Related papers: Quantum Algorithm for Simulating Hamiltonian Dynam…
Simulating time evolution of generic quantum many-body systems using classical numerical approaches has an exponentially growing cost either with evolution time or with the system size. In this work, we present a polynomially scaling hybrid…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the…
We apply the method of flow equations to describe quantum systems subject to a time-periodic drive with a time-dependent envelope. The driven Hamiltonian is expressed in terms of its constituent Fourier harmonics with amplitudes that may…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
Hamiltonian diagonalization is at the heart of understanding physical properties and practical applications of quantum systems. It is highly desired to design quantum algorithms that can speedup Hamiltonian diagonalization, especially those…
Quantum signal processing provides an optimal procedure for simulating Hamiltonian evolution on a quantum computer using calls to a block encoding of the Hamiltonian. In many situations it is possible to control between forward and reverse…
We introduce a hybrid classical-quantum algorithm for simulating a Hamiltonian of the form $H= \sum_{i=1}^K H_i = \sum_{i=1}^K H_{i_1} \otimes H_{i_2} \otimes \cdots \otimes H_{i_M}$. Given that the entries of all $\{ H_{i_1}, H_{i_2} ,…
Quantum algorithms for Hamiltonian simulation and linear differential equations more generally have provided promising exponential speed-ups over classical computers on a set of problems with high real-world interest. However, extending…
We introduce a new class of quantum models with time-dependent Hamiltonians of a special scaling form. By using a couple of time-dependent unitary transformations, the time evolution of these models is expressed in terms of related systems…
Hamiltonian simulation is a promising application for quantum computers to achieve a quantum advantage. We present classical algorithms based on tensor network methods to optimize quantum circuits for this task. We show that, compared to…
We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system…
In light of recent exciting progress in building up quantum computing facilities based on both optical and cold-atom techniques, the algorithms for quantum simulations of particle-physics systems are in rapid progress. In this paper, we…
Large-scale quantum devices provide insights beyond the reach of classical simulations. However, for a reliable and verifiable quantum simulation, the building blocks of the quantum device require exquisite benchmarking. This benchmarking…
Open quantum systems host a wide range of intriguing phenomena, yet their simulation on well-controlled quantum devices is challenging, owing to the exponential growth of the Hilbert space and the inherently non-unitary nature of the…
Partial differential equations (PDEs) are central to computational electromagnetics (CEM) and photonic design, but classical solvers face high costs for large or complex structures. Quantum Hamiltonian simulation provides a framework to…
We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
We develop a fourth-order Magnus expansion based quantum algorithm for the simulation of many-body problems involving two-level quantum systems with time-dependent Hamiltonians, $\mathcal{H}(t)$. A major hurdle in the utilization of the…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…