Simulating quantum systems on a quantum computer
TLDR
It is shown 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, and that ultimately the simulation of quantum field theory might be possible on large quantum computers.Abstract:
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 can9t 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.read more
Citations
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Quantum Computation and Quantum Information
TL;DR: This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.
Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms, two problems that are generally thought to be hard on classical computers and that have been used as the basis of several proposed cryptosystems.
Journal ArticleDOI
Quantum Simulation
TL;DR: The main theoretical and experimental aspects of quantum simulation have been discussed in this article, and some of the challenges and promises of this fast-growing field have also been highlighted in this review.
Journal ArticleDOI
Simulated quantum computation of molecular energies.
Alán Aspuru-Guzik,Alán Aspuru-Guzik,Alán Aspuru-Guzik,Anthony D. Dutoi,Anthony D. Dutoi,Anthony D. Dutoi,Peter J. Love,Peter J. Love,Peter J. Love,Martin Head-Gordon,Martin Head-Gordon,Martin Head-Gordon +11 more
TL;DR: 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.
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Ultimate physical limits to computation
TL;DR: The physical limits of computation as determined by the speed of light c, the quantum scale ℏ and the gravitational constant G are explored.
References
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Journal ArticleDOI
Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer
TL;DR: In this paper, the authors considered factoring integers and finding discrete logarithms on a quantum computer and gave an efficient randomized algorithm for these two problems, which takes a number of steps polynomial in the input size of the integer to be factored.
Journal ArticleDOI
Simulating physics with computers
TL;DR: In this paper, the authors describe the possibility of simulating physics in the classical approximation, a thing which is usually described by local differential equations, and the possibility that there is to be an exact simulation, that the computer will do exactly the same as nature.
Proceedings ArticleDOI
A fast quantum mechanical algorithm for database search
TL;DR: In this paper, it was shown that a quantum mechanical computer can solve integer factorization problem in a finite power of O(log n) time, where n is the number of elements in a given integer.
Book
Mathematical Foundations of Quantum Mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.
Mathematical Foundations of Quantum Mechanics
TL;DR: The Mathematical Foundations of Quantum Mechanics as discussed by the authors is a seminal work in theoretical physics that introduced the theory of Hermitean operators and Hilbert spaces and provided a mathematical framework for quantum mechanics.