arXiv subjects

Walter T. Strunz

Publications and source records attributed to Walter T. Strunz.

At least 19 recordsLinked to original sources

arXiv2026

Regularization of Riemannian optimization: Application to process tomography and quantum machine learning

Gradient descent algorithms on Riemannian manifolds have recently been proposed as a practical tool for optimizing quantum channels. We add rank-penalizing regularization terms to the cost functions of these methods (in the spirit of Lasso), driving the optimization towards channels with as few Kraus operators as possible. For quantum process tomography of rank-deficient channels, regularization both accelerates convergence and improves the fidelity of the solution compared to the unregularized case. For quantum classification tasks, it reduces the channel rank while maintaining classification accuracy, thereby revealing the minimum rank required by the given input data.

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arXiv2026

Quantum memory precludes mixed-unitary dynamics

Unital quantum channels, defined by their property of leaving the maximally mixed state invariant, form an important class of quantum operations. A distinguished subset of these channels can be represented as a probabilistic mixture of unitary evolutions. Characterizing channels that do not admit such a decomposition is in general a hard problem with significant implications for noise mitigation in quantum technologies and for fundamental problems in quantum information theory. Here we establish a link between mixed-unitarity of unital channels and the (quantum) nature of the memory effects in non-Markovian dynamics. Translating the problem into the language of process tensors, this connection yields a hierarchy of semidefinite programs that provides numerically efficient witnesses for non-mixed-unitary behavior, outperforming existing criteria. We demonstrate the power of this approach through illustrative examples of unital channels in dimensions three and four, and show how the method can detect non-mixed-unitary behavior based on incomplete channel tomography.

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arXiv2026

Non-Markovian dynamics of the giant atom beyond the rotating-wave approximation

We study the non-Markovian dynamics of a giant artificial atom coupled to a one-dimensional acoustic waveguide beyond the rotating-wave and weak-coupling approximations. By combining an optimized ESPRIT-based decomposition of the bath correlation function with the hierarchical equations of motion (HEOM), we achieve numerically exact simulations in regimes with long memory times, finite temperature, and strong system-bath coupling. Benchmarking against analytical results reveals the breakdown of perturbative non-Markovian approaches such as Redfield theory even at weak coupling in the presence of delay-induced memory. We further show that non-Markovian features, including excitation revivals, remain robust at finite temperature and can be enhanced by increasing the system-bath coupling strength. Our approach provides a versatile framework for studying non-Markovian quantum dynamics in structured environments relevant to giant-atom platforms.

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arXiv2026

How rare are Markovian quantum dynamics?

A profound understanding of decoherence and dissipation in quantum dynamics is crucial for the realistic modeling of the evolution of quantum systems. In open quantum dynamics one distinguishes between a memoryless, so-called Markovian evolution and dynamics incorporating memory effects, termed non-Markovian. In this work we study how prevalent memory effects are in the set of all such dynamics. We thus investigate how often a Markovian description is applicable. This question is approached by investigating randomly generated two-step qubit dynamics with respect to different concepts and witnesses of non-Markovianity. We observe that almost all dynamics are non-Markovian, and only a small (yet finite) fraction is Markovian. Furthermore, we study how this proportion changes when considering certain subclasses such as lower rank or mixed-unitary dynamics. Importantly, our results shed light on the relative ratios of -- and interrelations between -- the sets of dynamics that are non-Markovian with respect to different criteria. Finally, we investigate the fraction of dynamics in which the memory effects are necessarily of quantum nature and establish a connection between two recently developed concepts that characterize the quantumness of memory in non-Markovian dynamics.

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arXiv2026

Benchmarking Floquet Master Equations for Periodically Driven Open Quantum Systems

The dynamics of open quantum systems is commonly described by quantum master equations derived under the assumption of weak system-bath coupling and a separation of timescales between system and bath. When the system is additionally subjected to a periodic driving, the validity of the resulting Floquet master equations is further restricted to regimes of weak or high-frequency driving. Here, we benchmark a set of commonly used Floquet master equations for a model of two locally driven spins coupled to a shared Ohmic reservoir at finite temperature. We systematically probe the accuracy of the equations as a function of the driving parameters, thus identifying limits of their applicability. Dynamical maps predicted by each master equation are compared against numerically exact non-Markovian simulations, tracking the full relaxation dynamics. We find that the accuracy of each master equation closely reflects the assumptions underlying its derivation. For the Floquet-Lindblad equation, errors can be strongly amplified near resonances where the secular approximation breaks down, while approaches that avoid the secular approximation perform better and exhibit a more systematic dependence of the error on driving frequency and amplitude.

