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Related papers: Beyond Trotterization: Variational Product Formula…

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We present a general framework for finding the time-optimal evolution and the optimal Hamiltonian for a quantum system with a given set of initial and final states. Our formulation is based on the variational principle and is analogous to…

Quantum Physics · Physics 2007-05-23 Alberto Carlini , Akio Hosoya , Tatsuhiko Koike , Yosuke Okudaira

Multi-product formulas (MPF) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more…

Quantum Physics · Physics 2024-02-12 Sergiy Zhuk , Niall Robertson , Sergey Bravyi

Simulating the time evolution of quantum field theories given some Hamiltonian $H$ requires developing algorithms for implementing the unitary operator e^{-iHt}. A variety of techniques exist that accomplish this task, with the most common…

Variational quantum circuits have arisen as an important method in quantum computing. A crucial step of it is parameter optimization, which is typically tackled through gradient-descent techniques. We advantageously explore instead the use…

Quantum Physics · Physics 2024-12-24 Vignesh Anantharamakrishnan , Márcio M. Taddei

We use Pontryagin's minimum principle to optimize variational quantum algorithms. We show that for a fixed computation time, the optimal evolution has a bang-bang (square pulse) form, both for closed and open quantum systems with Markovian…

Quantum Physics · Physics 2017-05-30 Zhi-Cheng Yang , Armin Rahmani , Alireza Shabani , Hartmut Neven , Claudio Chamon

The Trotter-Suzuki approximation leads to an efficient algorithm for solving the time-dependent Schr\"odinger equation. Using existing highly optimized CPU and GPU kernels, we developed a distributed version of the algorithm that runs…

Computational Physics · Physics 2013-03-06 Peter Wittek , Fernando M. Cucchietti

Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…

Quantum Physics · Physics 2024-05-16 Nikita A. Zemlevskiy , Henry F. Froland , Stephan Caspar

When a time propagator $e^{\delta t A}$ for duration $\delta t$ consists of two noncommuting parts $A=X+Y$, Trotterization approximately decomposes the propagator into a product of exponentials of $X$ and $Y$. Various Trotterization…

Quantum Physics · Physics 2023-11-08 Tatsuhiko N. Ikeda , Asir Abrar , Isaac L. Chuang , Sho Sugiura

Quantum coherence inherently affects the dynamics and the performances of a quantum machine. Coherent control can, at least in principle, enhance the work extraction and boost the velocity of evolution in an open quantum system. Using…

Quantum Physics · Physics 2018-12-10 Vasco Cavina , Andrea Mari , Alberto Carlini , Vittorio Giovannetti

We present an efficient approach to simulate real-time quantum dynamics using Projected Variational Quantum Dynamics (PVQD), where the computational cost is reduced by strategically optimizing only a subset of the variational parameters at…

Quantum Physics · Physics 2026-01-06 Harshdeep Singh , Sonjoy Majumder , Sabyashachi Mishra

Hamiltonian simulation is one of the most promising applications of quantum computers, and the product formula is one of the most important methods for this purpose. Previous related work has mainly focused on the worst$-$case or…

Quantum Physics · Physics 2024-09-04 Langyu Li

Trotter product formulas constitute a cornerstone quantum Hamiltonian simulation technique. However, the efficient implementation of Hamiltonian evolution of nested commutators remains an under explored area. In this work, we construct…

Quantum Physics · Physics 2025-01-22 F. Casas , A. Escorihuela-Tomàs , P. A. Moreno Casares

This article proposes a formalism which unifies Hamiltonian simulation techniques from different fields. This formalism leads to a competitive method to construct the Hamiltonian simulation with a comprehensible, simple-to-implement circuit…

Quantum Physics · Physics 2025-01-22 Robin Ollive , Stephane Louise

Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points. A choice among these…

Quantum Physics · Physics 2015-03-05 Apoorva Patel

Implementing time evolution operators on quantum circuits is important for quantum simulation. However, the standard way, Trotterization, requires a huge numbers of gates to achieve desirable accuracy. Here, we propose a local variational…

Quantum Physics · Physics 2022-10-13 Kaoru Mizuta , Yuya O. Nakagawa , Kosuke Mitarai , Keisuke Fujii

We propose a general-purpose, self-adaptive approach to construct variational wavefunction ans\"atze for highly accurate quantum dynamics simulations based on McLachlan's variational principle. The key idea is to dynamically expand the…

In adiabatic quantum computing the aim is to track an eigenstate as the Hamiltonian changes. In the usual setup this is achieved using the natural time-dependent Hamiltonian evolution of the system and the main technical tool is the…

Quantum Physics · Physics 2026-05-29 Joseph Cunningham , Jérémie Roland

Understanding the dynamics of quantum systems is crucial in many areas of physics, but simulating many-body systems presents significant challenges due to the large Hilbert space to navigate and the exponential growth of computational…

Quantum Physics · Physics 2025-03-14 Sangjin Lee , Youngseok Kim , Seung-Woo Lee

We present a quantum variational algorithm based on a novel circuit that generates all permutations that can be spanned by one- and two-qubits permutation gates. The construction of the circuits follows from group-theoretical results, most…

Quantum Physics · Physics 2026-02-11 Dylan Laplace Mermoud , Andrea Simonetto , Sourour Elloumi

Quantum simulation, the simulation of quantum processes on quantum computers, suggests a path forward for the efficient simulation of problems in condensed-matter physics, quantum chemistry, and materials science. While the majority of…

Quantum Physics · Physics 2022-10-03 Paul K. Faehrmann , Mark Steudtner , Richard Kueng , Maria Kieferova , Jens Eisert