Engineering Nonequilibrium Dynamics of Open Quantum Systems

Decoherence is largely accepted to be responsible for the lack of quantum correlations at the macroscale. It explains the emergence of classical behavior from the quantum substrate. To beat decoherence and dissipation, one option is to tailor the environment-system coupling. Alternatively, novel recent paradigms fully embrace the open dynamics for state preparation and dissipative quantum computation. Yet, techniques to engineer the required many-body decoherence in the laboratory remain to be developed. I introduce a versatile scheme for the quantum simulation of the open dynamics of a many-body system embedded in an environment to which it couples via arbitrary many-body interactions. The approach exploits current technology for digital and analog quantum simulation of unitary dynamics harnessing noise as a resource, and can be readily implemented in various quantum experimental platforms such as trapped ions, superconducting circuits and cold atoms. Further, I pose the question as to what is the largest possible decoherence rate in a quantum system. To answer it, I introduce an expression for the decoherence rate under arbitrary Markovian dynamics, and use to investigate decoherence in complex many-body systems. I shall show that the decoherence rate can scale at most exponentially with the particle number. This 'extreme decoherence', which constitutes the ultimate bound to the decoherence pace achievable by physical processes, can be observed in chaotic quantum systems described by random matrix Hamiltonians. Such chaotic systems can be explored in a variety of experimental physical platforms including superconducting qubits, trapped ions and simulators with Rydberg atoms. [1] A. Chenu, M. Beau, J. Cao, and A. del Campo, PRL 118:140403 (2017) [2] Zhenyu Xu, L.-P. Garcia-Pintos, A. Chenu, and A. del Campo, PRL 122:014103 (2019)

Irreversibility is one of the most intriguing concepts in physics. While microscopic physical laws are perfectly reversible, macroscopic average behavior has a preferred direction in time. According to the second law of thermodynamics, this arrow of time is associated with a positive mean entropy production. We will discuss the physics of the quantum arrow of time and present results of recent experimental investigations of irreversibility in a nuclear magnetic resonance setup.

Colour centers in diamond are promising candidates for nanoscale quantum sensing and quantum enhanced imaging. In this talk, we will highlight new techniques enabling high spectral resolution in nanoscale NMR. We will also show experiments aiming to develop hyperpolarization enhanced NMR and MRI based on polarization transfer form optically pumped electron spins in diamond to nuclear spins.

A popular saying states that “there ain’t no such thing as a free lunch.” Although quite casually formulated, this phrase expresses nothing less than the gist of the second law of thermodynamics, namely, that non-ideal processes are always accompanied by the irreversible expense of a thermodynamic resource. Nevertheless, recent research in quantum control and quantum thermodynamics has seen growing popularity of so-called “shortcuts to adiabaticity,” i.e., fast processes with the same outcome as an ideal, infinitely slow process. While effectively adiabatic dynamics can be realised through a variety of techniques, often overlooked has been a critical assessment of the energetic resources required for their implementation. Recently several approaches to assess this "cost" have been proposed, thus providing a quantitative framework to critically compare and contrast these techniques. By focusing on paradigmatic settings involving only a few degrees of freedom, we assess the cost of achieving high fidelity control and in the process provide a hierarchy in the resource intensiveness of quantum control.

Recent study on isolated quantum many-body systems have revealed two different phases distinguished by their dynamics and spectral statistics. One is an ergodic phase whose spectral statistics exhibit universality of random matrices, and the other is a many-body localized phase where dynamics is constrained due to strong disorder. In this talk, we show that novel and rich physics concerning such localization and universality appears in non-Hermitian many-body systems, which have been utilized in diverse scientific disciplines from open quantum systems to biology. As a first topic, we analyze non-Hermitian quantum many-body systems in the presence of interaction and disorder [1]. We demonstrate that a novel real-complex transition occurs upon many-body localization of non-Hermitian interacting systems with asymmetric hopping that respect time-reversal symmetry. As a second topic, we show that "Dyson's threefold way," a threefold symmetry classification of universal spectral statistics of random matrices, is nontrivially extended to non-Hermitian random matrices [2]. We report our discovery of two distinct universality classes characterized by transposition symmetry, which is distinct from time-reversal symmetry due to non-Hermiticity. We show that the newly found universality classes indeed manifest themselves in dissipative quantum many-body ergodic systems described by non-Hermitian Hamiltonians. References: [1] RH, K. Kawabata, and M. Ueda, arXiv:1811.11319 (2018). [2] RH, K. Kawabata, N. Kura and M. Ueda, arXiv:1904.13082 (2019).

