Related papers: Simulating Hamiltonian dynamics with a truncated T…
A complex but important challenge in understanding quantum mechanical phenomena is the simulation of quantum many-body dynamics. Although quantum computers offer significant potential to accelerate these simulations, their practical…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
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…
Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
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…
Stochastic methods offer an effective way to suppress coherent errors in quantum simulation. In particular, the randomized compilation protocol may reduce circuit depth by randomly sampling Hamiltonian terms rather than following the…
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer. The existing algorithms generally approximate the time evolution operators, which may need a deep…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
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} ,…
We present the problem of approximating the time-evolution operator $e^{-i\hat{H}t}$ to error $\epsilon$, where the Hamiltonian $\hat{H}=(\langle G|\otimes\hat{\mathcal{I}})\hat{U}(|G\rangle\otimes\hat{\mathcal{I}})$ is the projection of a…
We present a quantum algorithm for simulating the dynamics of Hamiltonians that are not necessarily sparse. Our algorithm is based on the input model where the entries of the Hamiltonian are stored in a data structure in a quantum random…
Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required…
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
Nonequilibrium time evolution of large quantum systems is a strong candidate for quantum advantage. Variational quantum algorithms have been put forward for this task, but their quantum optimization routines suffer from trainability and…
Simulating physical systems has been an important application of classical and quantum computers. In this article we present an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant…
The accuracy of quantum dynamics simulation is usually measured by the error of the unitary evolution operator in the operator norm, which in turn depends on certain norm of the Hamiltonian. For unbounded operators, after suitable…
We introduce a family of identities that express general linear non-unitary evolution operators as a linear combination of unitary evolution operators, each solving a Hamiltonian simulation problem. This formulation can exponentially…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we…