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Related papers: Factorizing time evolution into elementary steps

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We describe a method to simulate Hamiltonian evolution on a quantum computer by repeatedly using a superposition of steps of a quantum walk, then applying a correction to the weightings for the numbers of steps of the quantum walk. This…

Quantum Physics · Physics 2017-02-15 Dominic W. Berry , Leonardo Novo

The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of fermionic Gaussian circuits and Ising…

Quantum Physics · Physics 2021-09-13 Nicholas C. Rubin , Joonho Lee , Ryan Babbush

A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…

Quantum Physics · Physics 2025-05-14 Qing-Song Li , Jiaxuan Zhang , Huan-Yu Liu , Qingchun Wang , Yu-Chun Wu , Guo-Ping Guo

Simulating the time evolution of a physical system at quantum mechanical levels of detail -- known as Hamiltonian Simulation (HS) -- is an important and interesting problem across physics and chemistry. For this task, algorithms that run on…

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…

Quantum Physics · Physics 2022-01-12 Viktor Novičenko , Giedrius Žlabys , Egidijus Anisimovas

We present a hierarchical computation approach for solving finite-time optimal control problems using operator splitting methods. The first split is performed over the time index and leads to as many subproblems as the length of the…

Optimization and Control · Mathematics 2013-04-09 Georgios Stathopoulos , Tamás Keviczky , Yang Wang

We propose a new method for simulating certain type of time-dependent Hamiltonian $H(t) = \sum_{i=1}^m \gamma_i(t) H_i$ where $\gamma_i(t)$ (and its higher order derivatives) is bounded, computable function of time $t$, and each $H_i$ is…

Quantum Physics · Physics 2024-10-21 Nhat A. Nghiem

A common starting point of traditional quantum algorithm design is the notion of a universal quantum computer with a scalable number of qubits. This convenient abstraction mirrors classical computations manipulating finite sets of symbols,…

Quantum Physics · Physics 2026-03-30 Lukas Brenner , Libor Caha , Xavier Coiteux-Roy , Robert Koenig

In a quantum computer any superposition of inputs evolves unitarily into the corresponding superposition of outputs. It has been recently demonstrated that such computers can dramatically speed up the task of finding factors of large…

Quantum Physics · Physics 2016-09-08 I. Chuang , Raymond Laflamme , P. Shor , W. Zurek

It is proposed that the ability for a quantum circuit to thermalize under time evolution is a valid way to compute linear algebra problems. The algorithm makes use of the eigenstate thermalization hypothesis and full ergodicity in quantum…

Quantum Physics · Physics 2026-05-27 Thomas E. Baker

An algorithm for the generation of shuttling sequences is necessary for the operation of a linear segmented ion-trap quantum computer. The present work provides an implementation of an algorithm that produces sequences proved to be optimal…

We present a new algorithm for reducing an arbitrary unitary matrix U into a sequence of elementary operations (operations such as controlled-nots and qubit rotations). Such a sequence of operations can be used to manipulate an array of…

Quantum Physics · Physics 2007-05-23 Robert R. Tucci

Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware. Synthesizing the corresponding quantum circuit is typically done by breaking the evolution into small time steps, also known as…

Motivated by the need to uncover some underlying mathematical structure of optimal quantum computation, we carry out a systematic analysis of a wide variety of quantum algorithms from the majorization theory point of view. We conclude that…

Quantum Physics · Physics 2009-11-07 Roman Orus , Jose I. Latorre , Miguel A. Martin-Delgado

Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal…

We show that the method of factorizing the evolution operator to fourth order with purely positive coefficients, in conjunction with Suzuki's method of implementing time-ordering of operators, produces a new class of powerful algorithms for…

Nuclear Theory · Physics 2009-11-07 S. A. Chin , C. R. Chen

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…

Quantum Physics · Physics 2021-06-22 Amir Kalev , Itay Hen

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 provide a general method for efficiently simulating time-dependent Hamiltonian dynamics on a circuit-model based quantum computer. Our approach is based on approximating the truncated Dyson series of the evolution operator, extending the…

Quantum Physics · Physics 2019-04-10 Maria Kieferova , Artur Scherer , Dominic Berry

We propose a novel method to sequentially optimize arbitrary single-qubit gates in parameterized quantum circuits for simulating real and imaginary time evolution. The method utilizes full degrees of freedom of single-qubit gates and…