title: Repeated quantum error correction on a continuously encoded qubit by real-time feedback.
abstract: Reliable quantum information processing in the face of errors is a major fundamental and technological challenge. Quantum error correction protects quantum states by encoding a logical quantum bit (qubit) in multiple physical qubits. To be compatible with universal fault-tolerant computations, it is essential that states remain encoded at all times and that errors are actively corrected. Here we demonstrate such active error correction on a continuously protected logical qubit using a diamond quantum processor. We encode the logical qubit in three long-lived nuclear spins, repeatedly detect phase errors by non-destructive measurements, and apply corrections by real-time feedback. The actively error-corrected qubit is robust against errors and encoded quantum superposition states are preserved beyond the natural dephasing time of the best physical qubit in the encoding. These results establish a powerful platform to investigate error correction under different types of noise and mark an important step towards fault-tolerant quantum information processing.
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: J
authors.initials: J
authors.lastname: Cramer
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: N
authors.initials: N
authors.lastname: Kalb
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: M A
authors.initials: MA
authors.lastname: Rol
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: B
authors.initials: B
authors.lastname: Hensen
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: M S
authors.initials: MS
authors.lastname: Blok
authors.affiliation: Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, UK.
authors.forename: M
authors.initials: M
authors.lastname: Markham
authors.affiliation: Element Six Innovation, Fermi Avenue, Harwell Oxford, Didcot, Oxfordshire OX11 0QR, UK.
authors.forename: D J
authors.initials: DJ
authors.lastname: Twitchen
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: R
authors.initials: R
authors.lastname: Hanson
authors.affiliation: QuTech, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.|Kavli Institute of Nanoscience, Delft University of Technology, PO Box 5046, 2600 GA Delft, The Netherlands.
authors.forename: T H
authors.initials: TH
authors.lastname: Taminiau