Optimal Blind Quantum Computation

TL;DR

This paper investigates the quantum communication resources needed for blind quantum computation, providing bounds and improvements on existing protocols based on the client's quantum capabilities.

Contribution

It introduces techniques for bounding quantum communication in blind quantum computation and proposes a generalized protocol requiring less quantum communication with advanced client devices.

Findings

UBQC protocol is within 8/3 factor of optimal for single-qubit clients

Generalized protocol reduces quantum communication exponentially for more capable clients

Provides bounds on resources necessary for blind quantum computation

Abstract

Blind quantum computation allows a client with limited quantum capabilities to interact with a remote quantum computer to perform an arbitrary quantum computation, while keeping the description of that computation hidden from the remote quantum computer. While a number of protocols have been proposed in recent years, little is currently understood about the resources necessary to accomplish the task. Here we present general techniques for upper and lower bounding the quantum communication necessary to perform blind quantum computation, and use these techniques to establish a concrete bounds for common choices of the client's quantum capabilities. Our results show that the UBQC protocol of Broadbent, Fitzsimons and Kashefi [1], comes within a factor of 8/3 of optimal when the client is restricted to preparing single qubits. However, we describe a generalization of this protocol which requires exponentially less quantum communication when the client has a more sophisticated device.