Periodically driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins lead to complicated dynamics. By applying the global passivity principle from quantum thermodynamics to periodically driven quantum systems, we obtain a set of constraints for each number of cycles. For pure initial states, the observable being constrained is the survival probability. We use our constraints to detect undesired coupling to unaccounted environments in quantum circuits as well as for detecting deviations from perfect periodic driving. To illustrate the applicability of these results to modern quantum systems we demonstrate our findings experimentally on on a trapped ion quantum computer, and on various IBM quantum computers. Specifically, we provide two experimental examples where these constraints surpass fundamental bounds on leakage detection based on the standard one-cycle detection scheme (including the second law of thermodynamics). The derived constraints treat the driven circuit as a black box and make no assumptions about it. Thus, by running the same circuit several times sequentially, this scheme can be used as a diagnostic tool for quantum circuits that cannot be classically simulated. Finally, we show that , in practice, testing an $n$-cycle constraint requires only $O(\sqrt{n})$ cycles.
Periodically driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins lead to complicated dynamics. By applying the global passivity principle from quantum thermodynamics to periodically driven quantum systems, we obtain a set of constraints for each number of cycles. For pure initial states, the observable being constrained is the survival probability. We use our constraints to detect undesired coupling to unaccounted environments in quantum circuits as well as for detecting deviations from perfect periodic driving. To illustrate the applicability of these results to modern quantum systems we demonstrate our findings experimentally on on a trapped ion quantum computer, and on various IBM quantum computers. Specifically, we provide two experimental examples where these constraints surpass fundamental bounds on leakage detection based on the standard one-cycle detection scheme (including the second law of thermodynamics). The derived constraints treat the driven circuit as a black box and make no assumptions about it. Thus, by running the same circuit several times sequentially, this scheme can be used as a diagnostic tool for quantum circuits that cannot be classically simulated. Finally, we show that , in practice, testing an n-cycle constraint requires only O(n) cycles.
Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics must satisfy. We derive a set of constraints for each number of cycles. For pure initial states, the observable being constrained is the recurrence probability. We use our constraints for detecting undesired coupling to unaccounted environments and drifts in the driving parameters. To illustrate the relevance of these results for modern quantum systems we demonstrate our findings experimentally on a trapped-ion quantum computer, and on various IBM quantum computers. Specifically, we provide two experimental examples where these constraints surpass fundamental bounds associated with known one-cycle constraints. This scheme can potentially be used to detect the effect of the environment in quantum circuits that cannot be classically simulated. Finally, we show that, in practice, testing an n -cycle constraint requires executing only O(n) cycles, which makes the evaluation of constraints associated with hundreds of cycles realistic.
Driven quantum systems are systems in which a set of parameters obeys a time-dependent protocol, both periodic and non-periodic. The study of these systems bridges theoretical advances with experimental realizations in a variety of platforms—these range from quantum dot arrays to molecular junctions to trapped ions. The theoretical study is challenging due to the inherent non-equilibrium nature of the problem. These systems offer an interesting playground for quantum thermodynamics. They can be studied as quantum machines, such as refrigerators, heat pumps or engines. This poses the challenge of redefining the laws of thermodynamics in the quantum realm. This effort implies taking into account the presence of coherence, entanglement and strong correlations with the environment. In this conceptual framework, we attempt to shed new light on specific setups with applications in quantum metrology. In the first part of the Thesis, we present novel results on the thermodynamics and transport properties of quantum dots. After thoroughly introducing the main methods, namely non-equilibrium Green's functions and scattering matrix techniques, we apply these tools to adiabatic charge pumping. In this context, quantum dots, subjected to external periodic driving, act as nano-mechanical engines, transferring charge from a source to a drain. We investigate the conditions under which the pumped charge becomes quantized and how thermodynamic quantities behave in this regime. Next, we will focus on the charge shuttle mechanism in movable quantum dots as an example of a quantum clock. This physical model describes transport through a molecular state bound to two leads by van der Waals forces, with an electric field pushing the molecule from the source to the drain. The periodic oscillations arising from the system's dissipative limit cycle solution provide the basis for time measurement. We examine quantum noise primarily associated with the tunnelling process. In the second part, we propose a quantum clock that utilizes the free energy resources generated by coupling to a quantum battery, consisting of an integrable spin chain driven out of equilibrium by a quench in a chosen parameter. The operating conditions of the clock in the manifold of parameters are examined, leading to the requirement of the crossing of the critical point in the battery. The lifetime of the battery's resources is found to be extensive in its size, even when choosing a global coupling observable in the battery.
Time-periodic quantum systems are present all over science and technology. They have been successfully studied using Floquet theory, and a broad diversity of interesting phenomena such as coherent destruction of tunnelling, dynamical localization and creation of new phases of matter have been discovered. Furthermore, periodic driving has also been introduced as a tool for engineering novel quantum systems that have no static analogue. Besides these remarkable achievements for isolated systems, in reality, systems always interact with their surroundings. Taking the effect of the environment into account, time-periodic quantum systems have been mainly described using the Floquet-Markov approach, which consists in deriving a weak coupling master equation in the Floquet basis. In this thesis, we focus on how to overcome these standard approximations in the description of driven open quantum systems. We start by providing a general review on the topics of isolated driven systems, open quantum systems and the Floquet-Markov approach, before presenting the main results of this work. Under the effect of high-frequency driving, we provide an analytic solution to a large class of open quantum systems. Our method relies on discrete symmetries of the system-bath Hamiltonian and grants access to the time evolution operator of the full system, including bath degrees of freedom. The solution can be interpreted as the stroboscopic evolution of a family of observables under the influence of an effective static Hamiltonian. This provides a flexible simulation procedure of nontrivial Hamiltonians. The results are exemplified with the driven spin-boson model, where a coherent control of dissipation is observed. By a novel combination of Floquet theory, full counting statistics and a Markovian embedding strategy (reaction coordinate mapping), more intricate scenarios with additional driven system-environment interactions are addressed. Hereby, we can access the dynamics and thermodynamics of a periodically driven thermal machine. For the particular case where the working medium is a two-level system, we identify four different operating regimes, including a heat engine and a refrigerator. As the coupling strength is increased, their efficiency and coefficient of performance decrease and the refrigerator regime disappears. Notably, our model reproduces the setup of laser cooling of trapped ions in a specific parameter limit. Following the same combination of methods, we investigate electron pumping through a single quantum dot with periodically modulated energy and tunnelling amplitudes. In the high-frequency regime, the direction of the current can be controlled with the driving phase and a rectification effect that is exclusive to the non-Markovian character of the model is observed. In the low-frequency regime, we apply an additional transformation to view the model as three independent transport channels and observe that the coupling strength also controls the current direction. Studying charge fluctuations we validate that our model behaves as a single-electron source.
As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process tomography is a natural way to characterize sources of experimental error, the intense measurement requirements make these strategies infeasible in all but the smallest of quantum systems. In this work, we formulate signatures of unitary evolution based on specific properties of periodically driven quantum systems. The absence of these signatures indicates a break either in the unitarity or periodicity condition on the evolution. We experimentally detect incoherent error on a trapped-ion quantum computer using these signatures. Our method is based on repeated measurements of a single observable, making this a low-cost evaluation of error with measurement requirements that scales according to the character of the dynamics, rather than the system size.
Periodically driven quantum systems offer an exceptional platform for quantum simulations due to the possibility to approximate their dynamics in terms of time-independent effective Hamiltonians. This, together with the recent experimental advances, has situated driven systems at center stage of engineered quantum-mechanical devices. The aim of this thesis is to develop theoretical methods in order to design optimal quantum simulations with driven systems. By applying the derived tools to experimentally relevant models, the applicability and significance of the methods are furthermore demonstrated. First, we introduce a method to derive accurate effective Hamiltonians by merging two seemingly unrelated tools: Floquet theory and flow equations. With this, the required analytical identification of the effective Hamiltonian in terms of the system's parameters is achieved. Second, we identify structural properties that determine the accessible effective dynamics of a system of particles on shaken optical lattices, which is arguably one of the most remarkable systems for many-body quantum simulations. In particular, we identify fundamental symmetries of the underlying lattice geometry that determine the emergence of new tunneling processes. Third, we develop an optimal control scheme to design polychromatic driving protocols that optimally simulate specifically targeted dynamics. We apply this scheme to demonstrate an optimal realization of Raman transitions with a Lambda system, a building block in many quantum simulations. Then, we employ it to implement a topological Chern insulator through suitably engineering the geometry-dependent tunneling of particles on a shaken hexagonal lattice. Hereby, a realistic route to experimentally test strongly-correlated topological phases of matter is provided. By determining structural properties of driven systems and suitable driving protocols, the methods described in this thesis open substantial possibilities for the development of optimal quantum simulations and, ultimately, reliable quantum technologies.
Abstract We investigate the long-time behavior of quantum N -level systems that are coupled to a Markovian environment and subject to periodic driving. As our main result, we obtain a general algebraic condition ensuring that all solutions of a periodic quantum master equation with Lindblad form approach a unique limit cycle. Quite intuitively, this criterion requires that the dissipative terms of the master equation connect all subspaces of the system Hilbert space during an arbitrarily small fraction of the cycle time. Our results provide a natural extension of Spohn’s algebraic condition for the approach to equilibrium to systems with external driving. Moreover, our theory leads to a rigorous condition for the emergence of dissipative discrete time crystals and covers also classical, periodically modulated Markov jump processes.