Periodic Reporting for period 1 - TaQC (Taming, controlling and harnessing quantum complexity)
Reporting period: 2023-04-03 to 2025-04-02
In the past decade, we have witnessed a proliferation of devices that leverage quantum effects and promise to fundamentally transform the technological and industrial landscape. Unlike previous paradigm shifts in the area of quantum technologies -- like the development of the transistor – which revolved around the speed-up and facilitation of classical tasks, the current generation of quantum technologies goes one important step further: it aims at harnessing the fundamentally different way that information itself is expressed, transformed, and processed in the quantum realm.
The formidable practical and foundational advances of the past years notwithstanding, much work still lies ahead in order to scale, control and harness quantum effects to the fullest extent, consequently making their power routinely and reliably available.
To date, most research on exploitable quantum phenomena has focused on entanglement as the basis for quantum technologies. This is a spatial quantum resource, in the sense that it describes quantum correlations that are shared by spatially separated parties. In complex quantum processes and devices, quantum information will not only be shared though, but also processed and transmitted, leading to quantum correlations in both space and time.
Consequently, the TaQC project aims to widen the scope and provide a comprehensive understanding of spatio-temporal quantum effects and develop the means to characterise, control and predict them. In particular, the project focuses on three main questions: (i) how do realistic constraints condition the distribution of spatio-temporal entanglement in a quantum process? (ii) how can general quantum processes be characterized and what can be learned about them efficiently? And (iii) how can optimal models for quantum processes be constructed and their resourcefulness be estimated?
The development of a robust theoretical framework to address these questions relies on insights from quantum information theory, quantum metrology, the theory of open quantum system dynamics as well as higher order quantum maps. Its implementation will provide a holistic understanding of quantum effects as they occur in complex quantum processes, and help pave the way towards their reliable and sustainable exploitation.
The formidable practical and foundational advances of the past years notwithstanding, much work still lies ahead in order to scale, control and harness quantum effects to the fullest extent, consequently making their power routinely and reliably available.
To date, most research on exploitable quantum phenomena has focused on entanglement as the basis for quantum technologies. This is a spatial quantum resource, in the sense that it describes quantum correlations that are shared by spatially separated parties. In complex quantum processes and devices, quantum information will not only be shared though, but also processed and transmitted, leading to quantum correlations in both space and time.
Consequently, the TaQC project aims to widen the scope and provide a comprehensive understanding of spatio-temporal quantum effects and develop the means to characterise, control and predict them. In particular, the project focuses on three main questions: (i) how do realistic constraints condition the distribution of spatio-temporal entanglement in a quantum process? (ii) how can general quantum processes be characterized and what can be learned about them efficiently? And (iii) how can optimal models for quantum processes be constructed and their resourcefulness be estimated?
The development of a robust theoretical framework to address these questions relies on insights from quantum information theory, quantum metrology, the theory of open quantum system dynamics as well as higher order quantum maps. Its implementation will provide a holistic understanding of quantum effects as they occur in complex quantum processes, and help pave the way towards their reliable and sustainable exploitation.
During the reporting period, we successfully achieved the intended scientific goals. Our work on the distribution and expression of quantum effects in complex quantum processes initially focused on analysing the influence of noise. In general, noise "classicalises" quantum correlations, reducing their usefulness for practical applications. Our investigation into the possible structures of quantum correlations under such noise revealed a hierarchy of inequivalent classes of spatio-temporal quantum correlations at the quantum-to-classical boundary. In addition to providing a comprehensive description of this layered structure, we mapped out the underlying mechanisms that give rise to the respective correlation sets within the hierarchy and explored their resourcefulness for quantum information tasks. Further examination of the influence of thermodynamic constraints on quantum processes led to the development of a higher-order resource theory of athermality, enabling the appraisal of thermodynamic resources in general quantum processes. This work also uncovered a strong connection between the information and heat transmission capabilities of quantum processes.
