Modular fault-tolerant quantum computing on a non-CSS code

arXiv (Cornell University)

Abstract

Modularization promises to break down the design and implementation complexity of large scale quantum processors into smaller manageable subtasks. In this approach, quantum channels, realized for instance through physical rerouting of qubits or quantum teleportation, connect multiple modules. