Simple Quantum Gradient Descent Without Coherent Oracle Access

TL;DR

This paper introduces a quantum gradient descent algorithm that operates efficiently with classical data, requiring fewer qubits and no coherent oracle access, thus simplifying quantum optimization processes.

Contribution

It presents a novel quantum gradient descent method based on quantum singular value transformation that avoids the need for coherent oracle access and reduces qubit requirements.

Findings

Logarithmic running time in the number of variables

Exponential reduction in qubit usage compared to previous methods

Quantum advantage achieved without coherent oracle access

Abstract

The gradient descent method aims at finding local minima of a given multivariate function by moving along the direction of its gradient, and hence, the algorithm typically involves computing all partial derivatives of a given function, before updating the solution iteratively. In the work of Rebentrost et al. [New Journal of Physics, 21(7):073023, 2019], the authors translated the iterative optimization algorithm into a quantum setting, with some assumptions regarding certain structure of the given function, with oracle or black-box access to some matrix that specifies the structure. Here, we develop an alternative quantum framework for the gradient descent problem, based on the seminal quantum singular value transformation framework. We show that given only classical information of function of interest, it is possible to construct a quantum gradient descent algorithm with a running time logarithmical in the number of variables. In particular, our framework consumes exponentially less qubits than the prior quantum gradient descent algorithm and removes the need for any coherent oracle access to classical information. Thus, our work provides another example demonstrating the power of quantum singular value transformation framework, and in particular, it adds another instance revealing that quantum coherent access is not necessary for quantum computational advantage.