Another significant milestone was the quantification of how the restriction of memory size -- a limitation inherent in all practical quantum devices -- bounds experimentally observable correlations in quantum processes. A priori, the numerical evaluation of these bounds is intractable even for small systems. To overcome this challenge, we developed a versatile algorithm that not only made the computation of these bounds feasible but also has direct applications in a wide range of optimisation problems in quantum information science that had previously eluded efficient numerical treatment. Additionally, based on these bounds, we constructed witnesses of memory size from partial experimental control, enabling the deduction of key properties of quantum processes while accessing only a small fraction of the data.
The development of methods to deduce the structural properties of arbitrary quantum processes and quantum devices represents another milestone of the project. The optimisation of quantum devices requires, as a first step, a comprehensive understanding of their underlying mathematical structure. We derived a systematic framework that facilitates such a structural characterisation of quantum objects under given constraints and provided its numerical implementation.
An important subset of naturally occurring quantum processes consists of stationary processes, i.e. processes that do not change over time. While well understood in the classical case, their comprehensive quantum generalisation had thus far remained elusive. We developed a conceptual framework for stationary processes in the quantum realm and mapped out the additional complexities that arise in the transition from the classical to the quantum case. Appraisal of the inherent power of stationary quantum processes for information-theoretic tasks was rendered possible through the introduction of novel resource monotones, which we derived. To enable the prediction of the behaviour of stationary quantum processes, we developed an efficient protocol to reconstruct their underlying generators from continuous streams of experimental data. This generalisation of existing reconstruction schemes for classical stationary processes constitutes another crucial milestone of the project, as it applies beyond the case of independent and identically distributed data generally considered in the field, allowing for the deduction of key properties of arbitrary complex quantum processes.
During the reporting period, we produced three peer-reviewed publications, with two more currently under review and four additional manuscripts in preparation. The widespread dissemination of the project's results was ensured through participation in four international conferences, as well as regular seminars at the host institution and during research visits.
Another significant milestone was the quantification of how the restriction of memory size -- a limitation inherent in all practical quantum devices -- bounds experimentally observable correlations in quantum processes. A priori, the numerical evaluation of these bounds is intractable even for small systems. To overcome this challenge, we developed a versatile algorithm that not only made the computation of these bounds feasible but also has direct applications in a wide range of optimisation problems in quantum information science that had previously eluded efficient numerical treatment. Additionally, based on these bounds, we constructed witnesses of memory size from partial experimental control, enabling the deduction of key properties of quantum processes while accessing only a small fraction of the data.
The development of methods to deduce the structural properties of arbitrary quantum processes and quantum devices represents another milestone of the project. The optimisation of quantum devices requires, as a first step, a comprehensive understanding of their underlying mathematical structure. We derived a systematic framework that facilitates such a structural characterisation of quantum objects under given constraints and provided its numerical implementation.
An important subset of naturally occurring quantum processes consists of stationary processes, i.e. processes that do not change over time. While well understood in the classical case, their comprehensive quantum generalisation had thus far remained elusive. We developed a conceptual framework for stationary processes in the quantum realm and mapped out the additional complexities that arise in the transition from the classical to the quantum case. Appraisal of the inherent power of stationary quantum processes for information-theoretic tasks was rendered possible through the introduction of novel resource monotones, which we derived. To enable the prediction of the behaviour of stationary quantum processes, we developed an efficient protocol to reconstruct their underlying generators from continuous streams of experimental data. This generalisation of existing reconstruction schemes for classical stationary processes constitutes another crucial milestone of the project, as it applies beyond the case of independent and identically distributed data generally considered in the field, allowing for the deduction of key properties of arbitrary complex quantum processes.
During the reporting period, we produced three peer-reviewed publications, with two more currently under review and four additional manuscripts in preparation. The widespread dissemination of the project's results was ensured through participation in four international conferences, as well as regular seminars at the host institution and during research visits.
In current and future complex quantum processes and devices, quantum information is not only shared but processed and transmitted, leading to quantum effects in both space and time. While the structure of entanglement – spatial quantum correlations – is understood and its certification from experimental data is a well developed field of research, the study of genuinely spatio-temporal quantum correlations is still in its early stages. More in-depth investigation, both at the theoretical and the experimental level, is necessary to obtain a comprehensive understanding of quantum resources in space and time as well as robust means to certify and exploit them.