Understanding the interplay between quantum chaos and decoherence is a longstanding problem. In this talk, we pose the question as to what is the ultimate limit to the rate of decoherence for complex quantum systems. We first introduce a decoherence rate that applies to arbitrary Markovian processes and used it to demonstrate that fluctuating chaotic systems described by random matrix theory exhibit extreme decoherence. The latter is characterized by a rate that grows exponentially with the particle number, thus surpassing the dynamics of nonchaotic k-body Hamiltonians. These findings suggest the use of quantum chaotic systems as a natural test bed for spontaneous wave function collapse models.

The description of open quantum systems is amenable to a broad range of theoretical tools. Those include the derivation of different types of reduced master equations from specific microscopic modes and under the validity of physically motivated assumptions. A conceptually different approach relies on the formulation of phenomenological master equations, which in the more abstract formalism yield to the description of open system dynamics in terms of quantum channels. Using quantum metrology as a thread, I will illustrate the interrelation and complementarity of different formalisms to describe open quantum systems in order to provide a comprehensive approach to determining fundamental limits to the ultimate achievable precision in metrology and sensing.

We consider a class of quantum lattice models in 1 + 1 dimensions, specifically local quantum circuits, which enjoy a particular ‘dual unitarity’ symmetry. In essence, this symmetry ensures that both the evolution ‘in time’ and that ‘in space’ are given in terms of unitary transfer matrices. We show that for this class of circuits one can compute explicitly all dynamical correlations of local observables by studying a simple one-qudit uni-stochastic quantum maps. Our result is exact, non-pertubative, and holds for any dimension d of the local Hilbert space. In the minimal case of qubits (d = 2) we also present a complete classification of all dual unitary circuits which allows us to single out a number of universality classes for the behaviour of the dynamical correlations. We stress that these systems are generically non-integrable and include ergodic and non-ergodic behavior.

The recent rise in high-fidelity quantum technological devices has necessitated detailed understanding of open quantum systems and how their environment influences their performance. However, it has remained unresolved how to include explicitly known correlations between a system and its environment in the dynamical evolution. In the standard weak-coupling (Born-Markov) regime, the explicit dependence of the dynamics on correlations are neglected. Beyond this regime, more general equations have been obtained, yet without explicit dependence on correlations. Here, we propose a correlation picture which allows to derive an exact dynamical equation with system-environment correlations included. We show that systematic approximations to this equation yield conveniently solvable master equations. Our formalism provides a powerful approach to describe open systems and may give new insight in fundamental processes such as thermalization.

The analysis of open quantum systems (OQS) has been successfully tackled for particular situations, for instance when the OQS is weakly coupled to an environment that can be described as a set of harmonic oscillators. Nevertheless, as I will discuss in this talk much less is known about other cases, like an OQS strongly coupled to an environment that may present significant anharmonicities or even strong correlations. While the progress of quantum technologies requires understanding such situations, both numerical and theoretical tools become more involved and less efficient. In this context, I will discuss how to describe and model the dynamics of open system coupled to anharmonic environments, and also the idea of using ultra-cold atoms to simulate the open system dynamics in a variety of configurations and regimes that are not reachable otherwise.

