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Lanczos recursion on a quantum computer for the Green's function
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The technique of quantum counting is used to obtain coefficients from a Lanczos recursion from a single ground-state wavefunction on the quantum computer as discussed by the authors, which can be used to compute the continued fraction representation of a general Green's function.Abstract:
The technique of quantum counting is used to obtain coefficients from a Lanczos recursion from a single ground-state wavefunction on the quantum computer. This is used to compute the continued fraction representation of a general Green's function, which can be useful in condensed matter, particle physics, and others. The wavefunction does not need to be re-prepared at each iteration. The quantum algorithm represents an exponential reduction in memory required over classical methods.read more
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Journal Article
Simulating Hamiltonian Dynamics with a Truncated Taylor Series
TL;DR: A simple, efficient method for simulating Hamiltonian dynamics on a quantum computer by approximating the truncated Taylor series of the evolution operator by using a method for implementing linear combinations of unitary operations together with a robust form of oblivious amplitude amplification.
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Density functionals and Kohn-Sham potentials with minimal wavefunction preparations on a quantum computer
TL;DR: This work demonstrates a general method for obtaining the exact functional as a machine learned model from a sufficiently powerful quantum computer and demonstrates how the classical user can access commonly used time- and temperature-dependent approximations from the ground state model.
The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chemistry
Davd Poulin,M.B. Hastings,Dave Wecker,Nathan Wiebe,Andrew C. Doherty,Matthias Troyer,Matthew B. Hastings +6 more
TL;DR: In this paper, it was shown that the complexity of the Trotter step required for an ensemble of random artificial molecules is closer to N6 in worst case for real model molecules, indicating that the random ensemble fails to accurately capture the statistical properties of real world molecules.
References
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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.
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.
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Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions
TL;DR: The dynamical mean field theory of strongly correlated electron systems is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition.
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An iteration method for the solution of the eigenvalue problem of linear differential and integral operators
TL;DR: In this article, a systematic method for finding the latent roots and principal axes of a matrix, without reducing the order of the matrix, has been proposed, which is characterized by a wide field of applicability and great accuracy, since the accumulation of rounding errors is avoided, through the process of minimized iterations.
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The density-matrix renormalization group
TL;DR: The density-matrix renormalization group (DMRG) as mentioned in this paper is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription.