Source-linked AI summary
All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
Ben Q. Baragiola, Giacomo Pantaleoni, Rafael N. Alexander, Angela Karanjai, Nicolas C. Menicucci
TL;DR
The paper addresses how GKP-encoded qubits can support fault-tolerant universal computation using Gaussian resources. It applies GKP error correction to Gaussian states, showing that vacuum-derived states can supply distillable magic states and that the resulting scheme is fault tolerant under sufficiently low physical noise.
Problem
Fault-tolerant universal quantum computing with GKP-encoded bosonic qubits requires resources beyond Gaussian Clifford operations, motivating a search for Gaussian sources of magic states.
Method
The paper applies two-step GKP error correction to Gaussian input states, including vacuum and thermal states, and evaluates whether the outputs are distillable magic states.
Results
Applying GKP error correction to vacuum produces distillable H-type magic states for nearly any measurement outcome, while thermal states succeed with nonzero probability when mean occupation is below 0.366.
Takeaways & Limitations
GKP-Clifford and Gaussian quantum computation combine without additional non-Gaussian resources to yield fault-tolerant, universal quantum computation at sufficiently low physical noise.
Takeaways & Limitations
Residual Gaussian imperfections from the correction operation are not analyzed in detail and are left for future work.
Abstract
from arXiv · showhide
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.