Related papers: Dynamical approximations for composite quantum sys…
Azbel' has recently carried out a WKB-analysis of the effects of a nonharmonic time-dependent perturbation embedded in an opaque potential barrier. He suggests the existence of three different transmission regimes: direct tunneling,…
We introduce a novel algorithm that leverages stochastic sampling techniques to compute the perturbative triples correction in the coupled-cluster (CC) framework. By combining elements of randomness and determinism, our algorithm achieves a…
Connecting multiple smaller qubit modules by generating high-fidelity entangled states is a promising path for scaling quantum computing hardware. The performance of such a modular quantum computer is highly dependent on the quality and…
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…
We analyze the performance of a quantum error correction code subject to physically motivated noise modeled by a Lindblad master equation. We consider dissipative and coherent single-qubit terms and two-qubit crosstalk, studying how…
Coupled cluster theory is one of the most popular post-Hartree-Fock methods for ab initio molecular quantum chemistry. The finite-size error of the correlation energy in periodic coupled cluster calculations for three-dimensional insulating…
We consider the numerical approximations of the Cahn-Hilliard equation with dynamic boundary conditions (C. Liu et. al., Arch. Rational Mech. Anal., 2019). We propose a first-order in time, linear and energy stable numerical scheme, which…
The projected ensemble is based on the study of the quantum state of a subsystem $A$ conditioned on projective measurements in its complement. Recent studies have observed that a more refined measure of the thermalization of a chaotic…
We present methods that can provide an exponential savings in the resources required to perform dynamic parameter estimation using quantum systems. The key idea is to merge classical compressive sensing techniques with quantum control…
We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…
Entanglement is a fundamental property of quantum systems, essential for non-trivial quantum programs. Identifying when qubits become entangled is critical for circuit optimization, and for arguing for the correctness of quantum algorithms.…
Correlation functions of quantum systems -- central objects in quantum field theories -- are defined in high-dimensional space-time domains. Their numerical treatment thus suffers from the curse of dimensionality, which hinders the…
We analyze a fully discrete finite element numerical scheme for the Cahn-Hilliard-Stokes-Darcy system that models two-phase flows in coupled free flow and porous media. To avoid a well-known difficulty associated with the coupling between…
Quantum statistical systems, composed of atoms or molecules interacting with each other through highly singular non-integrable potentials, are considered. The treatment of such systems cannot start with the standard approximations such as…
The development of numerical methods capable of simulating realistic materials with strongly correlated electrons, with controllable errors, is a central challenge in quantum many-body physics. Here we describe how a hybrid between…
We consider Hamiltonian simulation using the first order Lie-Trotter product formula under the assumption that the initial state has a high overlap with an energy eigenstate, or a collection of eigenstates in a narrow energy band. This…
We investigate the problem of estimating the tunneling frequency of a two-level atomic system embedded in a dissipative environment by employing a numerically rigorous hierarchical equations of motion method. The effect of…
This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…
Quantum-inspired classical algorithms has received much attention due to its exponential speedup compared to existing algorithms, under certain data storage assumptions. The improvements are noticeable in fundamental linear algebra tasks.…
In order to explore the effects of high levels of electron correlation on the real-time coupled cluster formalism and algorithmic behavior, we introduce a time-dependent implementation of the CC3 singles, doubles and approximate triples…