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arXiv2026

Exact Floquet dynamics of strongly damped driven quantum systems

We present an approach for efficiently simulating strongly damped quantum systems subjected to periodic driving, employing a periodic matrix product operator representation of the influence functional. This representation enables the construction of a numerically exact Floquet propagator that captures the non-Markovian open system dynamics, thus providing a dissipative analogue to the Floquet Hamiltonian of driven isolated quantum systems. We apply this method to study the asymptotic heating of a reservoir in spin-boson models, characterizing the deviation from equilibrium conditions. Moreover, we show how a local driving of two qubits can be utilized to stabilize a transient entanglement buildup of the qubits originating from the interaction with a common environment. Our results make it possible to directly study both stationary and transient dynamics of strongly damped and driven quantum systems within a transparent theoretical and numerical framework.

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arXiv2026

One-to-one correspondence between Hierarchical Equations of Motion and Pseudomodes for Open Quantum System Dynamics

We unite two of the most widely used approaches for strongly damped, non-Markovian open quantum dynamics, the Hierarchical Equations of Motion (HEOM) and the pseudomode method by proving two statements: First, every physical bath correlation function (BCF) that can be written as a sum of $N$ exponential terms can be obtained from a physical model with $N$ interacting pseudomodes which are damped in Lindblad form. Second, for every such BCF there exists a non-unitary, linear transformation which mirrors the evolution of the system-pseudomode state onto the HEOM hierarchy, and vice versa. Our proofs are constructive and we give explicit expressions for the mirror transformation as well as for the pseudomode Lindbladian corresponding to a given exponential BCF. This approach also gives insight and provides elegant derivations of the corresponding Hierarchy of stochastic Pure States (HOPS) method and its nearly-unitary version, nuHOPS. Our result opens several avenues for further optimization of non-Markovian open quantum system dynamics methods.

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arXiv2026

Uniform process tensor approach for the calculation of multi-time correlation functions of non-Markovian open systems

The process tensor framework to open quantum systems provides the most general description of multi-time correlations in non-Markovian quantum dynamics. A compressed representation of a process tensor in terms of matrix product operators (MPO) can be used for numerically exact calculations of multi-time correlation functions in systems strongly coupled to a non-Markovian reservoir. We show here that the numerical scaling for computing multi-dimensional spectra can be significantly improved using a time-translation invariant MPO representation of the process tensor obtained from the uniform time-evolving matrix product operator (uniTEMPO) method. In particular, this approach provides a spectral representation of the non-Markovian dynamics that gives direct access to correlation functions in Fourier-space, avoiding explicit real-time evolution. We calculate linear and 2D electronic spectra for an example system and discuss the performance and numerical scaling of our simulations.

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arXiv2025

Verifying Quantum Memory in the Dynamics of Spin Boson Models

We investigate the nature of memory effects in the non-Markovian dynamics of spin boson models. Local quantum memory criteria can be used to indicate that the reduced dynamics of an open system necessarily requires a quantum memory in its environment. We apply two such criteria, derived from different definitions put forward in the literature, to spin boson and two-spin boson models. For the computation of dynamical maps and process tensors, we employ a numerically exact method for non-Markovian open system dynamics based on matrix product operator influence functionals, that can be applied across broad parameter regimes. We find that, with access to single-intervention process tensors, one can generally predict quantum memory in the dynamics at low temperatures. Given instead only the dynamical map, we are still able to detect quantum memory in the case of resonant environments at short evolution times. Moreover, we confirm quantum memory in the stationary dynamical regime using process tensors with the correlated steady state of system and environment as initial condition.

