Quantum computers can solve problems that are beyond the capabilities of conventional computers. As quantum computers are expensive and hard to maintain, the typical model for performing quantum computation is to send the circuit to a quantum cloud provider. This leads to privacy concerns for commercial entities as an untrusted server can learn protected information from the provided circuit. Current proposals for Secure Quantum Computing (SQC) either rely on emerging technologies (such as quantum networks) or incur prohibitive overheads (for Quantum Homomorphic Encryption). The goal of our paper is to enable low-cost privacy-preserving quantum computation that can be used with current systems. We propose Enigma, a suite of privacy-preserving schemes specifically designed for the Quantum Approximate Optimization Algorithm (QAOA). Unlike previous SQC techniques that obfuscate quantum circuits, Enigma transforms the input problem of QAOA, such that the resulting circuit and the outcomes are unintelligible to the server. We introduce three variants of Enigma. Enigma-I protects the coefficients of QAOA using random phase flipping and fudging of values. Enigma-II protects the nodes of the graph by introducing decoy qubits, which are indistinguishable from primary ones. Enigma-III protects the edge information of the graph by modifying the graph such that each node has an identical number of connections. For all variants of Enigma, we demonstrate that we can still obtain the solution for the original problem. We evaluate Enigma using IBM quantum devices and show that the privacy improvements of Enigma come at only a small reduction in fidelity (1%-13%).

翻译：量子计算机能够解决传统计算机无法企及的问题。由于量子计算机成本高昂且难以维护，执行量子计算的典型模式是将量子电路发送至量子云提供商。这引发了商业实体的隐私担忧，因为不可信服务器可能从提交的电路中学习受保护信息。当前安全量子计算（Secure Quantum Computing, SQC）方案要么依赖新兴技术（如量子网络），要么引入难以承受的开销（如量子同态加密）。本文旨在实现适用于现有系统的低成本隐私保护量子计算。我们提出Enigma——一套专为量子近似优化算法（Quantum Approximate Optimization Algorithm, QAOA）设计的隐私保护方案。与以往混淆量子电路的SQC技术不同，Enigma通过转换QAOA的输入问题，使得生成的电路及输出结果对服务器不可解读。我们引入三种Enigma变体：Enigma-I通过随机相位翻转和数值模糊保护QAOA系数；Enigma-II通过引入与主量子比特不可区分的诱饵量子比特保护图节点；Enigma-III通过修改图结构使每个节点拥有相同连接数来保护图边信息。针对所有Enigma变体，我们证明仍能获得原问题解。基于IBM量子设备的评估表明，Enigma的隐私改进仅以1%-13%的保真度小幅降低为代价。