Shortcuts to adiabaticity for open systems in circuit quantum electrodynamics

Shortcuts to adiabaticity are powerful quantum control methods, allowing quick evolution into target states of otherwise slow adiabatic dynamics. Such methods have widespread applications in quantum technologies, and various shortcuts to adiabaticity protocols have been demonstrated in closed systems. However, realizing shortcuts to adiabaticity for open quantum systems has presented a challenge due to the complex controls in existing proposals. Here, we present the experimental demonstration of shortcuts to adiabaticity for open quantum systems, using a superconducting circuit quantum electrodynamics system. By applying a counterdiabatic driving pulse, we reduce the adiabatic evolution time of a single lossy mode from 800 ns to 100 ns. In addition, we propose and implement an optimal control protocol to achieve fast and qubit-unconditional equilibrium of multiple lossy modes. Our results pave the way for precise time-domain control of open quantum systems and have potential applications in designing fast open-system protocols of physical and interdisciplinary interest, such as accelerating bioengineering and chemical reaction dynamics.

Identifying optimal cycles in quantum thermal machines with reinforcement-learning

The optimal control of open quantum systems is a challenging task but has a key role in improving existing quantum information processing technologies. We introduce a general framework based on reinforcement learning to discover optimal thermodynamic cycles that maximize the power of out-of-equilibrium quantum heat engines and refrigerators. We apply our method, based on the soft actor-critic algorithm, to three systems: a benchmark two-level system heat engine, where we find the optimal known cycle; an experimentally realistic refrigerator based on a superconducting qubit that generates coherence, where we find a non-intuitive control sequence that outperforms previous cycles proposed in literature; a heat engine based on a quantum harmonic oscillator, where we find a cycle with an elaborate structure that outperforms the optimized Otto cycle. We then evaluate the corresponding efficiency at maximum power.

Quantum collisional thermostats

Collisional reservoirs are becoming a major tool for modelling open quantum systems. In their simplest implementation, an external agent switches on, for a given time, the interaction between the system and a specimen from the reservoir. Generically, in this operation the external agent performs work onto the system, preventing thermalization when the reservoir is at equilibrium. One can recover thermalization by considering an autonomous global setup where the reservoir particles colliding with the system possess a kinetic degree of freedom. The drawback is that the corresponding scattering problem is rather involved. Here, we present a formal solution of the problem in one dimension and for flat interaction potentials. The solution is based on the transfer matrix formalism and allows one to explore the symmetries of the resulting scattering map. One of these symmetries is micro-reversibility, which is a condition for thermalization. We then introduce two approximations of the scattering map that preserve these symmetries and, consequently, thermalize the system. These relatively simple approximate solutions constitute models of quantum thermostats and are useful tools to study quantum systems in contact with thermal baths. We illustrate their accuracy in a specific example, showing that both are good approximations of the exact scattering problem even in situations far from equilibrium. Moreover, one of the models consists of the removal of certain coherences plus a very specific randomization of the interaction time. These two features allow one to identify as heat the energy transfer due to switching on and off the interaction. Our results prompt the fundamental question of how to distinguish between heat and work from the statistical properties of the exchange of energy between a system and its surroundings.

Coherence migration in high-dimensional bipartite systems

The conservation law for first-order coherence and mutual correlation of a bipartite qubit state is first proposed by Svozilík et al. [Phys. Rev. Lett. 115, 220501 (2015)], and their theories laid the foundation for the study of coherence migration under unitary transformations. In this paper, we generalize the framework of first-order coherence and mutual correlation to an arbitrary $(m \otimes n)$-dimensional bipartite composite state by introducing an extended Bloch decomposition form of the state. We also generalize two kinds of unitary operators in high-dimensional systems, which can bring about coherence migration and help to obtain the maximum or minimum first-order coherence. Meanwhile, coherence migration in open quantum systems are investigated. We take depolarizing channels as examples and establish that the reduced first-order coherence of the principal system over time is completely transformed into mutual correlation of the $(2 \otimes 4)$-dimensional system-environment bipartite composite state. It is expected that our results may provide a valuable idea or method for controlling the quantum resource such as coherence and quantum correlations.

QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems

A full quantum mechanical treatment of open quantum systems via a Master equation is often limited by the size of the underlying Hilbert space. As an alternative, the dynamics can also be formulated in terms of systems of coupled differential equations for operators in the Heisenberg picture. This typically leads to an infinite hierarchy of equations for products of operators. A well-established approach to truncate this infinite set at the level of expectation values is to neglect quantum correlations of high order. This is systematically realized with a so-called cumulant expansion, which decomposes expectation values of operator products into products of a given lower order, leading to a closed set of equations. Here we present an open-source framework that fully automizes this approach: first, the equations of motion of operators up to a desired order are derived symbolically using predefined canonical commutation relations. Next, the resulting equations for the expectation values are expanded employing the cumulant expansion approach, where moments up to a chosen order specified by the user are included. Finally, a numerical solution can be directly obtained from the symbolic equations. After reviewing the theory we present the framework and showcase its usefulness in a few example problems.

Dynamics of Open Quantum Systems I, Oscillation and Decay

We develop a framework to analyze the dynamics of a finite-dimensional quantum system S in contact with a reservoir R. The full, interacting SR dynamics is unitary. The reservoir has a stationary state but otherwise dissipative dynamics. We identify a main part of the full dynamics, which approximates it for small values of the SR coupling constant, uniformly for all times t≥0. The main part consists of explicit oscillating and decaying parts. We show that the reduced system evolution is Markovian for all times. The technical novelty is a detailed analysis of the link between the dynamics and the spectral properties of the generator of the SR dynamics, based on Mourre theory. We allow for SR interactions with little regularity, meaning that the decay of the reservoir correlation function only needs to be polynomial in time, improving on the previously required exponential decay.In this work we distill the structural and technical ingredients causing the characteristic features of oscillation and decay of the SR dynamics. In the companion paper [27] we apply the formalism to the concrete case of an N-level system linearly coupled to a spatially infinitely extended thermal bath of non-interacting Bosons.

Dynamics of Open Quantum Systems II, Markovian Approximation

A finite-dimensional quantum system is coupled to a bath of oscillators in thermal equilibrium at temperature T>0. We show that for fixed, small values of the coupling constant λ, the true reduced dynamics of the system is approximated by the completely positive, trace preserving Markovian semigroup generated by the Davies-Lindblad generator. The difference between the true and the Markovian dynamics is O(|λ|1/4) for all times, meaning that the solution of the Gorini-Kossakowski-Sudarshan-Lindblad master equation is approximating the true dynamics to accuracy O(|λ|1/4) for all times. Our method is based on a recently obtained expansion of the full system-bath propagator. It applies to reservoirs with correlation functions decaying in time as 1/t4 or faster, which is a significant improvement relative to the previously required exponential decay.

Round table on open quantum systems

This is a discussion about open quantum systems and its application to the study of hard probes. It reviews some of the things that were said in the corresponding round table. Views are only my own.

Quarkonia dynamics in the QGP with open quantum systems

We investigate the real-time dynamics of a correlated heavy quarkantiquark pair inside the Quark-Gluon Plasma using new quantum master equations derived from first QCD principles and based on the work of Blaizot & Escobedo [4]. The full equations are directly numerically solved in one-dimension to reduce computing costs and is used to gain insight on the dynamics in both a static and evolving medium following a Björken-like temperature evolution. The effect of the initial state on the dynamics is also studied.