Efficient Quantum Pseudorandomness

TL;DR

This paper demonstrates that random quantum circuits can efficiently generate quantum pseudorandomness, enabling polynomial-time construction of quantum designs that emulate true randomness for various applications.

Contribution

It introduces the first polynomial-time construction of quantum unitary designs using random quantum circuits, advancing the understanding of quantum pseudorandomness.

Findings

Quantum circuits can produce pseudorandomness efficiently.

Quantum unitary designs can replace fully random operations.

Applications in quantum information and cryptography are enabled.

Abstract

Randomness is both a useful way to model natural systems and a useful tool for engineered systems, e.g. in computation, communication and control. Fully random transformations require exponential time for either classical or quantum systems, but in many case pseudorandom operations can emulate certain properties of truly random ones. Indeed in the classical realm there is by now a well-developed theory of such pseudorandom operations. However the construction of such objects turns out to be much harder in the quantum case. Here we show that random quantum circuits are a powerful source of quantum pseudorandomness. This gives the for the first time a polynomialtime construction of quantum unitary designs, which can replace fully random operations in most applications, and shows that generic quantum dynamics cannot be distinguished from truly random processes. We discuss applications of our result to quantum information science, cryptography and to understanding self-equilibration of closed quantum dynamics.