Constant-round Blind Classical Verification of Quantum Sampling

12/09/2020
by   Kai-Min Chung, et al.
0

In a recent breakthrough, Mahadev constructed a classical verification of quantum computation (CVQC) protocol for a classical client to delegate decision problems in BQP to an untrusted quantum prover under computational assumptions. In this work, we explore further the feasibility of CVQC with the more general sampling problems in BQP and with the desirable blindness property. We contribute affirmative solutions to both as follows. (1) Motivated by the sampling nature of many quantum applications (e.g., quantum algorithms for machine learning and quantum supremacy tasks), we initiate the study of CVQC for quantum sampling problems (denoted by SampBQP). More precisely, in a CVQC protocol for a SampBQP problem, the prover and the verifier are given an input x∈{0,1}^n and a quantum circuit C, and the goal of the classical client is to learn a sample from the output z ← C(x) up to a small error, from its interaction with an untrusted prover. We demonstrate its feasibility by constructing a four-message CVQC protocol for SampBQP based on the quantum Learning With Error assumption. (2) The blindness of CVQC protocols refers to a property of the protocol where the prover learns nothing, and hence is blind, about the client's input. It is a highly desirable property that has been intensively studied for the delegation of quantum computation. We provide a simple yet powerful generic compiler that transforms any CVQC protocol to a blind one while preserving its completeness and soundness errors as well as the number of rounds. Applying our compiler to (a parallel repetition of) Mahadev's CVQC protocol for BQP and our CVQC protocol for SampBQP yields the first constant-round blind CVQC protocol for BQP and SampBQP respectively, with negligible completeness and soundness errors.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

02/28/2022

Classical Verification of Quantum Computations in Linear Time

In the quantum computation verification problem, a quantum server wants ...
04/27/2020

Succinct Blind Quantum Computation Using a Random Oracle

In the universal blind quantum computation problem, a client wants to ma...
02/02/2020

Full-Blind Delegating Private Quantum Computation

The delegating private quantum computation (DQC) protocol with the unive...
01/05/2021

Single-preparation unsupervised quantum machine learning: concepts and applications

The term "machine learning" especially refers to algorithms that derive ...
12/10/2018

Impossibility of blind quantum sampling for classical client

Blind quantum computing enables a client, who can only generate or measu...
12/02/2019

Classical Verification of Quantum Computations with Efficient Verifier

In this paper, we extend the protocol of classical verification of quant...
12/21/2018

Round elimination in exact communication complexity

We study two basic graph parameters, the chromatic number and the orthog...
This week in AI

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