Securing and Verifying Computations on the Quantum Network

The aim of this research proposal is to develop new paradigms for secure and verifiable quantum computation. An important motivation comes from the rapid growth of quantum technologies and the prospect that quantum devices will be connected together into a diverse and heterogeneous computing environment called the quantum network. The nodes on the quantum network will have varying levels of quantum computing capability, as well as varying levels of trust. Parties on the network won't want to just communicate securely; they will want to also compute securely. This calls for the need to study quantum protocols for distributed computation that are efficient and privacy-preserving. Along the way, this research will also shed light on fundamental questions about quantum information, quantum complexity theory, and quantum cryptography. This research proposal has two main components. In the first component, we will investigate different methods to encrypt quantum computations. This will include, for example, investigating quantum analogues of Yao's garbled circuits protocol, and its applications to delegated computation and zero knowledge protocols. We will also investigate the concept of encoding quantum computations into quantum states, as an approach towards quantum program obfuscation and related functionalities such as quantum money and unclonable tokens. In the second component, we will investigate new approaches to verifying quantum computations. This includes designing ultra-efficient verification protocols, where a classical verifier can check the correctness of a complex, untrusted quantum device. The goal is to obtain non-interactive and efficient verification schemes that overcome the exponential complexity barrier encountered in, for example, the certification of 'quantum supremacy' experiments.