Probabilistic Fault-Tolerant Universal Quantum Computation and Sampling Problems in Continuous Variables

TL;DR

This paper introduces a CV-based quantum computational model capable of fault-tolerant universal quantum computing and sampling problems that challenge classical simulation, providing a practical framework for near-term quantum advantage experiments.

Contribution

It defines a CV quantum model with non-Gaussian elements that enables fault-tolerant universal computation and demonstrates classical hardness of associated sampling problems.

Findings

Model incorporates encodings for fault-tolerant universal quantum computing.

Sampling problems in the model are classically hard unless the polynomial hierarchy collapses.

Robustness of quantum advantage claims under experimental simplifications.

Abstract

Continuous-Variable (CV) devices are a promising platform for demonstrating large-scale quantum information protocols. In this framework, we define a general quantum computational model based on a CV hardware. It consists of vacuum input states, a finite set of gates - including non-Gaussian elements - and homodyne detection. We show that this model incorporates encodings sufficient for probabilistic fault-tolerant universal quantum computing. Furthermore, we show that this model can be adapted to yield sampling problems that cannot be simulated efficiently with a classical computer, unless the polynomial hierarchy collapses. This allows us to provide a simple paradigm for short-term experiments to probe quantum advantage relying on Gaussian states, homodyne detection and some form of non-Gaussian evolution. We finally address the recently introduced model of Instantaneous Quantum Computing in CV, and prove that the hardness statement is robust with respect to some experimentally relevant simplifications in the definition of that model.