Chaos and Scrambling in many-body quantum systems
Lead Research Organisation:
University of Bristol
Department Name: Physics
Abstract
A long standing issue has been to understand chaos in quantum many body systems. In particular, whilst chaos has long been understood in classical dynamics and in single-particle quantum mechanics, it has remained extremely challenging to understand what is mean by chaos in a a many-body quantum system. Nevertheless, the question of quantum chaos is of central importance in understanding many-body quantum dynamics, not least due its connection to how quantum mechanical systems thermalise. Over the last several years, a new characterisation of chaos in many-body quantum systems has been provided through a characterisation of information scrambling, the decay of out of time ordered correlators, and efficient operator spreading. The aim of this project will be to study new signatures of chaos and scrambling in many-body quantum systems, using techniques from holographic quantum theories and and quantum information theory.
In particular, over the last few years there have emerged surprising connections between
scrambling in many-body quantum systems and hydrodynamics, including surprising
connections between energy diffusion and chaos. Based on these connections, [1] proposed an effective hydrodynamic theory for scrambling in maximally chaotic systems, in which the scrambling of operators arises due to interactions with hydrodynamic degrees of freedom.
One output of this theory was a prediction of a new phenomenon in maximally
chaotic systems known as pole-skipping. This refers to a precise connection between the Lyapunov exponent and butterfly velocity that appear in out-of-time ordered correlation functions and the dispersion relations of hydrodynamic modes (collective excitations) of the system. An important tool for testing this phenomenon are holographic quantum field theories. Such field theories have a dual mathematical description in terms of the dynamics of black holes in anti-de Sitter space, using which one can compute both out-of-time ordered correlation functions and hydrodynamic modes of these quantum field theories.
The initial aim of this project will be to study the pole-skipping phenomenon mentioned above, in the context of quantum systems which are holographically dual to the rotating Myers-Perry-AdS black hole. Future work is likely to explore other aspects of chaos in many-body quantum systems. For example, this could include studying entanglement dynamics in many-body quantum systems or studying scrambling in other toy models e.g. quantum circuits.
In particular, over the last few years there have emerged surprising connections between
scrambling in many-body quantum systems and hydrodynamics, including surprising
connections between energy diffusion and chaos. Based on these connections, [1] proposed an effective hydrodynamic theory for scrambling in maximally chaotic systems, in which the scrambling of operators arises due to interactions with hydrodynamic degrees of freedom.
One output of this theory was a prediction of a new phenomenon in maximally
chaotic systems known as pole-skipping. This refers to a precise connection between the Lyapunov exponent and butterfly velocity that appear in out-of-time ordered correlation functions and the dispersion relations of hydrodynamic modes (collective excitations) of the system. An important tool for testing this phenomenon are holographic quantum field theories. Such field theories have a dual mathematical description in terms of the dynamics of black holes in anti-de Sitter space, using which one can compute both out-of-time ordered correlation functions and hydrodynamic modes of these quantum field theories.
The initial aim of this project will be to study the pole-skipping phenomenon mentioned above, in the context of quantum systems which are holographically dual to the rotating Myers-Perry-AdS black hole. Future work is likely to explore other aspects of chaos in many-body quantum systems. For example, this could include studying entanglement dynamics in many-body quantum systems or studying scrambling in other toy models e.g. quantum circuits.
Planned Impact
Our ambitions for the impact of the Quantum Engineering CDT are simple and clear: our PhD graduates will be the key talent that creates a new, thriving, globally-competitive quantum industry within the UK. In Bristol we will provide an entire ecosystem for innovation in quantum technologies (QT). Our strong and diverse research base includes strengths going from quantum foundations to algorithms, experimental quantum science to quantum hardware. What makes Bristol unique is our strong innovation and entrepreneurship focus that is deeply embedded in the entire culture of the CDT and beyond. This is reflected in our recent successful venture QTEC, the Quantum Technologies Enterprise Centre, and our Quantum Technologies Innovation Centre (QTIC), which are already enabling industry and entrepreneurs to set up their own QT activities in Bristol. This all occurs alongside internationally recognised incubators/accelerators SetSquared, EngineShed, and UnitDX.
At the centre of this ecosystem lies the CDT. We will not just be supplying existing industry with deeply trained talent, but they will become the CEOs and CTOs of new QT companies. We are already well along this path: 7 Bristol PhD students are currently involved in QT start-ups and 3 alumni have founded their own companies. We expect this number to rise significantly when the first CDT cohort graduates next year (2 students have already secured start-up positions). Equally, it is likely that our graduates will be the first quantum engineers to make new innovations in existing classical technology companies - this is an important aspect, as e.g. the existing photonics, aerospace and telecommunications industries will also need QT experts.
