QUINTYL

Quantum Information Theory with Liouvillians

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 Obiettivo del progetto (Objective)

'The project's main goal is composed of a scientific and an academic training component, and it is to be implemented in the Department of Mathematics at the Technical University of Munich in the research group of Prof. Michael Wolf.

The first scientific aim is to extend the mathematical framework underlying the 'dissipative paradigm' of quantum computing, placing special emphasis on continuous-time evolutions that may be controllable to a certain extent and may include non-Markovian elements. Providing such a rigorous toolbox and extending vital theorems from the Hamiltonian case to the dissipative paradigm forms the first two scientific objectives. Two further objectives use these tools to achieve the project's aim to incorporate controllable dissipative evolution into central parts of Quantum Information Theory. Namely, we aim to establish a Quantum-Shannon-Theory for the controllable time-continuous case - relevant for quantum memories - and explore its basic features. Further, we aim to investigate the computational complexity of dissipative state preparation in quantum many-body systems, contrasting it to Hamiltonian Complexity. These objectives will be achieved mainly through analytic work, also employing computer simulations.

Beyond research, the academic training component aims to prepare the fellow for a future career as an independent researcher. As specific objectives to achieve this, the fellow will mentor students and (co-)supervise research projects jointly with Prof. Wolf during the fellowship. Further, the fellow will (co-)teach a specialized lecture course and a seminar. Through active involvment in the research group and grants, the fellow aims to acquire essential leadership and management skills.

The project objectives are of high relevance to the Work Programme PEOPLE since they strengthen the human potential in research in Europe by supporting the fellow in attaining a leading independent position as professor at a European university.'

Introduzione (Teaser)

The marriage of information theory and quantum mechanics gave rise to the field of quantum computing. Now, scientists have advanced a mathematical formalism that promises to make practical implementation possible.

Descrizione progetto (Article)

Several years ago, a concept called dissipative quantum computing was proposed as a robust way to implement quantum algorithms. Dissipation refers to the process of irreversible energy loss. Since quantum mechanics is typically described using a mathematical formalism (Hamiltonian) in which total system energy is conserved, a new formalism was required.

Scientists launched the EU-funded project QUINTYL (Quantum information theory with Liouvillians) to advance the mathematical framework underlying quantum dissipative (noisy) time evolutions. The main objective was to incorporate controllable dissipative time evolution into key components of quantum information theory. Establishing the feasibility of dissipative approaches for the processing of quantum information could be a giant leap toward the realisation of a quantum computer.

Researchers achieved all initial goals, beginning with introduction of Fourier-based analyses methods into the mathematical frameworks describing quantum and classical stochastic (specifically, Markov) processes to control their convergence behaviours.

A new mathematical framework supports quantification of the storage capacity of noisy quantum memories. It was successfully applied to several control operations that could be applied during the storage time in the context of controllable dissipative time evolution and quantum computing. In addition, the analytical output will be useful for comparison to observations of experimental quantum memory implementations.

In other work, the team established bounds in the quantum domain that define fundamental energy restrictions on future implementations of quantum computers. The bounds also represent a trade-off between process time and energy efficiency. Other novel algorithms enable robust operation even in a poorly defined noisy environment. Implementation resulted in a significant acceleration in computation time for an unstructured search even compared to noiseless classical algorithms.

The mathematical foundations for quantum computing have been strengthened significantly, and results were widely disseminated within the scientific community. Outcomes are likely to have profound ramifications for the size and nature of problems that can be addressed in fields from cosmology to particle physics to biomedicine.