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Related papers: Hamiltonian simulation in the low-energy subspace

200 papers

We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged…

Quantum Physics · Physics 2024-08-27 Zhiyan Ding , Xiantao Li , Lin Lin

We describe a simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator. Our method can simulate the time evolution of a wide variety of…

Quantum Physics · Physics 2015-03-06 Dominic W. Berry , Andrew M. Childs , Richard Cleve , Robin Kothari , Rolando D. Somma

We show that adiabatic evolution of a low-dimensional lattice of quantum spins with a spectral gap can be simulated efficiently. In particular, we show that as long as the spectral gap \Delta E between the ground state and the first excited…

Quantum Physics · Physics 2007-05-23 Tobias J. Osborne

The local Hamiltonian problem consists of estimating the ground-state energy (given by the minimum eigenvalue) of a local quantum Hamiltonian. First, we show the existence of a good product-state approximation for the ground-state energy of…

Quantum Physics · Physics 2016-02-04 Fernando G. S. L. Brandão , Aram W. Harrow

This work aims to address the bottleneck issues of hardware resource limitation and decoherence error in the Hamiltonian simulation of quantum fluids, which are caused by the standard quantum Fourier transform and the evolution of momentum…

Quantum Physics · Physics 2026-04-21 Zhiyuan Zhang , Bolin Zhang , Yongguang Lv , Ruiqing He , Hengliang Guo , Jiandong Shang , Qiang Chen

We provide rigorous bounds for the error of the adiabatic approximation of quantum mechanics under four sources of experimental error: perturbations in the initial condition, systematic time-dependent perturbations in the Hamiltonian,…

Quantum Physics · Physics 2009-11-13 Michael J. O'Hara , Dianne P. O'Leary

We consider the simulation of the dynamics of one nonlocal Hamiltonian by another, allowing arbitrary local resources but no entanglement nor classical communication. We characterize notions of simulation, and proceed to focus on…

Quantum Physics · Physics 2009-11-07 C. H. Bennett , J. I. Cirac , M. S. Leifer , D. W. Leung , N. Linden , S. Popescu , G. Vidal

In this paper, we present a proof-of-concept quantum algorithm for simulating time-dependent Hamiltonian evolution by reducing the problem to simulating a time-independent Hamiltonian in a larger space using a discrete clock Hamiltonian…

Quantum Physics · Physics 2025-07-28 Zecheng Li , Chunhao Wang

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…

Quantum Physics · Physics 2017-07-07 Ian D. Kivlichan , Nathan Wiebe , Ryan Babbush , Alan Aspuru-Guzik

Given a renormalization scheme, we show how to formulate a tractable convex relaxation of the set of feasible local density matrices of a many-body quantum system. The relaxation is obtained by introducing a hierarchy of constraints between…

Quantum Physics · Physics 2024-04-11 Ilya Kull , Norbert Schuch , Ben Dive , Miguel Navascués

Quantum computing employs controllable interactions to perform sequences of logical gates and entire algorithms on quantum registers. This paradigm has been widely explored, e.g., for simulating dynamics of manybody systems by decomposing…

Quantum Physics · Physics 2025-05-21 S. Alipour , A. T. Rezakhani , Alireza Tavanfar , K. Mölmer , T. Ala-Nissila

We discuss the emulation of non-Hermitian dynamics during a given time window by a low-dimensional quantum system coupled to a finite set of equidistant discrete states acting as an effective continuum. We first emulate the decay of an…

Quantum Physics · Physics 2025-02-05 Eloi Flament , François Impens , David Guéry-Odelin

Variational methods play an important role in the study of quantum many-body problems, both in the flavor of classical variational principles based on tensor networks as well as of quantum variational principles in near-term quantum…

Quantum Physics · Physics 2026-02-18 J. Eisert

We investigate the feasibility of simulating different model Hamiltonians used in high-temperature superconductivity. We briefly discuss the most common models and then focus on the simulation of the so-called t-J-U Hamiltonian using…

Quantum Physics · Physics 2007-05-23 Alexander Klein , Dieter Jaksch

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world…

Machine Learning · Computer Science 2022-02-15 Nate Gruver , Marc Finzi , Samuel Stanton , Andrew Gordon Wilson

Stability of power networks is an increasingly important topic because of the high penetration of renewable distributed generation units. This requires the development of advanced (typically model-based) techniques for the analysis and…

Systems and Control · Computer Science 2018-09-14 T. W. Stegink , C. De Persis , A. J. van der Schaft

The quantum dynamics of a complex system can be efficiently described in Krylov space, the minimal subspace in which the dynamics unfolds. We apply the Krylov subspace method for Hamiltonian deformations, which provides a systematic way of…

Quantum Physics · Physics 2026-04-21 Kazutaka Takahashi , Pratik Nandy , Adolfo del Campo

Recent advances in both theoretical and computational methods have enabled large-scale, precision calculations of the properties of atomic nuclei. With the growing complexity of modern nuclear theory, however, also comes the need for novel…

Nuclear Theory · Physics 2024-11-26 R. Y. Cheng , K. Godbey , Y. B. Niu , Y. G. Ma , W. B. He , S. M. Wang

Estimating ground state energies of many-body Hamiltonians is a central task in many areas of quantum physics. In this work, we give quantum algorithms which, given any $k$-body Hamiltonian $H$, compute an estimate for the ground state…

We have composed the ideas of quantum renormalization group and quantum information by exploring the low energy states dynamic of entanglement resources of a system close to its quantum critical point. We demonstrate the low energy states…

Quantum Physics · Physics 2010-11-25 R. Jafari