# Scrambling of Quantum Information in Many-Body Systems

Lead Research Organisation:
University College London

Department Name: Physics and Astronomy

### Abstract

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.

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.

### Planned Impact

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.

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.

### Organisations

- University College London, United Kingdom (Collaboration, Fellow, Lead Research Organisation)
- Complutense University of Madrid, Spain (Collaboration)
- Perimeter Institute for Theoretical Physics (Collaboration)
- Autonomous University of Barcelona (UAB) (Project Partner)
- Wigner Research Centre for Physics, Hungary (Project Partner)

## People |
## ORCID iD |

Lluis Masanes (Principal Investigator / Fellow) |

### Publications

Alhambra Á
(2019)

*Entanglement fluctuation theorems*in Physical Review A
Galley T
(2018)

*Any modification of the Born rule leads to a violation of the purification and local tomography principles*in Quantum
Masanes L
(2019)

*The measurement postulates of quantum mechanics are operationally redundant.*in Nature communicationsDescription | We have discovered that quantum systems whose dynamics is local and time-periodic (Floquet systems) can display a strong form of quantum chaos. In the language of quantum computation: we have constructed an efficient method to generate pseudo-random quantum transformations; and this is a valuable resource required in many quantum algorithms. We have discovered a novel form of many-body localisation. This is relevant for understanding the physical properties of materials, and for the design of novel materials. |

Exploitation Route | We have developed an important tool to be used in the implementation of quantum algorithms. This can also be used for quantum communication protocols. We have discovered new materials we novel properties. This outcom is theoretical but we are trying to find practical applications. |

Sectors | Digital/Communication/Information Technologies (including Software),Security and Diplomacy |

Description | Collaboration for a novel from of localisation |

Organisation | University College London |

Country | United Kingdom |

Sector | Academic/University |

PI Contribution | My team at UCL includes the PhD student Tom Farshi, the postdoctoral researcher Dr Daniele Toniolo and myself. As a spin of our previous paper "Periodic dynamics generates pseudo-random unitaries", we are analysing a novel form of many-body localisation and corresponding phase transitions. This is important for the development of novel materials. |

Collaborator Contribution | Dr Arijeet Pal and PhD student Oliver Lunt, both from UCL, are probiding their expertise in the phenomenon of many-body localisation. They are also contributing with computational simulations of the systems that we are studying. |

Impact | We are currently finalising a research paper. |

Start Year | 2020 |

Description | Collaboration for the project: periodic dynamics generates pseudo-random unitaries |

Organisation | Complutense University of Madrid |

Country | Spain |

Sector | Academic/University |

PI Contribution | My team at UCL includes the PhD student Tom Farshi, the postdoctoral researcher Dr Daniele Toniolo and myself. We have mathematically proven 19 out of 22 theorems that are required to complete the article with title "Periodic dynamics generates pseudo-random unitaries". This article has been published in pre-print form, and is being reviewed in a refereed journal. This article constitutes the central goal of this project awarded by EPSRC. |

Collaborator Contribution | Dr Carlos Gonzalez-Guillen (Madrid Polytechnic University) is one of our project collaborators. He visited us from the 6th to the 12th of December of 2018 and from 4th to 8th Novermber 2019. He has mathematically proven 3 out of the 22 theorems that are crucial to complete the central goal of this project awarded by EPSRC. Dr Alvaro Martin-Alhambra (Perimeter Institute for Theoretical Physics) is one of our project collaborators. He visited us from the 6th to the 12th of December of 2018 and from 4th to 8th Novermber 2019. He has written the code for the simulations of the system that we are studying in this EPSRC project. With his simulations we can confirm the correctness of our proven theorems, and we can guess what are going to be the next theorems to be proven. Having two complementary sources of information, namely, mathematical proofs and computer simulations, is extremely fruitful for the development of our project. |

Impact | The outputs so far are mathematical theorems and computer simulations which tell us the physical behavior of the model that we are analyzing. This project is indeed multi-disciplinary; in particular this outcomes are relevant for condensed-matter physics and for quantum information science. From the condensed matter side, we have presented a new phase of matter with surprising properties. From the quantum information point of view, we have shown that quantum supremacy can be demonstrated with systems which have time-periodic dynamics, and hence are easier to implement. |

Start Year | 2018 |

Description | Collaboration for the project: periodic dynamics generates pseudo-random unitaries |

Organisation | Perimeter Institute for Theoretical Physics |

Country | Canada |

Sector | Academic/University |

PI Contribution | My team at UCL includes the PhD student Tom Farshi, the postdoctoral researcher Dr Daniele Toniolo and myself. We have mathematically proven 19 out of 22 theorems that are required to complete the article with title "Periodic dynamics generates pseudo-random unitaries". This article has been published in pre-print form, and is being reviewed in a refereed journal. This article constitutes the central goal of this project awarded by EPSRC. |

Collaborator Contribution | Dr Carlos Gonzalez-Guillen (Madrid Polytechnic University) is one of our project collaborators. He visited us from the 6th to the 12th of December of 2018 and from 4th to 8th Novermber 2019. He has mathematically proven 3 out of the 22 theorems that are crucial to complete the central goal of this project awarded by EPSRC. Dr Alvaro Martin-Alhambra (Perimeter Institute for Theoretical Physics) is one of our project collaborators. He visited us from the 6th to the 12th of December of 2018 and from 4th to 8th Novermber 2019. He has written the code for the simulations of the system that we are studying in this EPSRC project. With his simulations we can confirm the correctness of our proven theorems, and we can guess what are going to be the next theorems to be proven. Having two complementary sources of information, namely, mathematical proofs and computer simulations, is extremely fruitful for the development of our project. |

Impact | The outputs so far are mathematical theorems and computer simulations which tell us the physical behavior of the model that we are analyzing. This project is indeed multi-disciplinary; in particular this outcomes are relevant for condensed-matter physics and for quantum information science. From the condensed matter side, we have presented a new phase of matter with surprising properties. From the quantum information point of view, we have shown that quantum supremacy can be demonstrated with systems which have time-periodic dynamics, and hence are easier to implement. |

Start Year | 2018 |

Description | Bespoke course on quantum information at Santander Bank |

Form Of Engagement Activity | Participation in an activity, workshop or similar |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Industry/Business |

Results and Impact | Together with other professors from University College London we organised a beskpoke course con quantum information for the company Santander Bank. The topics where introductory and focused on the applications that might be interesting for the company. We prepared the content in a way that was accessible for the audience and we had a very good feedback. |

Year(s) Of Engagement Activity | 2020 |

Description | Expert advisor for science magazine Quanta |

Form Of Engagement Activity | A magazine, newsletter or online publication |

Part Of Official Scheme? | No |

Geographic Reach | International |

Primary Audience | Public/other audiences |

Results and Impact | Quanta is an online science magazine with an international and large readership which is translated to 7 languages. This magazine published an article (title: "Mysterious Quantum Rule Reconstructed From Scratch") which reports a paper of mine (title: "The measurement postulates of quantum mechanics are redundant") produced with this award. |

Year(s) Of Engagement Activity | 2019 |

URL | https://www.quantamagazine.org/the-born-rule-has-been-derived-from-simple-physical-principles-201902... |