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New Paper From CQT Finds Phases of Matter With Differing Computational Power

A study has turned upside down a typical way of looking at the connection between physics and information in quantum systems - with results that could lead to new insight into quantum computation.

The findings, by physicists at Singapore's Centre for Quantum Technologies (CQT) and their collaborators, were published on the 1st May in Nature Communications.

Many advances in computing and communication have emerged from the idea that information can be treated as a physical quantity subject to physical laws. After the link was first made in the mid 20th Century, the field of information theory extended to studying information subject to quantum laws. It's thanks to this newer research field, known as quantum information, that proposals for quantum computers and quantum cryptography for secure communication have come into being.

One of the pioneers of information theory, Rolf Landauer, famously wrote that "Information is inevitably physical". The new paper, says author Vlatko Vedral of CQT and the University of Oxford, UK, highlights the mirroring idea that "physics itself is also informational".

This figure illustrates the different phases of a two-dimensional Ising model as a function of model parameters γ and g. Phase 1A can exhibit quantum effects that Phase 1B and Phase 2 cannot. Adapted from Fig. 3 of Nature Commun. 3, 812 (2012).

In the paper, CQT's Mile Gu, Leong Chuan Kwek, also of Singapore's Nanyang Technological University, and Vlatko, with Jian Cui and Heng Fan from the Chinese Academy of Sciences in Beijing and Marcelo Franca Santos from the Universidade Federal de Minas Gerais in Brazil, consider the computational power of different quantum phases of matter.

Researchers know that when quantum matter shifts from one state to another, there is often a signature in an informational measure, such as entanglement. This has led to quantum information theory being used to study the physical properties of quantum phase transitions. But as the team points out in this paper, the reverse - the question of how physical phase transitions influence informational properties - is less studied. Different phases of the two-dimensional Ising model differ in their computational power.

"We look past the physical properties of the different phases and ask, 'Could different phases have different capacities to process information as well?' The answer turns out to be yes" says Mile.

The team looked at a simplified model of matter known as an Ising model, which can adopt different magnetic phases. The researchers analysed how the entropy of the model's paramagnetic and ferromagnetic phases change when an external magnetic field is applied, and found in the simplest case that the ferromagnetic phase has a capacity to exhibit quantum effects that the paramagnetic phase does not.

a difference was found not only in the simple one-dimensional Ising model, but also in the two-dimensional (XY) model. In some phases, the effects of variation of an external magnetic field could be simulated by classical computers. In others, the variation of the same magnetic field would lead to non-trivial quantum interaction within the system. This indicates that for some models of quantum computation, only certain phases have the potential to perform better than classical computers.

The researchers suggest the approach coube applied to studying a form of quantum computation known as 'adiabatic', in which the computation is implemented by applying external influences to quantum matter and the result deduced from its end state.

For more details, see "Quantum phases with differing computational power", Nature Communications.

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