The out-of-equilibrium behaviour of Rydberg gases is governed by emergent kinetic constraints. Such constraints are often used to mimic dynamical arrest or excluded volume effects in idealised models of glass forming substances and lead to a remarkably rich physics including non-equilibrium phase transitions and localisation phenomena. Moreover, Rydberg gases offer intriguing opportunities for the systematic exploration of the role of competing quantum and classical dynamical effects on non-equilibrium phase transitions. I will present recent results regarding this research direction, considering ordered and disordered Rydberg gases and competing classical and quantum processes, both in discrete and continuous time.

Abstract: We construct a topological invariant that classifies density matrices of symmetry protected topological orders in two‐dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the topological Uhlmann number nU. With it, we study thermal topological phases in several two‐dimensional models of topological insulators and superconductors, computing phase diagrams where the temperature T is on an equal footing with the coupling constants in the Hamiltonian. Moreover, we find novel thermal‐topological transitions between two non‐trivial phases in a model with high Chern numbers. At small temperature we recover the standard topological phases as the Uhlmann number approaches to the Chern number

In this talk I will demonstrate an explicit construction of a counter-diabatic driving protocol allowing for implementation of fast isothermal processes in an open system. I will show how one can realize this protocol using Floquet engineering and show its applications to designing a fast and efficient Otto engine. The protocol is relying on coherent dynamic and can not be obtained within the standard Markovian approximation of the bath. In the end I will discuss a general strategy of constructing local counter-diabatic protocols using Floquet engineering.

Counterdiabatic driving is a way of generating adiabatic dynamics at arbitrary pace, where excitations due to non-adiabaticity can be exactly compensated using the adiabatic gauge potential. However, obtaining and implementing this gauge potential in many-body systems is a formidable task, requiring knowledge of the spectral properties of the instantaneous Hamiltonians and control of highly nonlocal multibody interactions. We show how an approximate gauge potential can be built up as a series of nested commutators, which can be easily obtained and used to systematically suppress excitations. This gauge potential can then be generated up to arbitrary order using tools from periodically-driven (Floquet) systems through resonant oscillations of the instantaneous Hamiltonian with the driving term, such that approximate counterdiabatic driving protocols can be realized without leaving the available control space. This is illustrated on few- and many-body quantum systems, where the resulting fast-forward protocols provide a drastic increase in fidelity.

We propose a new protocol for engineering quantum many-body Hamiltonians with enhanced symmetries. The protocol is based on repeated pulsed application of a set of unitary operators $X_i$, with $X_i^2 = 1$, (which can be generalizedto $X^n = 1, n>2$) in a self-similar-in-time ("polyfractal”) manner. For local initial Hamiltonians, the protocol can simultaneously implement multiple global and local symmetries, with the accuracy improving superpolynomially with the fastest drive period. The effective Hamiltonian remains local and avoids heating over time scales that are stretched-exponentially long in the drive frequency. Such Floquet engineering can be used to realize novel quantum models, or in the case when two or more global symmetries $X_i$ anti-commute, engender a degenerate many-body spectrum that can be used to encode topological qubits controlled precisely by the same $X_i$. We also discuss how our protocol can be implemented robustly using a setup based on Majorana fermions. Networks of such Majoranas can be used to implement novel symmetry-protected topological phases, lattice gauge theories, among others.

The performance enhancements observed in various models of continuous quantum thermal machines have been linked to the buildup of coherences in a preferred basis. But, is this connection always an evidence of 'quantum-thermodynamic supremacy'? By force of example, we show that this is not the case. In particular, we compare a power-driven three-level quantum refrigerator with a four-level combined cycle, partly driven by power and partly by heat. We focus on the weak driving regime and find the four-level model to be superior since it can operate in parameter regimes in which the three-level model cannot, it may exhibit a larger cooling rate, and, simultaneously, a better coefficient of performance. Furthermore, we find that the improvement in the cooling rate matches the increase in the stationary quantum coherences exactly. Crucially, though, we also show that the thermodynamic variables for both models follow from a classical representation based on graph theory. This implies that we can build incoherent stochastic-thermodynamic models with the same steady-state operation or, equivalently, that both coherent refrigerators can be emulated classically. More generally, we prove this for any N-level weakly driven device with a 'cyclic' pattern of transitions. Therefore, even if coherence is present in a thermal machine, it is often unnecessary for the underlying energy conversion process.

