Scrambling of Quantum Information in Many-Body Systems

Quantum Information Theory (QIT) aims at exploiting the laws of quantum mechanics to outperform all classical information-processing methods. This is an intellectually and technologically extremely challenging endeavour, as the goal is to understand the ultimate physical limits of information processing, and to harness them for communication, encryption, computation and sensing. The Nobel Prizes to Haroche and Wineland (2012) and to Haldane, Kosterlitz and Thouless (2016) recognise the importance of this field.

Dr. Masanes' theoretical research contributes to the development of "quantum simulators", one of the most relevant applications of QIT. Quantum simulators allow to physically implement any mathematical quantum model and observe its time evolution. This task is impossible with our current super-computers. The reason for this is that classical computers are so inefficient at simulating quantum systems that the process would take thousands of years. In contrast, quantum simulators allow us to observe the behaviour of any theoretical model within quantum physics, regardless of its mathematical complexity. Hence, they will become a powerful tool in many areas of science and industry, like the chemical, pharmaceutic and nano-technology industrires. Remarkably, quantum simulators are already being constructed with present-day quantum technology.

In addition to new applications of quantum technology, QIT exports results and methods to produce breakthroughs and insights in other areas of physics. Some examples are the development of computational methods to study the properties of matter, the derivation of Einstein's gravity equations from the entanglement structure of a field theory, and the PI's proof of the Third Law of Thermodynamics from first principles, a subject of controversy going back to Nernst and Einstein.

To introduce one of the main goals of this proposal, we recall that one of the most used approximation in the physical sciences is to describe a system that has been evolving for some time by a thermal or maximal-entropy state. This approximation is used even in closed quantum systems, where entropy does not increase. Remarkably, and despite its importance, it is still not well understood when this approximation holds. The proposed research applies mathematical tools from QIT to address the following question. When does thermalisation happen? The reason why QIT has the potential to solve this problem is that the central mechanism for thermalisation in quantum systems is the growth of entanglement, and entanglement is one of the central subjects of study within QIT.

The physics of thermalisation is particularly relevant for nanotechnology, because in the microscopic regime the relative size of thermal effects is large. Hence, harnessing thermal physics could allow for pushing the frontiers of technology at the nano scale. Also, thermalisation is fundamental within the holographic formulation of Quantum Gravity, where certain thermalisation processes in field theory describe the gravitational free fall of a particle towards a black hole and its subsequent evaporation. A complete understanding of this process could provide an answer to the famous black-hole information paradox, formulated by Hawking in 1976.

Another goal of the proposed research is to simplify the construction of some of the building blocks of quantum computers. These building blocks are devices that scramble quantum information as much as it is allowed by the laws of quantum mechanics. This scrambling operation is required in many quantum applications, and can be seen as a sort of artificial thermalisation. Comparing artificial and natural processes of thermalisation is a very innovative approach that will allow to quantify the "amount of scrambling" that is present in a given system, in a manner that is relevant to QIT applications like quantum computation.

The research proposed simultaneously develops both, technological applications and basic science. These technological applications are framed within quantum information science, a discipline that exploits the novel quantum technologies to perform information-processing tasks that are either impossible or too inefficient to perform with non-quantum means. This revolutionary technology will have a big impact on society, as it will produce a new generation of computers with unprecedented power, more secure communications and transactions, and extremely high precision measurements. Quantum technology is already generating a vigorous economy in which important technology firms (e.g. Google, IBM, Toshiba and Hewlett Packard) are participating. The UK government has recognised that Quantum Technologies could generate "a £1 billion future industry for the UK" and has launch the UK National Quantum Technologies Programme with an investment of £270 million.

More particularly, this research contributes to the development of quantum computers, devices that will outperform any of our current super-computers. Small-scale quantum computers have already been constructed, but full-size practical quantum computers are usually presented as a long-term goal. However, there is a big project in the UK for building an impressive medium-size quantum computer for the year 2020, the so-called Q20:20 machine. Importantly, this machine has been designed to facilitate the interconnection of many of them, providing a potential pathway for the construction of a full-size quantum computer in a not-so-far future.

Another application of quantum technology to which this research is contributing is quantum simulators. These devices are capable of simulating any quantum system, a task that is impossible even with our best current super-computers. Quantum simulators will allow us to analyse and monitor the behaviour of molecules, materials and nano-devices at the quantum level and with unprecedented precision. This is expected to bring a revolution in the chemical and pharmaceutical industries, in the design of new intelligent materials, and in the quantum and nano technologies. Remarkably, practical quantum simulators outperforming current super-computers are already being constructed. Hence, here we are looking at the near future for the benefits for society in terms of technology and economic opportunities.

Regarding basic science, the research proposed aims at deepening our understanding of thermalisation processes. This problem is currently attracting a lot of renewed interest due to the existence of new mathematical tools coming from the quantum information community, and because it plays an important role in many contemporary research directions like nano-scale physics and quantum gravity. The problem of thermalisation also touches most of the fields within the physical sciences and some fields within chemistry and biology. Hence, this proposal has potential to produce a big impact at a foundational level. For example, by providing a mathematical justification of widely-used approximations in all these fields. In addition to this, a better understanding of thermal physics could improve the control of microscopic physical devices, with the subsequent benefit for nano-technology, a discipline which also promises to have a big impact on society.

It is of fundamental importance for our society that the general public is scientifically well informed. The PI has a commitment with outreach and an outstanding track record. His research has been widely reported in the press, including the New York Times and the New Scientist in several occasions (see the Pathways for Impact document). With the help of the UCL's office of Media Relations, the PI will continue with his outreach activities.