Related in: MedlinePlus