# Quantum gradient descent for linear systems and least squares.

@inproceedings{Kerenidis2017QuantumGD, title={Quantum gradient descent for linear systems and least squares.}, author={Iordanis Kerenidis and Anupam Prakash}, year={2017} }

Quantum machine learning and optimization are exciting new areas that have been brought forward by the breakthrough quantum algorithm of Harrow, Hassidim and Lloyd for solving systems of linear equations. The utility of {classical} linear system solvers extends beyond linear algebra as they can be leveraged to solve optimization problems using iterative methods like gradient descent. In this work, we provide the first quantum method for performing gradient descent when the gradient is an affine… CONTINUE READING

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#### References

##### Publications referenced by this paper.

SHOWING 1-10 OF 33 REFERENCES

## Quantum Recommendation Systems

VIEW 9 EXCERPTS

## and R

VIEW 6 EXCERPTS

HIGHLY INFLUENTIAL

## and S

VIEW 4 EXCERPTS

HIGHLY INFLUENTIAL

## and A

VIEW 1 EXCERPT

## Quantum Speed-ups for Semidefinite Programming

VIEW 1 EXCERPT

## and S

VIEW 1 EXCERPT