By Zixin Huang, Pieter Kok, and Cosmo Lupo
Submitted to arXiv on 25 March 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−Hmin(X) secret bits, where Hmin(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.
