Quantum-Classical Tradeoffs in the Random Oracle Model

11/23/2022
by   Yassine Hamoudi, et al.
0

We study tradeoffs between quantum and classical queries for hybrid algorithms that have black-box access to a random oracle. Although there are several established techniques for proving query lower bounds for both quantum and classical algorithms, there is no such widely applicable technique for hybrid algorithms and the optimal tradeoffs for many fundamental problems are still unknown x2013 an optimal tradeoff for the search problem was only shown recently by Rosmanis, although not in the random oracle model. For another fundamental problem, collision finding, the optimal tradeoff was not known. In this work, we develop a framework for recording a query transcript for quantum-classical algorithms that represents the knowledge gained by the algorithm. The main feature of this framework is to allow us to record queries in two incompatible bases x2013 classical queries in the standard basis and quantum queries in the Fourier basis x2013 in a consistent way. We call the framework the hybrid compressed oracle as it naturally interpolates between the classical way of recording queries and the compressed oracle framework of Zhandry for recording quantum queries. We demonstrate its applicability by giving a simpler proof of the optimal quantum-classical tradeoff for search and by showing an optimal tradeoff for collision finding.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
10/22/2020

On the Compressed-Oracle Technique, and Post-Quantum Security of Proofs of Sequential Work

We revisit the so-called compressed oracle technique, introduced by Zhan...
research
03/16/2021

Tight Bounds for Inverting Permutations via Compressed Oracle Arguments

In his seminal work on recording quantum queries [Crypto 2019], Zhandry ...
research
02/20/2020

Quantum Time-Space Tradeoffs by Recording Queries

We use the recording queries technique of Zhandry [Zha19] to prove lower...
research
06/21/2023

Quantum and classical query complexities for determining connectedness of matroids

Connectivity is a fundamental structural property of matroids, and has b...
research
06/02/2023

Efficient Quantum State Synthesis with One Query

We present a polynomial-time quantum algorithm making a single query (in...
research
06/23/2022

Learning quantum symmetries with interactive quantum-classical variational algorithms

A symmetry of a state |ψ⟩ is a unitary operator of which |ψ⟩ is an eigen...
research
10/13/2022

Non-uniformity and Quantum Advice in the Quantum Random Oracle Model

QROM (quantum random oracle model), introduced by Boneh et al. (Asiacryp...

Please sign up or login with your details

Forgot password? Click here to reset