Quantum mechanics

Gaussian

Quantum computer

Quantum error correction

Eigenvalues and eigenvectors

Computer science

Pauli exclusion principle

Distributed computing

Statistical physics

Universality (dynamical systems)

Physics

Pauli matrices

Fault tolerance

Mathematics

Quantum

Qubit

Boson

Physical Review Letters

The Gottesman-Kitaev-Preskill (GKP) encoding of a qubit within an oscillator is particularly appealing for fault-tolerant quantum computing with bosons because Gaussian operations on encoded Pauli eigenstates enable Clifford quantum computing with error correction. We show that applying GKP error correction to Gaussian input states, such as vacuum, produces distillable magic states, achieving universality without additional non-Gaussian elements. Fault tolerance is possible with sufficient squeezing and low enough external noise. Thus, Gaussian operations are sufficient for fault-tolerant, universal quantum computing given a supply of GKP-encoded Pauli eigenstates.

All-Gaussian Universality and Fault Tolerance with the Gottesman-Kitaev-Preskill Code