Related papers: Quantum Property Testing for Solvable Groups
The main promise of quantum computing is to efficiently solve certain problems that are prohibitively expensive for a classical computer. Most problems with a proven quantum advantage involve the repeated use of a black box, or oracle,…
Property testers form an important class of sublinear algorithms. In the standard property testing model, an algorithm accesses the input function via an oracle that returns function values at all queried domain points. In many realistic…
Multicalibration [HJKRR18] is an algorithmic fairness perspective that demands that the predictions of a predictor are correct conditional on themselves and membership in a collection of potentially overlapping subgroups of a population.…
In this work, we consider a family of sure-success quantum algorithms, which is grouped into even and odd members for solving a generalized Grover search problem. We prove the matching conditions for both groups and give the corresponding…
We show here that every non-adaptive property testing algorithm making a constant number of queries, over a fixed alphabet, can be converted to a sample-based (as per [Goldreich and Ron, 2015]) testing algorithm whose average number of…
In group testing, the task is to identify defective items by testing groups of them together using as few tests as possible. We consider the setting where each item is defective with a constant probability $\alpha$, independent of all other…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
A quantum computer can efficiently find the order of an element in a group, factors of composite integers, discrete logarithms, stabilisers in Abelian groups, and `hidden' or `unknown' subgroups of Abelian groups. It is already known how to…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
A test of quantumness is a protocol where a classical user issues challenges to a quantum device to determine if it exhibits non-classical behavior, under certain cryptographic assumptions. Recent attempts to implement such tests on current…
The group testing problem asks for efficient pooling schemes and algorithms that allow to screen moderately large numbers of samples for rare infections. The goal is to accurately identify the infected samples while conducting the least…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
Quantum spatial search has been widely studied with most of the study focusing on quantum walk algorithms. We show that quantum walk algorithms are extremely sensitive to systematic errors. We present a recursive algorithm which offers…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…
We study the ability of efficient quantum verifiers to decide properties of exponentially large subsets given either a classical or quantum witness. We develop a general framework that can be used to prove that QCMA machines, with only…
We prove that quantum computation is polynomially equivalent to classical probabilistic computation with an oracle for estimating the value of simple sums, quadratically signed weight enumerators. The problem of estimating these sums can be…
We propose an efficient scheme for verifying quantum computations in the `high complexity' regime i.e. beyond the remit of classical computers. Previously proposed schemes remarkably provide confidence against arbitrarily malicious…
[PLEASE SEE COMMENT] We consider the isomorphism problem for finite abelian groups and finite meta-cyclic groups. We prove that for a dense set of positive integers $n$, isomorphism testing for abelian groups of black-box type of order $n$…
This paper studies whether quantum proofs are more powerful than classical proofs, or in complexity terms, whether QMA=QCMA. We prove three results about this question. First, we give a "quantum oracle separation" between QMA and QCMA. More…
Given a prior probability distribution over a set of possible oracle functions, we define a number of queries to be useless for determining some property of the function if the probability that the function has the property is unchanged…