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arXiv2025

Revealing the quantum nature of memory in non-Markovian dynamics on IBM Quantum

We investigate memory effects in non-Markovian dynamics on superconducting quantum processors provided by IBM Quantum. We use a collision-model approach to implement suitable single- and two-qubit dynamics with a gate-based quantum circuit. Coupling the system of interest to an ancilla allows for a characterization of the process with respect to non-Markovian memory effects in general, as well as concerning the quantumness of that memory. We demonstrate that current noisy quantum hardware is capable of verifying quantum memory in single-qubit dynamics. We then discuss why a generalization of this dynamics to the two-qubit case cannot directly be simulated in a way that allows quantum memory to be observed. Nevertheless, we present an alternative toy example that demonstrates how quantum memory of two-qubit dynamics can be witnessed using current noisy quantum computers.

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arXiv2025

Operational work fluctuation theorem for open quantum systems

The classical Jarzynski equality establishes an exact relation between the stochastic work performed on a system driven out of thermal equilibrium and the free energy difference in a corresponding quasi-static process. This fluctuation theorem bears experimental relevance, as it enables the determination of the free energy difference through the measurement of externally applied work in a nonequilibrium process. In the quantum case, the Jarzynski equality only holds if the measurement procedure of the stochastic work is drastically changed: it is replaced by a so-called two-point measurement (TPM) scheme that requires the knowledge of the initial and final Hamiltonian and therefore lacks the predictive power for the free energy difference that the classical Jarzynski equation is known for. Here, we propose a quantum fluctuation theorem that is valid for externally measurable quantum work determined during the driving protocol. In contrast to the TPM case, the theorem also applies to open quantum systems and the scenario can be realized without knowing the system Hamiltonian. Our fluctuation theorem comes in the form of an inequality and therefore only yields bounds to the true free energy difference. The inequality is saturated in the quasiclassical case of vanishing energy coherences at the beginning and at the end of the protocol. Thus, there is a clear quantum disadvantage.

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arXiv2025

Genuine Quantum effects in Dicke-type Models at large atom numbers

We investigate the occurrence of genuine quantum effects and beyond mean-field physics in the balanced and unbalanced open Dicke model with a large, yet finite number of atoms $N$. Such driven and dissipative quantum many-body systems have recently been realized in experiments involving ultracold gases inside optical cavities and are known to obey mean-field predictions in the thermodynamic limit $N\to\infty$. Here we show quantum effects that survive for large but finite $N$, by employing a novel open-system dynamics method that allows us to obtain numerically exact quantum dynamical results for atom numbers up to a mesoscopic $N\approx 1000$. While we find that beyond-mean-field effects vanish quickly with increasing $N$ in the balanced Dicke model, we are able to identify parameter regimes in the unbalanced Dicke model that allow genuine quantum effects to persist even for mesoscopic $N$. They manifest themselves in a strong squeezing of the steady state and a modification of the steady-state phase diagram that cannot be seen in a mean-field description. This is due to the fact that the steady-state limit $t\rightarrow \infty$ and thermodynamic limit $N\rightarrow \infty$ do not commute.

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arXiv2025

nuHOPS: A quantum trajectory method for highly excited environments in non-Markovian open quantum dynamics

Systems in contact with an environment provide a ubiquitous challenge in quantum dynamics. Many fascinating phenomena can arise if the coupling is strong, leading to non-Markovian dynamics of the system, or collective, where the environment can become highly excited. We introduce a significant improvement of the Hierarchy of Pure States (HOPS) approach, which is able to efficiently deal with such highly excited, non-Markovian environments in a nearly unitary way. As our method relies on quantum trajectories, we can obtain dynamics efficiently, also for large system sizes by i) avoiding the quadratic scaling of a density matrix and ii) exploiting the localization properties of the trajectories with an adaptive basis. We provide the derivation of the nuHOPS (nearly unitary Hierarchy of Pure States) method, compare it to the original HOPS and discuss numerical subtleties based on an illustrative dephasing model. Finally, we show its true power using the Dicke model as the paradigmatic example of many emitters decaying superradiantly inside a cavity. We reach numerically exact solutions for up to 1000 emitters. We apply our method to study emerging higher order correlations in the emitter system or the cavity mode environment and their scaling with the number of emitters.