The TaQC project has provided significant foundational, platform agnostic advances in all of these areas. The exploration of correlation structures in the presence of noise has yielded, for the first time, a stratification of the space of quantum processes with classical memory and offered new insights into their practical capabilities. Given the ubiquitousness of detrimental noise, memory of this type will be dominantly present and controllable in near-term quantum devices, making this categorisation an important tool for further explorations. Analogously, the provided higher-order resource theory of athermality enables the analysis of thermodynamic properties of entire quantum devices and processes, rather than their individual building blocks, as was previously the state-of-the art.
The results of the TaQC project on the influence of memory size on observable correlations introduces a powerful tool to certify the properties of quantum processes from limited experimental control. This, in turn, opens up a novel avenue towards the efficient learning and characterisation of complex quantum devices. In addition, the algorithm developed for the numerical evaluation of the corresponding memory size witnesses is designed to automatically compress the number of free variables. Beyond the case of memory witnesses, this technique offers a feasible approach to the numerical optimsation of heretofore computationally intractable problems in quantum information theory. Similarly, the developed techniques to deduce the structural properties of general quantum processes now enable their optimisation under physical constraints and and provide the theoretical underpinnings for the systematic study of general quantum devices.
Furthermore, the TaQC project has conceptualised the important class of stationary processes in the quantum realm, and developed a roadmap of previously unknown quantum effects that these processes can display beyond their classical counterparts. Together with the developed resource monotones these insights provide a novel lens into the capabilities and complexity of stationary quantum processes. The developed protocol for the reconstruction of generative models offers, for the first time, an efficient way to predict the behaviour of stationary quantum processes with memory from continuous experimental data. By accounting for long-term correlations, this approach extends beyond the case of independent and identically distributed data previously considered in tomographic setups, enabling the study of strongly correlated natural and engineered quantum processes.
Overall, our work has resulted in a multitude of novel theoretical tools for the characterisation, certification and reconstruction of general quantum processes, paving a way for the systematic control and exploitation of genuinely quantum spatio-temporal correlations in the next generation of quantum experiments and devices.
The TaQC project has provided significant foundational, platform agnostic advances in all of these areas. The exploration of correlation structures in the presence of noise has yielded, for the first time, a stratification of the space of quantum processes with classical memory and offered new insights into their practical capabilities. Given the ubiquitousness of detrimental noise, memory of this type will be dominantly present and controllable in near-term quantum devices, making this categorisation an important tool for further explorations. Analogously, the provided higher-order resource theory of athermality enables the analysis of thermodynamic properties of entire quantum devices and processes, rather than their individual building blocks, as was previously the state-of-the art.
The results of the TaQC project on the influence of memory size on observable correlations introduces a powerful tool to certify the properties of quantum processes from limited experimental control. This, in turn, opens up a novel avenue towards the efficient learning and characterisation of complex quantum devices. In addition, the algorithm developed for the numerical evaluation of the corresponding memory size witnesses is designed to automatically compress the number of free variables. Beyond the case of memory witnesses, this technique offers a feasible approach to the numerical optimsation of heretofore computationally intractable problems in quantum information theory. Similarly, the developed techniques to deduce the structural properties of general quantum processes now enable their optimisation under physical constraints and and provide the theoretical underpinnings for the systematic study of general quantum devices.
Furthermore, the TaQC project has conceptualised the important class of stationary processes in the quantum realm, and developed a roadmap of previously unknown quantum effects that these processes can display beyond their classical counterparts. Together with the developed resource monotones these insights provide a novel lens into the capabilities and complexity of stationary quantum processes. The developed protocol for the reconstruction of generative models offers, for the first time, an efficient way to predict the behaviour of stationary quantum processes with memory from continuous experimental data. By accounting for long-term correlations, this approach extends beyond the case of independent and identically distributed data previously considered in tomographic setups, enabling the study of strongly correlated natural and engineered quantum processes.
Overall, our work has resulted in a multitude of novel theoretical tools for the characterisation, certification and reconstruction of general quantum processes, paving a way for the systematic control and exploitation of genuinely quantum spatio-temporal correlations in the next generation of quantum experiments and devices.