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In their Comment [P. Hakonen and E. B. Sonin, preceding comment, Phys. Rev. X 11, 018001 (2021)PRXHAE2160-3308], Hakonen and Sonin (HS) object to our conclusion on the absence of a dissipation-induced superconducting-to-insulating quantum phase transition (DQPT) in resistively shunted Josephson junctions (RSJJs) originally predicted by Schmid and Bulgadaev (SB). Their objections are based on the account they make of a theory explaining the DQPT in terms of Bloch bands which was developed in the 1980s and early 1990s. In this Reply, we point to several issues in the Comment which undermine the objections HS formulate against our work.

Quantum heat transfer through a generic superconducting set-up consisting of a tunable transmon qubit placed between resonators that are termined by thermal reservoirs is explored. Two types of architectures are considered, a sequential and a beam splitter setting. Applying the numerical exact hierarchical equation of motion (HEOM) approach, steady state properties are revealed, and experimentally relevant parameter sets are identified. Benchmark results are compared with predictions based on approximate treatments to demonstrate their failure in broad ranges of parameter space. These findings may allow to improve future designs for heat control in superconducting devices., 16 pages, 17 figures

openaire: EC/H2020/681311/EU//QUESS The urgent need for reliable simulation tools to match the extreme accuracy needed to control tailored quantum devices highlights the importance of understanding open quantum systems and their modeling. To this end, we compare here the commonly used Redfield and Lindblad master equations against numerically exact results in the case of one and two resonant qubits transversely coupled at a single point to a Drude-cut ohmic bath. All the relevant parameters are varied over a broad range, which allows us to give detailed predictions about the validity and physically meaningful applicability of the weak-coupling approaches. We characterize the accuracy of the approximate approaches by comparing the maximum difference of their system evolution superoperators with numerically exact results. After optimizing the parameters of the approximate models to minimize the difference, we also explore if and to what extent the weak-coupling equations can be applied at least as phenomenological models. Optimization may lead toan accurate reproduction of experimental data, but yet our results are important to estimate the reliability of the extracted parameter values such as the bath temperature. Our findings set general guidelines for the range of validity of the usual Born-Markov master equations and indicate that they fail to accurately describe the physics in a surprisingly broad range of parameters, in particular, at low temperatures. Since quantum-technological devices operate there, their accurate modeling calls for a careful choice of methods.

Master equations of Lindblad type have attained prominent status in the fields of quantum optics and quantum information since they are guaranteed to satisfy fundamental notions of quantum dynamics such as complete positivity. When Lindblad operators are used to describe thermal reservoirs in contact with an open quantum system, the fundamental laws of thermodynamics and the fluctuation-dissipation theorem provide additional mandatory criteria. We show several examples of innocent-looking Lindblad operators which have questionable properties in this regard. Compatibility criteria between Hamiltonian and Lindblad terms as well as consequences of their violation are discussed. An alternative stochastic approach to dissipative quantum dynamics is outlined and illustrated through a harmonic-chain model for which the approach of local Lindblad operators fails.

We investigate the optimal control of open quantum systems, in particular, the mutual influence of driving and dissipation. A stochastic approach to open-system control is developed, using a generalized version of Krotov's iterative algorithm, with no need for Markovian or rotating-wave approximations. The application to a harmonic degree of freedom reveals cooperative effects of driving and dissipation that a standard Markovian treatment cannot capture. Remarkably, control can modify the open-system dynamics to the point where the entropy change turns negative, thus achieving cooling of translational motion without any reliance on internal degrees of freedom., 5 pages, 3 figures; 6 page supplement, v2: major revision for wider scope, additional data, change of title, v3: fixed typo, v4: minor changes for clarity, extended supplement

Current fluctuations in a dissipative two-state system have been studied using a novel quantum dynamics simulation method. After a transformation of the path integrals, the tunneling dynamics is computed by deterministic integration over the real-time paths under the influence of colored noise. The nature of the transition from coherent to incoherent dynamics at low temperatures is re-examined., 4 pages, 4 figures; to appear in Phys. Rev. Letters

The impressive progress in fabricating and controlling superconducting devices for quantum information processing has reached a level where reliable theoretical predictions need to account for quantum correlations that are not captured by the conventional modeling of contemporary quantum computers. This applies particularly to the qubit initialization as the process which crucially limits typical operation times. Here we employ numerically exact methods to study realistic implementations of a transmon qubit embedded in electromagnetic environments focusing on the most important system-reservoir correlation effects such as the Lamb shift and entanglement. For the qubit initialization we find a fundamental trade-off between speed and accuracy which sets intrinsic constraints in the optimization of future reset protocols. Instead, the fidelities of quantum logic gates can be sufficiently accurately predicted by standard treatments. Our results can be used to accurately predict the performance of specific set-ups and also to guide future experiments in probing low-temperature properties of qubit reservoirs., 15 pages, 5 figures. Updated to published version