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arXiv2025

Entropic witness for quantum memory in open system dynamics

The dynamics of open quantum system are often modeled by non-Markovian processes that account for memory effects arising from interactions with the environment. It is well-known that the memory provided by the environment can be classical or quantum in nature. Remarkably, the quantumness of the memory can be witnessed locally by measurements on the open system alone, without requiring access to the environment. However, existing witnesses are computationally challenging for systems beyond qubits. In this work, we present a tractable criterion for quantum memory based on the von Neumann entropy, which is easily computable for systems of any dimension. Using this witness, we investigate the nature of memory in a class of physically motivated finite-dimensional qudit dynamics. Moreover, we demonstrate that this criterion is also suitable for detecting quantum memory in continuous-variable systems. As an illustrative example, we analyze non-Markovian Gaussian dynamics of a damped harmonic oscillator.

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arXiv2024

Dynamical Phase Transitions, Caustics, and Quantum Dark Bands

We provide a new perspective on quantum dynamical phase transitions (DPTs) by explaining their origin in terms of caustics that form in the Fock space representation of the many-body state over time, using the fully connected transverse field Ising model as an example. In this way we establish a connection between DPTs in a quantum spin system and an everyday natural phenomenon: The dark band between the primary and seconday bows (caustics) in rainbows known as Alexander's dark band. The DPT occurs when the Loschmidt echo crosses the switching line between the evanescent tails of two back-to-back Airy functions that dress neighbouring fold caustics in Fock space and is the time-dependent analogue of what is seen as a function of angle in the sky. The structural stability and universal properties of caustics, as described mathematically by catastrophe theory, explains the generic occurrence of DPTs in the model and suggests that our analysis has wide applicability. Based on our thorough analytical understanding we propose a protocol which can be used to verify the existence of a DPT in a finite system experiment.

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arXiv2024

Local disclosure of quantum memory in non-Markovian dynamics

Non-Markovian processes may arise in physics due to memory effects of environmental degrees of freedom. For quantum non-Markovianity, it is an ongoing debate to clarify whether such memory effects have a verifiable quantum origin, or whether they might equally be modeled by a classical memory. In this contribution, we propose a criterion to test locally for a truly quantum memory. The approach is agnostic with respect to the environment, as it solely depends on the local dynamics of the system of interest. Experimental realizations are particularly easy, as only single-time measurements on the system itself have to be performed. We study memory in a variety of physically motivated examples, both for a time-discrete case, and for time-continuous dynamics. For the latter, we are able to provide an interesting class of non-Markovian master equations with classical memory that allows for a physically measurable quantum trajectory representation.

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arXiv2024

Open Quantum System Dynamics from Infinite Tensor Network Contraction

Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of a tensor network. We show that for Gaussian environments highly efficient contraction to matrix product operator (MPO) form can be achieved with infinite MPO evolution methods, leading to significant computational speed-up over existing proposals. The result structurally resembles open system evolution with carefully designed auxiliary degrees of freedom, as in hierarchical or pseudomode methods. Here, however, these degrees of freedom are generated automatically by the MPO evolution algorithm. Moreover, the semi-group form of the resulting propagator enables us to explore steady-state physics, such as phase transitions.

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arXiv2024

Dynamics of a strongly coupled quantum heat engine -- computing bath observables from the hierarchy of pure states

We present a fully quantum dynamical treatment of a quantum heat engine and its baths based on the Hierarchy of Pure States (HOPS), an exact and general method for open quantum system dynamics. We show how the change of the bath energy and the interaction energy can be determined within HOPS, for arbitrary coupling strength and smooth time dependence of the modulation protocol. The dynamics of all energetic contributions during the operation can be carefully examined both, in its initial transient phase and also later, in its periodic steady state. A quantum Otto engine with a qubit as inherently nonlinear work medium is studied in a regime where the energy associated with the interaction Hamiltonian plays an important role for the global energy balance and, thus, must not be neglected when calculating its power and efficiency. We confirm that the work required to drive the coupling with the baths depends sensitively on the speed of the modulation protocol. Remarkably, departing from the conventional scheme of well-separated phases by allowing for temporal overlap, we discover that one can even gain energy from the modulation of the bath interactions. We visualize these various work contributions using the analogue of state change diagrams of thermodynamic cycles. We offer a concise, full presentation of HOPS with its extension to bath observables, as it serves as a universal tool for the numerically exact description of general quantum dynamical (thermodynamic) scenarios far from the weak-coupling limit.

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