Sebastian Deffner

We implement a variational quantum algorithm for Gibbs state preparation of a transverse-field Ising model on IonQ's quantum computers. To this end, we train the variational parameters via classical simulation and perform state tomography on the quantum devices to evaluate the fidelity of the prepared Gibbs state. As a main result, we find that fidelity decreases (non-monotonically) as a function of the inverse temperature $β$ of the system. Fidelity also decreases as a function of the size of the system. Interestingly, we find that a Gibbs state prepared for a specified $β$ is a better representative of a Gibbs state prepared for a $\textit{lower}$ $β$; or in other words, thermal fluctuations in the quantum hardware lead to digital heating, that is, an increase in the temperature of the prepared Gibbs state above what was intended.

Quantum Darwinism explains how tenets of classical reality, such as objectivity and repeatability, emerge within a quantum universe. As a mathematical framework, Quantum Darwinism also provides guiding principles that determine what physical models support emergent classical behavior, what specific observables obey classical laws, and much more. For instance, in a recent work we elucidated that the limit under which Kirkwood-Dirac quasiprobability distributions become effectively classical coincides with the regime where the underlying physical model obeys the rules of Quantum Darwinism. In the present work, we study the breaking of Quantum Darwinism in a specific model and how that translates to non-classical measurement statistics. Interestingly, this provides effective tools for benchmarking the genuine quantum characteristics of NISQ hardware, which we demonstrate with IonQ's trapped-ion and IBM's superconducting quantum computing platforms.

Only very recently, rescaling time has been recognized as a way to achieve adiabatic dynamics in fast processes. The advantage of time-rescaling over other shortcuts to adiabaticity is that it does not depend on the eigenspectrum and eigenstates of the Hamiltonian. However, time-rescaling requires that the original dynamics are adiabatic, and in the rescaled time frame the Hamiltonian exhibits non-trivial time-dependence. In this work, we show how time-rescaling can be applied to Dirac dynamics, and we show that all time-dependence can be absorbed into the effective potentials through a judiciously chosen unitary transformation. This is demonstrated for two experimentally relevant scenarios, namely for ion traps and adiabatic creation of Weyl points.

Quantum information scrambling refers to the loss of local recoverability of quantum information, which has found widespread attention from high energy physics to quantum computing. In the present analysis we propose a possible starting point for the development of a comprehensive framework for the thermodynamics of scrambling. To this end, we prove that the growth of entanglement as quantified by the mutual information is lower bounded by the time-dependent change of Out-Of-Time-Ordered Correlator. We further show that the rate of increase of the mutual information can be upper bounded by the sum of local entropy productions, and the exchange entropy arising from the flow of information between separate partitions of a quantum system. Our results are illustrated for the ion trap system, that was recently used to verify information scrambling in an experiment, and for the Sachdev-Ye-Kitaev model.

We propose an experimental scheme to realize a nano heat engine with a single ion. An Otto cycle may be implemented by confining the ion in a linear Paul trap with tapered geometry and coupling it to engineered laser reservoirs. The quantum efficiency at maximum power is analytically determined in various regimes. Moreover, Monte Carlo simulations of the engine are performed that demonstrate its feasibility and its ability to operate at maximum efficiency of 30% under realistic conditions.

We propose a scheme to investigate the nonequilibrium work distribution of a quantum particle under well controlled transformations of the external potential, exploiting the versatility of a single ion in a segmented linear Paul trap. We describe in detail how the motional quantum state of a single ion can be prepared, manipulated and finally read out to fully determine the free energy difference in both harmonic and anharmonic potentials. Uniquely to our system, we show how an ion may be immersed in an engineered laser--field reservoir. Trapped ions therefore represent an ideal tool for investigating the Jarzynski equality in open and closed quantum systems.