The portfolio of talent with which each CDT graduate will be equipped makes them uniquely suited to many roles in this future QT space. They will have a deep knowledge of their subject, having produced world-leading research, but will also understand how to turn basic science into a product. They will have worked with individuals in their cohort with very different skills background, making them invaluable to companies in the future who need these interdisciplinary team skills to bring about quantum innovations in their own companies. Such skills in teamworking, project management, and self-lead innovation are evidenced by the hugely successful Quantum Innovation Lab (QIL). The idea and development of QIL is entirely student-driven: it brings together diverse industrial partners such as Deutsche Bank, Hitachi, and MSquared Lasers, Airbus, BT, and Leonardo - the competition to take part in QIL shows the hunger by national industry for QT in general, and our students' skills and abilities specifically. With this in mind, our Programme has been co-developed with local, UK, and international companies which are presently investing in QT, such as Airbus, BT, Google, Heilbronn, Hitachi, HPE, IDQuantique, Keysight, Microsoft, Oxford Instruments, and Rigetti. The technologies we target should lead to products in the short and medium term, not just the longer term. The first UK-wide fibre-based quantum communication network will likely involve an academic-industrial partnership with our CDT graduates leading the way. Quantum sensing devices are likely to be the product of individual innovators within the CDT and supported by QTIC in the form of spin-outs. Our graduates will be well-positioned to contribute to the advancement of quantum simulation and computing hardware, as developed by e.g. our partners Google, Microsoft and Rigetti. New to the CDT will be enhanced training in quantum software: this is an area where the UK has a strong chance to play a key role. Our CDT graduates will be able to contribute to all aspects of the software stack required for first-generation quantum computers and simulators, the potential impact of which is shown by the current flurry of global activity in this area.
At the centre of this ecosystem lies the CDT. We will not just be supplying existing industry with deeply trained talent, but they will become the CEOs and CTOs of new QT companies. We are already well along this path: 7 Bristol PhD students are currently involved in QT start-ups and 3 alumni have founded their own companies. We expect this number to rise significantly when the first CDT cohort graduates next year (2 students have already secured start-up positions). Equally, it is likely that our graduates will be the first quantum engineers to make new innovations in existing classical technology companies - this is an important aspect, as e.g. the existing photonics, aerospace and telecommunications industries will also need QT experts.
The portfolio of talent with which each CDT graduate will be equipped makes them uniquely suited to many roles in this future QT space. They will have a deep knowledge of their subject, having produced world-leading research, but will also understand how to turn basic science into a product. They will have worked with individuals in their cohort with very different skills background, making them invaluable to companies in the future who need these interdisciplinary team skills to bring about quantum innovations in their own companies. Such skills in teamworking, project management, and self-lead innovation are evidenced by the hugely successful Quantum Innovation Lab (QIL). The idea and development of QIL is entirely student-driven: it brings together diverse industrial partners such as Deutsche Bank, Hitachi, and MSquared Lasers, Airbus, BT, and Leonardo - the competition to take part in QIL shows the hunger by national industry for QT in general, and our students' skills and abilities specifically. With this in mind, our Programme has been co-developed with local, UK, and international companies which are presently investing in QT, such as Airbus, BT, Google, Heilbronn, Hitachi, HPE, IDQuantique, Keysight, Microsoft, Oxford Instruments, and Rigetti. The technologies we target should lead to products in the short and medium term, not just the longer term. The first UK-wide fibre-based quantum communication network will likely involve an academic-industrial partnership with our CDT graduates leading the way. Quantum sensing devices are likely to be the product of individual innovators within the CDT and supported by QTIC in the form of spin-outs. Our graduates will be well-positioned to contribute to the advancement of quantum simulation and computing hardware, as developed by e.g. our partners Google, Microsoft and Rigetti. New to the CDT will be enhanced training in quantum software: this is an area where the UK has a strong chance to play a key role. Our CDT graduates will be able to contribute to all aspects of the software stack required for first-generation quantum computers and simulators, the potential impact of which is shown by the current flurry of global activity in this area.
Studentship Projects
| Project Reference | Relationship | Related To | Start | End | Student Name |
|---|---|---|---|---|---|
| EP/S023607/1 | 01/09/2019 | 29/02/2028 | |||
| 2431601 | Studentship | EP/S023607/1 | 21/09/2020 | 20/09/2024 | Anthony Thompson |