Towards experimental classical verification of quantum computation

TL;DR

This paper demonstrates a proof-of-principle classical verification protocol for quantum computations on a small quantum processor, paving the way for scalable, trust-independent verification of quantum devices in the future.

Contribution

It provides the first experimental implementation of a classical verification protocol for quantum computation using a trapped-ion system, based on Mahadev's theoretical protocol.

Findings

Successful demonstration of a simplified verification protocol on a small quantum processor

Validation of the protocol's potential for verifying untrusted quantum devices

Discussion of scalability and future applications in quantum advantage and randomness certification

Abstract

With today's quantum processors venturing into regimes beyond the capabilities of classical devices [1-3], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical computers [4,5]. In a recent breakthrough in computer science [6-8], a protocol was developed that allows the verification of the output of a computation performed by an untrusted quantum device based only on classical resources. Here, we follow these ideas, and demonstrate in a first, proof-of-principle experiment a verification protocol using only classical means on a small trapped-ion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gate-level benchmarking [9], or additional quantum resources in case we do not have access to or trust in the device to be tested [5]. While our experimental demonstration uses a simplified version [10] of Mahadev's protocol [6] we demonstrate the necessary steps for verifying fully untrusted devices. A scaled-up version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on post-quantum secure trapdoor functions within an interactive proof [11]. The conceptually straightforward, but technologically challenging scaled-up version of the interactive proofs, considered here, can be used for a variety of additional tasks such as verifying quantum advantage [8], generating [12] and certifying quantum randomness [7], or composable remote state preparation [13].