Quantum Garbled Circuits

TL;DR

This paper introduces a quantum garbling scheme that enables secure quantum computation encoding, facilitating applications like zero-knowledge proofs for complex quantum classes, a significant advancement in quantum cryptography.

Contribution

It presents the first quantum garbling scheme for general circuits and demonstrates its application in designing a simple zero-knowledge proof system for QMA.

Findings

Developed a quantum randomized encoding scheme for quantum circuits.

Designed a zero-knowledge protocol for QMA with single-bit challenge.

Achieved properties like delayed input revelation in the protocol.

Abstract

We present a garbling scheme for quantum circuits, thus achieving a decomposable randomized encoding scheme for quantum computation. Specifically, we show how to compute an encoding of a given quantum circuit and quantum input, from which it is possible to derive the output of the computation and nothing else. In the classical setting, garbled circuits (and randomized encodings in general) are a versatile cryptographic tool with many applications such as secure multiparty computation, delegated computation, depth-reduction of cryptographic primitives, complexity lower-bounds, and more. However, a quantum analogue for garbling general circuits was not known prior to this work. We hope that our quantum randomized encoding scheme can similarly be useful for applications in quantum computing and cryptography. To illustrate the usefulness of quantum randomized encoding, we use it to design a conceptually-simple zero-knowledge (ZK) proof system for the complexity class $\mathbf{QMA}$. Our protocol has the so-called $\Sigma$ format with a single-bit challenge, and allows the inputs to be delayed to the last round. The only previously-known ZK $\Sigma$-protocol for $\mathbf{QMA}$ is due to Broadbent and Grilo (FOCS 2020), which does not have the aforementioned properties.