Quantum simulators are widely seen as one of the most promising near-term applications of quantum technologies. These devices are expected to be able to simulate complex quantum systems that are not efficiently simulatable on a classical computer. However, it remains unclear to what extent a device without fault tolerant error correction can output reliable results in the presence of realistic imperfections. In this talk I will present two implementations of quantum simulators that allow us to study experimentally the power and limitations of these analog devices. First, I will describe a small-scale programmable quantum processor based on the optimal control of the dynamics within the electronic ground state of single neutral atoms. By theoretically studying spin models which present quantum critical behavior, such as the transverse field Ising and the Lipkin-Meshkov-Glick models, we characterize how well different quantities related to the quantum dynamics, can be extracted from a noisy simulation, and relate the observed behavior with the onset of quantum chaos in these systems. Then, I will describe a measurement-based feedback simulator based on a large ensemble of symmetrically coupled neutral atoms, which is suitable for exploring the emergence of chaos from quantum dynamics.

The general desire to break the symmetry of reciprocity in engineered photonic structures has garnered an immense amount of recent interest, as nonreciprocity is fundamental for the design of optical devices which allow for unidirectional routing of photonic signals. Especially, nonreciprocal microwave-frequency devices are crucial to efforts at quantum-information processing with superconducting circuits. However, although nonreciprocal concepts are realizable in quantum architectures, nonreciprocity itself holds up to the classical level and is not inherently quantum; the fundamental aspects of nonreciprocity in the quantum regime have yet to be fully investigated. A first question one might ask is, if a nonreciprocal, and therewith as well dissipative, system can generate entanglement between it’s constituents? In this talk we will address this question and discuss under which conditions bi-bipartite system can generate entanglement.

In the last years, superconducting quantum circuits have opened new avenues in the study of the spin-boson model physics and open quantum systems. Unlike traditional approaches that focus on the spin degree of freedom and its decoherence, superconductors allow for a detailed characterization of the state of the environment, thanks to amplification and low-noise homodyne measurements. This makes it possible to study the non-equilibrium dynamics of quantum emitters (superconducting qubits) interacting with non-classical states of the bosonic fields (microwave photons) in extreme regimes of interaction. In this talk I will review our collaboration with various groups in studying the spin-boson model, from strong to ultrastrong coupling [1,2]. I will detail our theoretical effort to model such experiments, from matrix product states to scattering theory and polaron models [3], and new methods to probe the spin-boson interactions using coherent states and homodyne measurements [4]. [1] Forn-Díaz, P., et al. "Ultrastrong coupling of a single artificial atom to an electromagnetic continuum in the nonperturbative regime." Nature Physics 13.1 (2017): 39. [2] Haeberlein, Max, et al. "Spin-boson model with an engineered reservoir in circuit quantum electrodynamics." arXiv preprint arXiv:1506.09114 (2015). [3] Shi, Tao, Yue Chang, and Juan José García-Ripoll. "Ultrastrong coupling few-photon scattering theory." Physical review letters 120.15 (2018): 153602. [4] Ramos, Tomás, and Juan José García-Ripoll. "Multiphoton scattering tomography with coherent states." Physical review letters 119.15 (2017): 153601.

I will introduce boundary time-crystals where continuous time-translation symmetry breaking occurs at the boundary (or generically in a macroscopic portion) of a many-body quantum system. After introducing their definition and properties, I analyse in details a solvable model. I will provide examples of other systems where boundary time crystalline phases can occur. The existence of the boundary time crystals is intimately connected to the emergence of time-periodic steady state in the thermodynamic limit of a many-body open quantum system. Connection to quantum synchronisation will be also discussed. References: [1] F. Iemini, A. Russomanno, J. Keeling, M. Schirò, M. Dalmonte, and R. Fazio, Phys. Rev. Lett. 121, 035301 (2018)

Almost everything a fault-tolerant quantum computer will do will be dedication to a single task: error correction. Performing computations will essentially be a side effect of the error correction process. To determine the performance of such a device, we can therefore focus on how well it implements the detection and correction of errors. In this talk I will present results from a minimal implementation of the repetition code on the 16 qubit Rueschlikon device. I will also propose tests based on the surface code that could be applied to the emerging generation of quantum processors.

