An Almost-Quadratic Lower Bound for Quantum Formula Size

TL;DR

This paper extends Nechiporuk's method to quantum formulas, establishing an almost-quadratic lower bound of n^2 / log^2 n for explicit functions, significantly advancing quantum formula complexity theory.

Contribution

It introduces a novel extension of classical lower bound techniques to quantum formulas, providing the first near-quadratic lower bound for explicit functions.

Findings

Quantum formulas require at least n^2 / log^2 n size for certain functions

Extension of Nechiporuk's method to quantum computing models

Previous bounds were limited to specific functions like majority

Abstract

We show that Nechiporuk's method for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an n^2 / log^2 n lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas (by Yao) states that the majority function does not have a linear-size quantum formula.