Related papers: Loschmidt echo approach to Krylov-subspace approxi…
The McLachlan "minimum-distance" principle for optimizing approximate solutions of the time-dependent Schrodinger equation is revisited, with a focus on the local-in-time error accompanying the variational solutions. Simple, exact…
In this paper we present a novel extended Krylov subspace reduced-order modeling technique to efficiently simulate time- and frequency-domain wavefields in open complex structures. To simulate the extension to infinity, we use an optimal…
We show how procedures which can correct phase and amplitude errors can be directly applied to correct errors due to quantum entanglement. We specify general criteria for quantum error correction, introduce quantum versions of the Hamming…
The Kitaev honeycomb model is an approximate topological quantum error correcting code in the same phase as the toric code, but requiring only a 2-body Hamiltonian. As a frustrated spin model, it is well outside the commuting models of…
We show how the Loschmidt echo of a product state after a quench to a conformal invariant critical point and its leading finite time corrections can be predicted by using conformal field theories (CFT). We check such predictions with tensor…
Quantum algorithms based on classical processing of individual samples have recently emerged as the most effective and robust methods to approximate ground-state wave functions of many-body quantum systems on pre-fault-tolerant and…
A quantum phase transition is generally thought to imprint distinctive characteristics on the nonequilibrium dynamics of a closed quantum system. Specifically, the Loschmidt echo after a sudden quench to a quantum critical point $-$…
Digital quantum simulation has broad applications in approximating unitary evolution of Hamiltonians. In practice, many simulation tasks for quantum systems focus on quantum states in the low-energy subspace instead of the entire Hilbert…
Many astrophysical simulations involve extreme dynamic range of timescales around 'special points' in the domain (e.g. black holes, stars, planets, disks, galaxies, shocks, mixing interfaces), where processes on small scales couple strongly…
A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…
The reproducing kernel Hilbert space (RKHS) embedding method is a recently introduced estimation approach that seeks to identify the unknown or uncertain function in the governing equations of a nonlinear set of ordinary differential…
The equilibration dynamics of a closed quantum system is encoded in the long-time distribution function of generic observables. In this paper we consider the Loschmidt echo generalized to finite temperature, and show that we can obtain an…
Quantum simulation of complex many-body systems beyond classical computational capabilities provides a promising route toward understanding novel quantum phases and their transitions. In particular, analog quantum simulators with global…
In this work, we propose a quantum-mechanically measurable basis for the computation of spread complexity. Current literature focuses on computing different powers of the Hamiltonian to construct a basis for the Krylov state space and the…
The breakthrough of quantum error correction brought with it the picture of quantum information as a sort of combination of two complementary types of classical information, "amplitude" and "phase". Here I show how this intuition can be…
To simulate bosons on a qubit- or qudit-based quantum computer, one has to regularize the theory by truncating infinite-dimensional local Hilbert spaces to finite dimensions. In the search for practical quantum applications, it is important…
We consider the data-driven approximation of the Koopman operator for stochastic differential equations on reproducing kernel Hilbert spaces (RKHS). Our focus is on the estimation error if the data are collected from long-term ergodic…
It is well-known that sparse grid algorithm has been widely accepted as an efficient tool to overcome the "curse of dimensionality" in some degree. In this note, we first give the error estimate of hyperbolic cross (HC) approximations with…
We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in many-body systems and…
We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate linearization in a higher-dimensional space through the exact…