Classical-Quantum Separations in Certain Classes of Boolean Functions– Analysis using the Parity Decision Trees

04/27/2020
by   Chandra Sekhar Mukherjee, et al.
0

In this paper we study the separation between the deterministic (classical) query complexity (D) and the exact quantum query complexity (Q_E) of several Boolean function classes using the parity decision tree method. We first define the Query Friendly (QF) functions on n variables as the ones with minimum deterministic query complexity (D(f)). We observe that for each n, there exists a non-separable class of QF functions such that D(f)=Q_E(f). Further, we show that for some values of n, all the QF functions are non-separable. Then we present QF functions for certain other values of n where separation can be demonstrated, in particular, Q_E(f)=D(f)-1. In a related effort, we also study the Maiorana McFarland (M-M) type Bent functions. We show that while for any M-M Bent function f on n variables D(f) = n, separation can be achieved as n/2≤ Q_E(f) ≤⌈3n/4⌉. Our results highlight how different classes of Boolean functions can be analyzed for classical-quantum separation exploiting the parity decision tree method.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/14/2020

Exact Quantum Query Algorithms Outperforming Parity – Beyond The Symmetric functions

The Exact Quantum Query model is the least explored query model, and alm...
research
11/29/2019

Hybrid Decision Trees: Longer Quantum Time is Strictly More Powerful

In this paper, we introduce the hybrid query complexity, denoted as Q(f;...
research
10/22/2020

Separation Results for Boolean Function Classes

We show (almost) separation between certain important classes of Boolean...
research
03/22/2021

Fourier Growth of Parity Decision Trees

We prove that for every parity decision tree of depth d on n variables, ...
research
02/05/2023

Level-p-complexity of Boolean functions using Thinning, Memoization, and Polynomials

This paper describes a purely functional library for computing level-p-c...
research
04/20/2018

Enumeration in Incremental FPT-Time

In this paper, we study the relationship of parametrised enumeration com...
research
06/07/2021

Deterministic Iteratively Built KD-Tree with KNN Search for Exact Applications

K-Nearest Neighbors (KNN) search is a fundamental algorithm in artificia...

Please sign up or login with your details

Forgot password? Click here to reset