Quantum jumps are emblematic of all things quantum. Certainly that is so in the popular mind. And more than merely an echo from the past, the term “quantum jump” still holds a prominent position within the lexicon of modern physics today. What, however, is the character of the jump on close inspection? Is it discontinuous and discrete, as in Bohr’s original conception? Or is it some form of continuous Schrödinger evolution that might be monitored and reconstructed, even interrupted and turned around? I consider the jumps of single trapped ions observed in the mid-1980s [1], where the view from quantum trajectory theory favours the latter option. I present that view and support it with experimental results [2], which recover the continuous and deterministic path of quantum jumps in a superconducting circuit from conditional quantum state tomography. [1] W. Nagourney et al., Phys. Rev. Lett. 56, 2797 (1986); T. Sauter et al., Phys. Rev. Lett. 57, 1696 (1986); J. C. Bergquist et al., Phys. Rev. Lett. 57, 1699 (1986). [2] Z. K. Minev, S. O. Mundhada, S. Shankar, P. Rheinhold, R. Gutiérrez-Jáuregui, R. J. Schoelkopf, M. Mirrahimi, H. J. Carmichael, and M. H. Devoret, arXiv:1803.00545 (2018).

Qubit systems offer unique opportunities for sensing and estimation. On the one hand, the use of entangled qubit states can yield measurement precision that exceeds the optimal bounds achievable classically. On the other hand, the exquisite sensitivity of qubits to their surrounding environment makes them natural spectrometers of their own noise. In this talk, I will present recent results on both parameter estimation and spectral estimation by qubit sensors in realistic correlated noise environments. I will first consider the paradigmatic setting of frequency estimation by Ramsey interferometry and show how spatiotemporally correlated quantum noise, characterized by frequency-asymmetric spectra, can introduce additional sources of uncertainty due to uncontrolled entanglement of the qubit sensors mediated by the bath. In particular, I will discuss how this analysis is directly relevant to amplitude sensing experiments with trapped ion crystals. I will then highlight some of our efforts toward developing control methods for quantum noise spectroscopy. In particular, I will describe how protocols inspired by both dynamical decoupling and spin-locking relaxometry may be used to characterize non-Gaussian noise sources as well as noise correlations, and outline experimental validation using superconducting qubit devices.

The information acquired during the monitoring of a quantum system provides a state description that can differ greatly from the description given by agents ignorant of the outcomes. While the lack of information in the latter results in a mixed density matrix following open system dynamics, the measurement back-action in the former case provides a more accurate description. I discuss the consequences of such measurement back-action to two problems in quantum theory, the derivation of limits to the speed of evolution, and the process of spontaneous symmetry breaking, focusing on the different descriptions that agents provide of a given system.

We characterize the conditions which allow us to describe the general, non-Markovian dynamics of an open quantum system by means of a simpler model, consisting in an enlarged set of degrees of freedom undergoing a Markovian (Lindbladian) dynamics. After presenting the equivalence theorem between the two systems, we show how to exploit it to build up in a systematic and certied way auxiliary models, which can be treated efficiently by means of existing numerical techniques.

Quasi-periodic systems in one dimension display extremely rich transport properties, including a localisation transition with a mobility edge and anomalous sub-diffusive behaviour in certain regimes. Here we exploit the mobility edge and unusual band structure of a quasi-periodic system to create an energy filter for energy and particle transport. We show how this can be used to construct a highly efficient heat engine that extracts electrochemical power from a temperature gradient. This points to the significant potential of quasi-periodic systems for quantum thermodynamics.

