
A quantum algorithm for simulating nonsparse Hamiltonians
We present a quantum algorithm for simulating the dynamics of Hamiltonia...
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Quantum linear systems algorithms: a primer
The HarrowHassidimLloyd (HHL) quantum algorithm for sampling from the ...
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Quantum Data Fitting Algorithm for Nonsparse Matrices
We propose a quantum data fitting algorithm for nonsparse matrices, whi...
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Nearly tight Trotterization of interacting electrons
We consider simulating quantum systems on digital quantum computers. We ...
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Quantum Chebyshev's Inequality and Applications
In this paper we provide new quantum algorithms with polynomial speedup...
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Fast BlackBox Quantum State Preparation
Quantum state preparation is an important ingredient for other higherle...
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Fast inversion, preconditioned quantum linear system solvers, and fast evaluation of matrix functions
Preconditioning is the most widely used and effective way for treating i...
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The power of blockencoded matrix powers: improved regression techniques via faster Hamiltonian simulation
We apply the framework of blockencodings, introduced by Low and Chuang (under the name standardform), to the study of quantum machine learning algorithms using quantum accessible data structures. We develop several tools within the blockencoding framework, including quantum linear system solvers using blockencodings. Our results give new techniques for Hamiltonian simulation of nonsparse matrices, which could be relevant for certain quantum chemistry applications, and which in turn imply an exponential improvement in the dependence on precision in quantum linear systems solvers for nonsparse matrices. In addition, we develop a technique of variabletime amplitude estimation, based on Ambainis' variabletime amplitude amplification technique, which we are also able to apply within the framework. As applications, we design the following algorithms: (1) a quantum algorithm for the quantum weighted least squares problem, exhibiting a 6th power improvement in the dependence on the condition number and an exponential improvement in the dependence on the precision over the previous best algorithm of Kerenidis and Prakash; (2) the first quantum algorithm for the quantum generalized least squares problem; and (3) quantum algorithms for estimating electricalnetwork quantities, including effective resistance and dissipated power, improving upon previous work in other input models.
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