Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Fortschritte der Physik

Efficient Simulation of Quantum Systems by Quantum Computers

Christof Zalka

Published Nov 1, 1998• 110 citations
Publisher

Abstract

We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a conventional simulation of the corresponding classical system. Ultimately the simulation of quantum field theory might be possible on large quantum computers.

DOI
10.1002/(sici)1521-3978(199811)46:6/8<877::aid-prop877>3.0.co;2-a

Related papers

Simulating quantum systems on a quantum computer

Christof Zalka

We show that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a performance which can't be expected from any classical simulation of a quantum system. We then show how quantities of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum computers.

arXiv:quant-ph/9603026•Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences•Jan 8, 1998•391 citations

Simulating Quantum Mechanics on a Quantum Computer

Bruce M. Boghosian, Washington Taylor

Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac and gauge particles are discussed.

•Jan 15, 1997•98 citations

Simulating quantum mechanics on a quantum computer

Bruce M. Boghosian, Washington Taylor

Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac or gauge particles are discussed.

arXiv:quant-ph/9701019•Physica D Nonlinear Phenomena•Sep 1, 1998•120 citations

The cost of simulating classically tractable quantum circuits and dynamics

Su Yeon Chang, Supanut Thanasilp, Zoë Holmes +1 more

Determining whether a quantum evolution can be efficiently simulated classically is central to understanding the boundary between classical and quantum computation. However, polynomial-time simulability is an asymptotic statement, and does not by itself determine whether the (quantum-inspired) classical simulation is actually practical. Indeed, different polynomial scalings can lead to vastly different computational costs, particularly when expensive preprocessing or quantum data acquisition is required. In this work, we ask whether classically simulable quantum dynamics are in practice more resource-efficient to simulate classically than to execute directly on quantum hardware. We analyze this question using three resource metrics, quantum sample, quantum time, and classical time complexity, for several widely studied classically simulable circuit families. Using representative hardware-level estimates, we identify regimes in which quantum simulation can be faster despite the existence of a polynomial-time classical algorithm, as well as regimes in which classical simulation remains more efficient. At the same time, the large quantum sampling cost needed to characterize unknown input states can make this polynomial-time classical simulation prohibitively expensive with current cloud-based hardware access prices. Ultimately, our work indicates that guarantees of classical simulability with polynomial resources alone are insufficient to determine the preferred implementation.

quant-pharXiv:2609.11847•Sep 11, 2026•0 citations

Quantum Simulation of the Dirac Particle

Marcin Ostrowski

In this paper, we examine whether a quantum computer can efficiently simulate time evolution of the Dirac particle. We consider a Gaussian wave packet scattered by a step potential. We compare the results obtained from a quantum algorithm with the results of classical simulations (Cayley's method) and analytical calculations.

Open Systems & Information Dynamics•Mar 1, 2015•3 citations

Non-Linear Quantum Simulation of Quantum Field Theory

Jincheng Zhang

This paper explores the application of a novel quantum simulation technique – a non-linear quantum simulation of quantum field theory – to address limitations in classical calculations of complex quantum systems. We propose a modified Feynman path integral method, enhanced with non-linear interactions, to provide a more accurate and efficient representation of particle interactions and quantum field behavior. This work aims to significantly advance the field of quantum field theory by extending its computational capabilities. The core claim is that this approach offers a potentially faster and more accurate method for simulating complex quantum systems than existing classical techniques. The mechanism involves a quantum version of the Feynman path integral method, incorporating non-linear interactions to achieve improved results. This research is driven by the inherent computational cost limitations of traditional methods and the desire to unlock more accurate representations of quantum phenomena.

•Sep 3, 2026•0 citations
We show that the time evolution of the wave function of a quantum mechanical many particle system can be implemented very efficiently on a quantum computer. The computational cost of such a simulation is comparable to the cost of a conventional simulation of the corresponding classical system. Ultimately the simulation of quantum field theory might be possible on large quantum computers.
We show that the time evolution of the wave function of a quantum–mechanical many–particle system can be simulated precisely and efficiently on a quantum computer. The time needed for such a simulation is comparable to the time of a conventional simulation of the corresponding classical system, a performance which can't be expected from any classical simulation of a quantum system. We then show how quantities of interest, like the energy spectrum of a system, can be obtained. We also indicate that ultimately the simulation of quantum field theory might be possible on large quantum computers.
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac and gauge particles are discussed.
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrödinger equation for interacting many-body systems are presented in some detail. These algorithms would make it possible to simulate nonrelativistic quantum systems on a quantum computer with an exponential speedup compared to simulations on classical computers. Issues involved in simulating relativistic systems of Dirac or gauge particles are discussed.
Determining whether a quantum evolution can be efficiently simulated classically is central to understanding the boundary between classical and quantum computation. However, polynomial-time simulability is an asymptotic statement, and does not by itself determine whether the (quantum-inspired) classical simulation is actually practical. Indeed, different polynomial scalings can lead to vastly different computational costs, particularly when expensive preprocessing or quantum data acquisition is required. In this work, we ask whether classically simulable quantum dynamics are in practice more resource-efficient to simulate classically than to execute directly on quantum hardware. We analyze this question using three resource metrics, quantum sample, quantum time, and classical time complexity, for several widely studied classically simulable circuit families. Using representative hardware-level estimates, we identify regimes in which quantum simulation can be faster despite the existence of a polynomial-time classical algorithm, as well as regimes in which classical simulation remains more efficient. At the same time, the large quantum sampling cost needed to characterize unknown input states can make this polynomial-time classical simulation prohibitively expensive with current cloud-based hardware access prices. Ultimately, our work indicates that guarantees of classical simulability with polynomial resources alone are insufficient to determine the preferred implementation.
This paper explores the application of a novel quantum simulation technique – a non-linear quantum simulation of quantum field theory – to address limitations in classical calculations of complex quantum systems. We propose a modified Feynman path integral method, enhanced with non-linear interactions, to provide a more accurate and efficient representation of particle interactions and quantum field behavior. This work aims to significantly advance the field of quantum field theory by extending its computational capabilities. The core claim is that this approach offers a potentially faster and more accurate method for simulating complex quantum systems than existing classical techniques. The mechanism involves a quantum version of the Feynman path integral method, incorporating non-linear interactions to achieve improved results. This research is driven by the inherent computational cost limitations of traditional methods and the desire to unlock more accurate representations of quantum phenomena.