Quantum mechanics allows us to post-select events that cannot be observed classically. Even though these events are rare we cannot create a classical set-up that allows us to observe such an effect. Strong projective measurements that lead to the wave-function collapse of the measured system also could perturb its coupled environment. While such control has been mostly used for quantum state preparation of small nuclear spin ensembles and in cavity QED experiments, inducing/transducing quantum mechanical properties onto the measurement statistics itself has not been achieved. We experimentally and theoretically demonstrate this fundamental effect in a central spin model, where the measurement (back-to)-back action of the measured central spin and its coupled environment onto each other lead to non-classical (Quantum Random Walk like) measurement statistics of the central spin. Using Nitrogen Vacancy centers in diamond as the central spin, and its projective single-shot readout at low temperatures, we show how the coherent nuclear-spin environment to which it is coupled allows its measurement statistics display non-classical features. The long-life time of the spin environment correlating subsequent measurements also leads to bath-engineering i.e., a modified bath spectrum, resulting in an enhanced coherence time ($T_2^*$) of the central spin. The observed non-classical statistics and bath purification could be important for quantumness certification protocols and for quantum state engineering.

Quantum detailed balance conditions and quantum fluctuation relations are two important concepts in the dynamics of open quantum systems; both concern how such systems behave when they thermalize because of interaction with an environment. I show that for thermalizing quantum dynamics the quantum detailed balance conditions yield validity of a quantum fluctuation relation (where only forward-time dynamics is considered). This implies that to have such a quantum fluctuation relation (which in turn enables a precise formulation of the second law of thermodynamics for quantum systems) it suffices to fulfill the quantum detailed balance conditions. I, however, argue that the converse is not necessarily true; there exit cases of thermalizing dynamics which feature the quantum fluctuation relation without satisfying detailed balance.

We report the theoretical discovery and characterization of higher-order Floquet topological phases dynamically generated in a periodically driven system with mirror symmetries. We demonstrate numerically and analytically that these phases support lower-dimensional Floquet bound states, such as corner Floquet bound states at the intersection of edges of a two-dimensional system, protected by the nonequilibrium higher-order topology induced by the periodic drive. We characterize higher-order Floquet topologies of the bulk Floquet Hamiltonian using mirror-graded Floquet topological invariants. This allows for the characterization of a new class of higher-order ``anomalous'' Floquet topological phase, where the corners of the open system host Floquet bound states with the same as well as with double the period of the drive. Moreover, we show that bulk vortex structures can be dynamically generated by a drive that is spatially inhomogeneous. We show these bulk vortices can host multiple Floquet bound states. This ``stirring drive protocol'' leverages a connection between higher-order topologies and previously studied fractionally charged, bulk topological defects. Our work establishes Floquet engineering of higher-order topological phases and bulk defects beyond equilibrium classification and offers a versatile tool for dynamical generation and control of topologically protected Floquet corner and bulk bound states.

We give rigorous analytical results about the behavior of two-point correlation functions in quantum many body systems undergoing unitary dynamics (also known as dynamical response functions or Green’s functions). These appear in the characterization of wide range of statistical and non-equilibrium phenomena, including quantum transport, fluctuation-dissipation theorems, linear response theory or scattering experiments. First, using recent results from large deviation theory, we are able to show that in a large class of models the correlation functions factorize at late times, proving that dissipation emerges out of the unitary dynamics of the system. We also show that the fluctuations around this late-time value are bounded by the “effective dimension”, which generally decays exponentially with system size. This result connects the behavior of correlation functions to the physics of equilibration of quenched systems. Moreover, for autocorrelation functions such as (including the symmetric and antisymmetric versions) we provide an upper bound on the timescale at which they reach the “dissipated” late time value. Remarkably, this turns out to be related to local expectation values only, and it doesn’t increase with system size. We give numerical examples that illustrate how this upper bound is in fact a good estimate, and we argue this timescale can be understood in terms of an emergent fluctuation-dissipation theorem. Our study extends to larger classes of two point functions. In particular, we also show that the Kubo correlation function that controls the linear response theory evolves under a similar timescale.

