Protecting the output of a quantum computer with random circuit samplers
Zixin Huang, Pieter Kok, Cosmo Lupo · arXiv (Cornell University) · 2020
Random quantum circuit samplers have been used to demonstrate the exponential speed-up of quantum processors beyond what is tractable classically [Arute, K. et al., Nature 574, 505 (2019)]. However, useful applications for these samplers have so far been elusive. Here, we propose random circuit as efficient devices for protecting the output of a quantum computer. We consider a scenario where the server performs universal fault-tolerant quantum computation and the user gains access to the output using a pseudo-random circuit. We show that a private key much smaller than the size of the output may prevent unauthorised access. For an $n$-qubit computation, a standard approach requires an $n$-bit key to scramble the state. We provide an information-theoretic proof showing that obfuscation can be achieved with order $n - H_\mathrm{min}(\mathsf{X})$ secret bits, where $H_\mathrm{min}(\mathsf{X})$ is the min-entropy of the output of the computation. As interesting computations are expected to have large min-entropy, this represents a substantial reduction of the key size.