AI Chat AI Image Generator AI Video Text to Speech

Open Problems Related to Quantum Query Complexity

09/14/2021

∙

by Scott Aaronson, et al.

∙

∙

I offer a case that quantum query complexity still has loads of enticing and fundamental open problems – from relativized QMA versus QCMA and BQP versus IP, to time/space tradeoffs for collision and element distinctness, to polynomial degree versus quantum query complexity for partial functions, to the Unitary Synthesis Problem and more.

page 1

page 2

page 3

page 4

research

∙ 08/24/2020

An Optimal Separation of Randomized and Quantum Query Complexity

We prove that for every decision tree, the absolute values of the Fourie...

0 Alexander A. Sherstov, et al. ∙

research

∙ 01/14/2018

Algorithmic Polynomials

The approximate degree of a Boolean function f(x_1,x_2,...,x_n) is the m...

0 Alexander A. Sherstov, et al. ∙

research

∙ 03/30/2021

A note about claw function with a small range

In the claw detection problem we are given two functions f:D→ R and g:D→...

0 Andris Ambainis, et al. ∙

research

∙ 11/17/2022

Approaching the Soundness Barrier: A Near Optimal Analysis of the Cube versus Cube Test

The Cube versus Cube test is a variant of the well-known Plane versus Pl...

0 Dor Minzer, et al. ∙

research

∙ 05/15/2018

Time-Space Complexity of Quantum Search Algorithms in Symmetric Cryptanalysis

Performance of cryptanalytic quantum search algorithms is mainly inferre...

0 Panjin Kim, et al. ∙

research

∙ 11/20/2018

Improved Quantum Multicollision-Finding Algorithm

The current paper improves the number of queries of the previous quantum...

0 Akinori Hosoyamada, et al. ∙

research

∙ 07/21/2023

A Generalized Quantum Branching Program

Classical branching programs are studied to understand the space complex...

0 Debajyoti Bera, et al. ∙