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Related papers: Hamiltonian Simulation by Qubitization

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The discretization approximation method commonly used to simulate the dynamics of quantum system coupled to the environment in continuum often suffers from the periodically partial recovery of initial state because of the effect of finite…

Quantum Physics · Physics 2025-05-07 H. T. Cui , Y. A. Yan , M. Qin , X. X. Yi

We propose a simple realization of a quantum simulator of the Riemann-Hurwitz (RH) \zeta\ function based on a truncation of its Dirichlet representation. We synthesize a nearest-neighbour-interaction Hamiltonian, satisfying the property…

Quantum Physics · Physics 2013-06-05 Boyan T. Torosov , Giuseppe Della Valle , Stefano Longhi

In this paper we develop an analogue of Hamilton-Jacobi theory for the time-evolution operator of a quantum many-particle system. The theory offers a useful approach to develop approximations to the time-evolution operator, and also…

Statistical Mechanics · Physics 2019-08-07 Michael Vogl , Pontus Laurell , Aaron D. Barr , Gregory A. Fiete

In this paper, we present a method for the Hamiltonian simulation in the context of eigenvalue estimation problems which improves earlier results dealing with Hamiltonian simulation through the truncated Taylor series. In particular, we…

Quantum Physics · Physics 2018-11-01 Ammar Daskin , Sabre Kais

Motivated by experimental limitations commonly met in the design of solid state quantum computers, we study the problems of non-local Hamiltonian simulation and non-local gate synthesis when only homogeneous local unitaries are performed in…

Quantum Physics · Physics 2007-05-23 Ll. Masanes , G. Vidal , J. I. Latorre

Quantum computers (QCs) have the potential to solve critical problems significantly faster than today's most advanced supercomputers. One major challenge in realizing this technology is designing robust electrostatic pulses to realize…

Quantum Physics · Physics 2025-11-18 Dhilan Nag , Suhun Kim , Cole Johnson , Collin Sumrell

Optimal control techniques provide a means to tailor the control pulses required to generate customized quantum gates, which helps to improve the resilience of quantum simulations to gate errors and device noise. However, the significant…

Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its…

Quantum Physics · Physics 2026-03-11 Mikel Garcia-de-Andoin , Thorge Müller , Gonzalo Camacho

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

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…

Quantum Physics · Physics 2021-05-26 Dong An , Di Fang , Lin Lin

A quantum algorithm for solving the advection equation by embedding the discrete time-marching operator into Hamiltonian simulations is presented. One-dimensional advection can be simulated directly since the central finite difference…

Quantum Physics · Physics 2024-07-17 Peter Brearley , Sylvain Laizet

A non-Hermitian operator with a real spectrum and a complete set of eigenvectors may serve as the Hamiltonian operator for a unitary quantum system provided that one makes an appropriate choice for the defining inner product of the physical…

Quantum Physics · Physics 2009-11-13 Ali Mostafazadeh

Iterative phase estimation has long been used in quantum computing to estimate Hamiltonian eigenvalues. This is done by applying many repetitions of the same fundamental simulation circuit to an initial state, and using statistical…

Quantum Physics · Physics 2019-07-25 Ian D. Kivlichan , Christopher E. Granade , Nathan Wiebe

The controls enacting logical operations on quantum systems are described by time-dependent Hamiltonians that often include rapid oscillations. In order to accurately capture the resulting time dynamics in numerical simulations, a very…

Quantum Physics · Physics 2021-09-29 Ross Shillito , Jonathan A. Gross , Agustin Di Paolo , Élie Genois , Alexandre Blais

Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…

Quantum Physics · Physics 2019-04-09 Changpeng Shao

Hamiltonian learning is a cornerstone for advancing accurate many-body simulations, improving quantum device performance, and enabling quantum-enhanced sensing. Existing readily deployable quantum metrology techniques primarily focus on…

Quantum Physics · Physics 2025-10-10 Suying Liu , Xiaodi Wu , Murphy Yuezhen Niu

Trotter and linear-combination-of-unitary (LCU) are two popular Hamiltonian simulation methods. We propose Hamiltonian simulation algorithms using LCU to compensate Trotter error, which enjoy both of their advantages. By adding few gates…

Quantum Physics · Physics 2025-03-31 Pei Zeng , Jinzhao Sun , Liang Jiang , Qi Zhao

Simulating plasma physics on quantum computers is difficult because most problems of interest are nonlinear, but quantum computers are not naturally suitable for nonlinear operations. In weakly nonlinear regimes, plasma problems can be…

The construction of quantum circuits to simulate Hamiltonian evolution is central to many quantum algorithms. State-of-the-art circuits are based on oracles whose implementation is often omitted, and the complexity of the algorithm is…

Quantum Physics · Physics 2024-06-12 Boris Arseniev , Dmitry Guskov , Richik Sengupta , Jacob Biamonte , Igor Zacharov

We achieve query-optimal quantum simulations of non-Hermitian Hamiltonians $H_{\mathrm{eff}} = H_R + iH_I$, where $H_R$ is Hermitian and $H_I \succeq 0$, using a bivariate extension of quantum signal processing (QSP) with non-commuting…

Quantum Physics · Physics 2026-05-13 Joshua M. Courtney