Autonomous quantum error correction utilizes the engineered coupling of a quantum system to a dissipative ancilla to protect quantum logical states from decoherence. We show that the Knill-Laflamme condition, stating that the environmental error operators should act trivially on a subspace, which then becomes the code subspace, is sufficient for logical qudits to be protected against Markovian noise. It is proven that the error caused by the total Lindbladian evolution in the code subspace can be suppressed up to very long times in the limit of large engineered dissipation, by explicitly deriving how the error scales with both time and engineered dissipation strength. To demonstrate the potential of our approach for applications, we implement our general theory with binomial codes, a class of bosonic error-correcting codes, and outline how they can be implemented in a fully autonomous manner to protect against photon loss in a microwave cavity. https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.012317

In order to model realistic quantum devices that are out of equilibrium, it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems has been restricted either to weak system-bath couplings, or to special cases where specific numerical techniques become effective. Here we present a general and yet exact numerical approach that efficiently describes the time evolution of a quantum system coupled to a non-Markovian environment [1]. The method combines path integral techniques [2] with tensor networks [3], and at its core is a time-evolving matrix product operator (TEMPO) description of quantum dynamics. We demonstrate the power and flexibility of TEMPO by numerically identifying the localisation transition of the Ohmic spin-boson model [4], and considering a model with widely separated environmental timescales arising for a pair of spins embedded in a common environment. In the latter model, we are able to directly calculate the time evolution of the bath displacement close to the two quantum dots, and show how these influence the dot dynamics. We will finish by discussing some new predictions on the spectrum and dynamics of a quantum dot, that is driven strongly out of equilibrium. We observe the breakdown of polaron physics at strong driving. References: [1] A. Strathearn, P. Kirton, D. Kilda, J. Keeling, and B. W. Lovett, Efficient non-Markovian quantum dynamics using time-evolving matrix product operators, arXiv:1711.09641 (2017) [2] N. Makri and D. E. Makarov Tensor propagator for iterative quantum time evolution of reduced density matrices J. Chem. Phys. 102, 4600 (1995) [3] R. Orús, A practical introduction to tensor networks, A practical introduction to tensor networks, Ann. Phys. 349 117 (2014) [4] A. J. Leggett et al. Dynamics of the dissipative two-state system, Rev. Mod. Phys. 59, 1 (1987)

The quantum speed limit (QSL) inequality gives a fundamental lower bound on the operation time for the quantum control. Since it is related to the time-energy uncertainty relation, the QSL has gathered significant interest among researchers in different fields. It is also relevant to applied physics, where QSL has been studied in various fields such as quantum computation, quantum metrology, quantum optimal control, and quantum thermodynamics. In actual experiments, the effect of the environment cannot be neglected, and extending the QSL to open quantum systems is needed. However, previous studies in formulating the QSLs remain as a formal mathematical expression. From their results, it is difficult to extract physical mechanism determining the speed in quantum dynamics. In the presentation, we discuss the QSL for open quantum systems described by the Lindblad master equation and formulate the QSL by using physical quantities such as the energy fluctuation and the entropy production [1]. These well-established quantities allow us to obtain intuition about how one can speed up quantum operations in open systems. In addition, the obtained QSL unifies the previously obtained results for isolated quantum and classical stochastic [2] systems. We further identify a quantity characterizing the speed of the state transformation which has not been reported in previous literatures. In the thermodynamically quasi-adiabatic regime, we show a nontrivial connection between this new quantity and the energy fluctuation of the counter-diabatic Hamiltonian used in shortcuts to adiabaticity. It may suggest further connection between the finite-time quantum control theory and QSLs. [1] K. Funo, N. Shiraishi, and K. Saito "Speed limit for open quantum systems" New Journal of Physics 21, 013006 (2019). [2] N. Shiraishi, K. Funo, and K. Saito "Speed Limit for Classical Stochastic Processes" Physical Review Letters 121, 070601 (2018).