Control and complexity in quantum statistical mechanics

Informations projet

Cocoquest

N° de convention de subvention: 101043705

DOI

10.3030/101043705

Date de signature de la CE 2 Mai 2022

Date de début 1 Juin 2022

Date de fin 31 Mai 2027

Financé au titre de

• European Research Council (ERC)

Coût total

€ 1 865 833,75

Contribution de l’UE

€ 1 865 833,75

Coordonné par

TECHNISCHE UNIVERSITAET WIEN
Austria

Periodic Reporting for period 1 - Cocoquest (Control and complexity in quantum statistical mechanics)

Période du rapport: 2022-06-01 au 2024-11-30

Résumé du contexte et des objectifs généraux du projet

The project aims to develop a truly quantum theory of thermodynamics. Many thermodynamic quantities in the classical realm implicitly assume the cost of measurement and control can be ignored and obtaining knowledge about a state comes with no backaction. This couldn't be further from the truth in quantum systems. Measurements cost a lot of energy and while unprecedented control of microscopic degrees of freedom is possible it comes at a cost that typically exceeds the energy scale of the system.

In this project we aim to get a full thermodynamic understanding of the measurement process, unravel the limitations and costs of controlling quantum systems and applying these insights to fundamental questions in experimental quantum technologies.

Travail effectué depuis le début du projet jusqu’à la fin de la période considérée dans le rapport et principaux résultats atteints jusqu’à présent

We formulated a hypothesis on the thermodynamic nature of measurements, the measurement equilibration hypothesis (MEH), positing that the 'collapse' of the quantum wave function can be fully understood in terms of pure state equilibration ideas, extending thermalisation hypotheses to out of equilibrium scenarios involving information acquisition. We proved that quantum processes do not adhere to the same thermodynamic limitations, expressed in classical system by so called thermodymaic uncertainty relations (TUR). Indeed, we can show that precision is not fundamentally bounded by entropy produced in the process. Furthermore we prove a fundamental trade-off between precision and resolution of clocks, study the impact of imperfect clocks on quantum circuits, derive optimal procedures for Landauer erasure of information. Finally, we put forward the first fully autonomous model of quantum computation (aQPU) that allows for a full accounting of thermodynamic resources in information processing. On the way to these main results we happened upon many further results in the mathematical characterisation of quantum states, entanglement theory, quantum many-body systems and other thermodynamic insights. Altogether more than 30 papers were put on the preprint server or published in the first period of the grant.

Progrès au-delà de l’état des connaissances et impact potentiel prévu (y compris l’impact socio-économique et les conséquences sociétales plus larges du projet jusqu’à présent)

The formulation of the measurement equilibration hypothesis opens new avenues in the foundations of quantum mechanics. We would need further examples and extensive numeric studies to successfully confirm the hypothesis and understand the requirements for emergent measurement.

The insights into precision of quantum processes could enable new designs of ultra-precise quantum technologies. We need to take these results from abstract Hamiltonian formulations to actual experimental platforms and understand how closely these idealised systems can be approximated in practive before the true potential is understood.

The results about fundamental limits of clocks will help us to better understand the thermodynamic nature of the arrow of time and the limits of miniaturising clocks with high precision and high resolution. As we took stability for granted, the next step would be to fundamentally model the inevitable drift of Hamiltonian parameters and to what extent they can be corrected and taken into account to connect our research to the contemporary understanding of atomic clocks.

The thermodynamics of complexity and information processing as well as the first fully autonomous model of quantum computation will hopefully reveal the fundamental limits of the energy cost/heat dissipation required for quantum computation and provide a realistic outlook on potentially achievable energy advantages in quantum computation and what is actually required to achieve them.