The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation

04/05/2018
by   Shantanav Chakraborty, et al.
0

We apply the framework of block-encodings, introduced by Low and Chuang (under the name standard-form), to the study of quantum machine learning algorithms using quantum accessible data structures. We develop several tools within the block-encoding framework, including quantum linear system solvers using block-encodings. Our results give new techniques for Hamiltonian simulation of non-sparse 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 non-sparse matrices. In addition, we develop a technique of variable-time amplitude estimation, based on Ambainis' variable-time 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 6-th 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 electrical-network quantities, including effective resistance and dissipated power, improving upon previous work in other input models.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/27/2022

Quantum Regularized Least Squares

Linear regression is a widely used technique to fit linear models and fi...
research
01/15/2023

An improved quantum algorithm for low-rank rigid linear regressions with vector solution outputs

Let A∈ℝ^n× d, ∈̱ℝ^n and λ>0, for rigid linear regression _ Z() = ...
research
03/22/2018

A quantum algorithm for simulating non-sparse Hamiltonians

We present a quantum algorithm for simulating the dynamics of Hamiltonia...
research
02/22/2018

Quantum linear systems algorithms: a primer

The Harrow-Hassidim-Lloyd (HHL) quantum algorithm for sampling from the ...
research
05/19/2023

Efficient quantum linear solver algorithm with detailed running costs

As we progress towards physical implementation of quantum algorithms it ...
research
12/16/2020

Nearly tight Trotterization of interacting electrons

We consider simulating quantum systems on digital quantum computers. We ...
research
07/26/2023

Dense outputs from quantum simulations

The quantum dense output problem is the process of evaluating time-accum...

Please sign up or login with your details

Forgot password? Click here to reset