Quantum interpolation of polynomials

TL;DR

This paper establishes tight quantum lower bounds for interpolating polynomials using black-box access to input/output pairs, advancing understanding of quantum query complexity for polynomial evaluation.

Contribution

It provides asymptotically tight lower bounds for quantum interpolation of polynomials, even when zero is among the input points, which was previously unresolved.

Findings

Quantum lower bounds are asymptotically tight for polynomial interpolation.

The bounds hold even when zero is among the input points.

Results improve understanding of quantum query complexity for polynomial evaluation.

Abstract

We consider quantum interpolation of polynomials. We imagine a quantum computer with black-box access to input/output pairs (x_i, f(x_i)), where f is a degree-d polynomial, and we wish to compute f(0). We give asymptotically tight quantum lower bounds for this problem, even in the case where 0 is among the possible values of x_i.