相关论文: Quantum Complexity of Time Evolution with Chaotic …
The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatment, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less…
We address the time decay of the Loschmidt echo, measuring sensitivity of quantum dynamics to small Hamiltonian perturbations, in one-dimensional integrable systems. Using semiclassical analysis, we show that the Loschmidt echo may exhibit…
We study the universal structure of late-time ensembles obtained from unitary dynamics in quantum chaotic systems with symmetries, such as charge or energy conservation. We find that although quantum states do not ergodically explore the…
In this paper we study the notion of complexity under time evolution in chaotic quantum systems with holographic duals. Continuing on from our previous work, we turn our attention to the issue of Krylov complexity upon the insertion of a…
This work develops a symplectic framework for quantum computing to be applied to classical Hamiltonian systems, exploiting the intrinsic geometric compatibility between unitary quantum evolution and symplectic phase-space dynamics in a…
Recent proposals suggest that a notion of generalized complexity, analogous to generalized entropy, may be necessary for understanding the dynamics of holographic complexity in settings where quantum effects are non-negligible, such as…
It is demonstrated that almost any S-matrix of quantum field theory in curved spaces posses an infinite set of complex poles (or branch cuts). These poles can be transformed into complex eigenvalues, the corresponding eigenvectors being…
We consider the problem of learning the evolution operator for the time-dependent Schr\"{o}dinger equation, where the Hamiltonian may vary with time. Existing neural network-based surrogates often ignore fundamental properties of the…
In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational…
The circuit complexity for Hamiltonian simulation of the sparsified SYK model with $N$ Majorana fermions and $q=4$ (quartic interactions) which retains holographic features (referred to as `minimal holographic sparsified SYK') with $k\ll…
Quantum systems whose classical counterparts are chaotic typically have highly correlated eigenvalues and level statistics that coincide with those from ensembles of full random matrices. A dynamical manifestation of these correlations…
Quantum chaos refers to signatures of classical chaos found in the quantum domain. Recently, it has become common to equate the exponential behavior of out-of-time order correlators (OTOCs) with quantum chaos. The quantum-classical…
The presence of nonanalyticity in observables is a manifestation of phase transitions. Through the study of two paradigmatic topological models in one and two dimensions, in this work we show that the circuit complexity based on our…
Holographic entanglement entropy was recently recast in terms of Riemannian flows or 'bit threads'. We consider the Lorentzian analog to reformulate the 'complexity=volume' conjecture using Lorentzian flows -- timelike vector fields whose…
Quantum geometrodynamics with intrinsic time development is presented. Paradigm shift from full space-time covariance to spatial diffeomorphism invariance yields a non-vanishing Hamiltonian, a resolution of the `problem of time', and…
We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from…
It is known that mixed quantum states are highly entropic states of imperfect knowledge (i.e., incomplete information) about a quantum system, while pure quantum states are states of perfect knowledge (i.e., complete information) with…
Unitary $k$-designs are central to quantum information and quantum many-body physics as efficient proxies for Haar-random dynamics. We study how chaotic Hamiltonian evolution can generate unitary $k$-designs. Standard approaches typically…
We consider unitary dynamical evolutions on n qubits caused by time dependent pair-interaction Hamiltonians and show that the running time of a parallelized two-qubit gate network simulating the evolution is given by the time integral over…
We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>.…