Quantum advantage for computations with limited space

Dmitri Maslov, Jin-Sung Kim, Sergey Bravyi, Theodore J. Yoder, Sarah Sheldon

Published 2020-08-14Version 1

Quantum computations promise the ability to solve problems intractable in the classical setting. Restricting the types of computations considered often allows to establish a provable theoretical advantage by quantum computations, and later demonstrate it experimentally. In this paper, we consider space-restricted computations, where input is a read-only memory and only one (qu)bit can be computed on. We show that $n$-bit symmetric Boolean functions can be implemented exactly through the use of quantum signal processing as restricted space quantum computations using $O(n^2)$ gates, but some of them may only be evaluated with probability $\frac{1}{2} {+} \tilde{O}(\frac{1}{\sqrt{n}})$ by analogously defined classical computations. We experimentally demonstrate computations of $3$- and a $4$-bit symmetric Boolean functions by quantum circuits, leveraging custom two-qubit gates, with algorithmic success probability exceeding the best possible classically. This establishes and experimentally verifies a different kind of quantum advantage -- one where a quantum bit stores more useful information for the purpose of computation than a classical bit. This suggests that in computations, quantum scrap space is more valuable than analogous classical space and calls for an in-depth exploration of space-time tradeoffs in quantum circuits.