Quantum simulations of one dimensional quantum systems

@article{Somma2016QuantumSO,
title={Quantum simulations of one dimensional quantum systems},
author={Rolando D. Somma},
journal={Quantum Inf. Comput.},
year={2016},
volume={16},
pages={1125-1168}
}
• R. Somma
• Published 21 March 2015
• Computer Science
• Quantum Inf. Comput.
We present quantum algorithms for the simulation of quantum systems in one spatial dimension, which result in quantum speedups that range from superpolynomial to polynomial. We first describe a method to simulate the evolution of the quantum harmonic oscillator (QHO) based on a refined analysis of the Trotter-Suzuki formula that exploits the Lie algebra structure. For total evolution time $t$ and precision $\epsilon>0$, the complexity of our method is $O(\exp(\gamma \sqrt{\log(N/\epsilon… 38 Citations Figures and Tables from this paper Quantum Algorithms for Simulating the Lattice Schwinger Model • Computer Science Quantum • 2020 This work performs a tight analysis of low-order Trotter formula simulations of the Schwinger model, using recently derived commutator bounds, and gives upper bounds on the resources needed for simulations in both scenarios. Corrected quantum walk for optimal Hamiltonian simulation • Computer Science Quantum Inf. Comput. • 2016 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, to obtain complexity which is the same as the lower bound up to double-logarithmic factors for all parameter regimes. Quantum algorithms for Gibbs sampling and hitting-time estimation • Computer Science • 2016 This work presents quantum algorithms for solving two problems regarding stochastic processes, one of which estimates the hitting time of a Markov chain and the other quadratically improves the dependence on 1/\epsilon and$1/\Delta of the analog classical algorithm for hitting-time estimation.
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References

SHOWING 1-10 OF 61 REFERENCES
Quantum Algorithms for Quantum Field Theories
• Physics
Science
• 2012
A quantum algorithm to compute relativistic scattering probabilities in a massive quantum field theory with quartic self-interactions in spacetime of four and fewer dimensions is developed and achieves exponential speedup over the fastest known classical algorithm.
Using Quantum Computers for Quantum Simulation
• Physics
Entropy
• 2010
The theoretical and experimental development of quantum simulation using quantum computers is surveyed, from the first ideas to the intense research efforts currently underway.
Simulating a quantum magnet with trapped ions
• Physics
• 2008
To gain deeper insight into the dynamics of complex quantum systems we need a quantum leap in computer simulations. We cannot translate quantum behaviour arising from superposition states or
Quantum algorithms for fermionic simulations
• Physics, Computer Science
• 2001
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems,
Quantum simulations of physics problems
• Physics
SPIE Defense + Commercial Sensing
• 2003
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue
Simulating Quantum Dynamics On A Quantum Computer
• Computer Science
• 2010
A range of techniques to simulate Hamiltonians with badly behaved derivatives are proposed, including using adaptive time steps, adapting the order of the integrators, and omitting regions about discontinuities.
Quantum computation and quantum information
• T. Paul
• Physics
Mathematical Structures in Computer Science
• 2007
This special issue of Mathematical Structures in Computer Science contains several contributions related to the modern field of Quantum Information and Quantum Computing. The first two papers deal
Simulating chemistry using quantum computers.
• Physics
Annual review of physical chemistry
• 2011
This review discusses to what extent the ideas in quantum computation, now a well-established field, have been applied to chemical problems and describes algorithms that achieve significant advantages for the electronic-structure problem, the simulation of chemical dynamics, protein folding, and other tasks.
Simulated Quantum Computation of Molecular Energies
• Physics
Science
• 2005
Calculations of the water and lithium hydride molecular ground-state energies have been carried out on a quantum computer simulator using a recursive phase-estimation algorithm and mapping of the molecular wave function to the quantum bits are described.
Preparing ground States of quantum many-body systems on a quantum computer.
• Physics
Physical review letters
• 2009
A quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems, and this result is presented to the case of interacting quantum particles.