In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.In the study of quantum transport, much has been known about dynamics near thermal equilibrium. However, quantum transport far away from equilibrium is much less well understood---the linear response approximation does not hold for physics far out of equilibrium in general. In this work, motivated by recent cold atom experiments on probing quantum many-body dynamics of a one-dimensional XXZ spin chain, where a transition from ballistic to diffusive dynamics has been established by increasing the interaction strengths, we study the strong interaction limit of the one-dimensional spinless fermion model, which is dual to the XXZ spin chain. We develop a highly efficient computation algorithm for simulating the nonequilibrium dynamics of this system exactly, and examine the nonequilibrium dynamics starting from a density modulation quantum state. We find ballistic transport in this strongly correlated setting and show that a plane-wave description emerges at long-time evolution. We also observe a sharp distinction between transport velocities in short and long times as induced by interaction effects and provide a quantitative interpretation for the long-time transport velocity. We expect our results to shed light on the understanding of the dynamics of the XXZ spin chain in the strong interaction regime.

arXiv:2206.13023Physical Review ANov 28, 20221 citation

Out-of-Equilibrium Quantum Dynamics

Yuto Ashida

Springer thesesJan 1, 20200 citations

Dynamics and Simulation of Open Quantum Systems

Michael P. Zwolak

All systems are open to an essentially uncontrollable environment that acts as a source of decoherence and dissipation. In some cases the environment's only effect is to add a weak relaxation mechanism and thus can be ignored for short timescales. In others, however, the presence of the environment can fundamentally alter the behavior of the system. Such is the case in mesoscopic superconductors where the environment can stabilize superconductivity and in spin-boson systems where the environment induces a localization transition. Likewise, in technological applications we are often interested in systems operating far from equilibrium. Here the environment might act as a particle reservoir or strong driving force. In all these examples, we need accurate methods to describe the influence of the environment on the system and to solve for the resulting dynamics or equilibrium states. In this thesis, we develop computational and conceptual approaches to efficiently simulate quantum systems in contact with an environment. Our starting point is the use of numerical renormalization techniques. Thus, we restrict our attention to one-dimensional lattices or small quantum systems coupled to an environment. We have developed several complementary algorithms: a superoperator renormalization algorithm for simulating real-time Markovian dynamics and for calculating states in thermal equilibrium; a blocking algorithm for simulating integro-differential equations with long-time memory; and a tensor network algorithm for branched lattices, which can be used to simulate strongly dissipative systems. Further, we provide support for an idea that to generically and accurately simulate the real-time dynamics of strongly dissipative systems, one has to include all or part of the environment within the simulation. In addition, we discuss applications and open questions.All systems are open to an essentially uncontrollable environment that acts as a source of decoherence and dissipation. In some cases the environment's only effect is to add a weak relaxation mechanism and thus can be ignored for short timescales. In others, however, the presence of the environment can fundamentally alter the behavior of the system. Such is the case in mesoscopic superconductors where the environment can stabilize superconductivity and in spin-boson systems where the environment induces a localization transition. Likewise, in technological applications we are often interested in systems operating far from equilibrium. Here the environment might act as a particle reservoir or strong driving force. In all these examples, we need accurate methods to describe the influence of the environment on the system and to solve for the resulting dynamics or equilibrium states. In this thesis, we develop computational and conceptual approaches to efficiently simulate quantum systems in contact with an environment. Our starting point is the use of numerical renormalization techniques. Thus, we restrict our attention to one-dimensional lattices or small quantum systems coupled to an environment. We have developed several complementary algorithms: a superoperator renormalization algorithm for simulating real-time Markovian dynamics and for calculating states in thermal equilibrium; a blocking algorithm for simulating integro-differential equations with long-time memory; and a tensor network algorithm for branched lattices, which can be used to simulate strongly dissipative systems. Further, we provide support for an idea that to generically and accurately simulate the real-time dynamics of strongly dissipative systems, one has to include all or part of the environment within the simulation. In addition, we discuss applications and open questions.

Aug 30, 20076 citations

Simulation of time-dependent quantum dynamics using quantum computers

Erik Lötstedt, Takanori Nishi, Kaoru Yamanouchi

Advances in atomic, molecular, and optical physicsJan 1, 20240 citations

Out-of-time-order correlators in electronic structure using Quantum Computers

K. J. Joven, V. M. Bastidas

Operator spreading has profound implications in diverse fields ranging from statistical mechanics and blackhole physics to quantum information. The usual way to quantify it is through out-of-time-order correlators (OTOCs), which are the quantum analog to Lyapunov exponents in classical chaotic dynamics. In this work we explore the phenomenon of operator spreading in quantum simulation of electronic structure in quantum computers. To substantiate our results, we focus on a hydrogen chain $H_4$ and demonstrate that operator spreading is enhanced when the chain is far from its equilibrium geometry. We also investigate the dynamics of bipartite entanglement and its dependence on the partition's size. Our findings reveal distinctive signatures closely resembling area- and volume-laws in equilibrium and far-from-equilibrium geometries, respectively. Our results provide insight of operator spreading of coherent errors in quantum simulation of electronic structure and can be experimentally implemented in various platforms available today.Operator spreading has profound implications in diverse fields ranging from statistical mechanics and blackhole physics to quantum information. The usual way to quantify it is through out-of-time-order correlators (OTOCs), which are the quantum analog to Lyapunov exponents in classical chaotic dynamics. In this work we explore the phenomenon of operator spreading in quantum simulation of electronic structure in quantum computers. To substantiate our results, we focus on a hydrogen chain $H_4$ and demonstrate that operator spreading is enhanced when the chain is far from its equilibrium geometry. We also investigate the dynamics of bipartite entanglement and its dependence on the partition's size. Our findings reveal distinctive signatures closely resembling area- and volume-laws in equilibrium and far-from-equilibrium geometries, respectively. Our results provide insight of operator spreading of coherent errors in quantum simulation of electronic structure and can be experimentally implemented in various platforms available today.

arXiv:2405.12289May 20, 20241 citation

Simulation of Time-Dependent Quantum Dynamics Using Quantum Computers

Erik Lötstedt, Kaoru Yamanouchi

Topics in applied physicsJan 1, 20240 citations

H_4

and demonstrate that operator spreading is enhanced when the chain is far from its equilibrium geometry. We also investigate the dynamics of bipartite entanglement and its dependence on the partition's size. Our findings reveal distinctive signatures closely resembling area- and volume-laws in equilibrium and far-from-equilibrium geometries, respectively. Our results provide insight of operator spreading of coherent errors in quantum simulation of electronic structure and can be experimentally implemented in various platforms available today.