Impossibility of blind quantum sampling for classical client

TL;DR

This paper proves that a fully classical client cannot blindly delegate certain quantum sampling tasks without causing a collapse in computational complexity hierarchy, highlighting fundamental limitations in blind quantum delegation.

Contribution

It establishes a no-go theorem showing classical clients cannot blindly delegate sampling of specific quantum models without collapsing the polynomial hierarchy.

Findings

Classical clients cannot blindly delegate DQC1 sampling.

Classical clients cannot blindly delegate IQP sampling.

The delegation protocol involves sending a bit string and receiving a single bit.

Abstract

Blind quantum computing enables a client, who can only generate or measure single-qubit states, to delegate quantum computing to a remote quantum server in such a way that the input, output, and program are hidden from the server. It is an open problem whether a completely classical client can delegate quantum computing blindly. In this paper, we show that if a completely classical client can blindly delegate sampling of subuniversal models, such as the DQC1 model and the IQP model, then the polynomial-time hierarchy collapses to the third level. Our delegation protocol is the one where the client first sends a polynomial-length bit string to the server and then the server returns a single bit to the client. Generalizing the no-go result to more general setups is an open problem.