Related papers: Time evolution of matrix product operators with en…
We significantly enhance the simulation accuracy of initial Trotter circuits for Hamiltonian simulation of quantum systems by integrating first-order Riemannian optimization with tensor network methods. Unlike previous approaches, our…
We obtain a time-evolution operator for a forced optomechanical quantum system using Lie algebraic methods when the normalized coupling between the electromagnetic field and a mechanical oscillator, $G/\omega_m$, is not negligible compared…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…
In designing quantum control, it is generally required to simulate the controlled system evolution with a classical computer. However, computing the time evolution operator can be quite resource-consuming since the total Hamiltonian is…
We propose a method to simulate the real time evolution of one dimensional quantum many-body systems at finite temperature by expressing both the density matrices and the observables as matrix product states. This allows the calculation of…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We present efficient quantum algorithms for simulating time-dependent Hamiltonian evolution of general input states using an oracular model of a quantum computer. Our algorithms use either constant or adaptively chosen time steps and are…
We present a quantum algorithm for simulating the time evolution generated by any bounded, time-dependent operator $-A$ with non-positive logarithmic norm, thereby serving as a natural generalization of the Hamiltonian simulation problem.…
We describe a simple method for simulating time-independent Hamiltonian $H$ that could be decomposed as $H = \sum_{i=1}^m H_i$ where each $H_i$ can be efficiently simulated. Approaches relying on product formula generally work by splitting…
We study the computational complexity of simulating the time-dependent expectation value of a local operator in a one-dimensional quantum system by using temporal matrix product states. We argue that such cost is intimately related to that…
We introduce a method based on matrix product states (MPS) for computing spectral functions of (quasi) one-dimensional spin chains, working directly in momentum space in the thermodynamic limit. We simulate the time evolution after applying…
In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pade and Arnoldi approximations to the evolution operator. By comparing…
We develop a general approach for monitoring and controlling evolution of open quantum systems. In contrast to the master equations describing time evolution of density operators, here, we formulate a dynamical equation for the evolution of…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…
Variational formulations of time-dependent PDEs in space and time yield $(d+1)$-dimensional problems to be solved numerically. This increases the number of unknowns as well as the storage amount. On the other hand, this approach enables…
We propose a tensor-network (TN) approach for solving classical optimization problems that is inspired by spectral filtering and sampling on quantum states. We first shift and scale an Ising Hamiltonian of the cost function so that all…
Matrix-product states have become the de facto standard for the representation of one-dimensional quantum many body states. During the last few years, numerous new methods have been introduced to evaluate the time evolution of a…
We develop a Lie algebraic approach to systematically calculate the evolution operator of the generalized two-dimensional quadratic Hamiltonian with time-dependent coefficients. Although the development of the Lie algebraic approach…
This paper presents a new parameter estimation algorithm for the adaptive control of a class of time-varying plants. The main feature of this algorithm is a matrix of time-varying learning rates, which enables parameter estimation error…