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In this work, we show how Gibbs or thermal states appear dynamically in closed quantum many-body systems, building on the program of dynamical typicality. We introduce a novel perturbation theorem for physically relevant weak system-bath couplings that is applicable even in the thermodynamic limit. We identify conditions under which thermalization happens and discuss the underlying physics. Based on these results, we also present a fully general quantum algorithm for preparing Gibbs states on a quantum computer with a certified runtime and error bound. This complements quantum Metropolis algorithms, which are expected to be efficient but have no known runtime estimates and only work for local Hamiltonians.
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Thermal states are the bedrock of statistical physics. Nevertheless, when and how they actually arise in closed quantum systems is not fully understood. We consider this question for systems with local Hamiltonians on finite quantum lattices. In a first step, we show that states with exponentially decaying correlations equilibrate after a quantum quench. Then we show that the equilibrium state is locally equivalent to a thermal state, provided that the free energy of the equilibrium state is sufficiently small and the thermal state has exponentially decaying correlations. As an application, we look at a related important question: When are thermal states stable against noise? In other words, if we locally disturb a closed quantum system in a thermal state, will it return to thermal equilibrium? We rigorously show that this occurs when the correlations in the thermal state are exponentially decaying. All our results come with finite-size bounds, which are crucial for the growing field of quantum thermodynamics and other physical applications.
We study the role of the system-bath coupling for the generalized canonical thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure states of the universe [formed by a system S plus its surrounding heat bath $B$] to a canonical equilibrium state of S. We present an exactly solvable, but universal model for this kinematic thermalization with an explicit consideration about the energy shell deformation due to the interaction between S and B. By calculating the state numbers of the universe and its subsystems S and B in various deformed energy shells, it is found that, for the overwhelming majority of the universe states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between S and B. Particularly, the kinematic decoherence is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of S. It is pointed out that the non-vanishing off-diagonal elements due to the finiteness of bath and the stronger system-bath interaction might offer more novelties of the quantum thermalization.
We demonstrate non-classical cooling on the IBMq cloud quantum computer. We implement a recently proposed refrigeration protocol which relies upon indefinite causal order for its quantum advantage. We use quantum channels which, when used in a well-defined order, are useless for refrigeration. We are able to use them for refrigeration, however, by applying them in a superposition of different orders. Our protocol is by nature relatively robust to noise, and so can be implemented on this noisy platform. As far as the authors are aware, this is the first example of cloud quantum refrigeration.
Quantum information scrambling under many-body dynamics is of fundamental interest. The tripartite mutual information can quantify the scrambling via its negative value. Here, we first study the quench dynamics of tripartite mutual information in a non-integrable Ising model where the strong and weak thermalization are observed with different initial states. We numerically show that the fastest scrambling can occur when the energy density of the chosen initial state possesses the maximum density of states. We then present an experimental protocol for observing weak and strong thermalization in a superconducting qubit array. Based on the protocol, the relation between scrambling and thermalization revealed in this work can be directly verified by superconducting quantum simulations.
We develop a scheme for engineering genuine thermal states in analog quantum simulation platforms by coupling local degrees of freedom to driven, dissipative ancilla pseudospins. We demonstrate the scheme in a many-body quantum spin lattice simulation setting. A Born-Markov master equation describing the dynamics of the many-body system is developed, and we show that if the ancilla energies are periodically modulated, with a carefully chosen hierarchy of timescales, one can effectively thermalize the many-body system. Through analysis of the time-dependent dynamical generator, we determine the conditions under which the true thermal state is an approximate dynamical fixed point for general system Hamiltonians. Finally, we evaluate the thermalization protocol through numerical simulation and discuss prospects for implementation on current quantum simulation hardware.
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