QMA Lower Bounds for Approximate Counting

02/06/2019 ∙ by William Kretschmer, et al. ∙ 0

We prove a query complexity lower bound for QMA protocols that solve approximate counting: estimating the size of a set given a membership oracle. This gives rise to an oracle A such that SBP^A ⊂QMA^A, resolving an open problem of Aaronson [2]. Our proof uses the polynomial method to derive a lower bound for the SBQP query complexity of the AND of two approximate counting instances. We use Laurent polynomials as a tool in our proof, showing that the "Laurent polynomial method" can be useful even for problems involving ordinary polynomials.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.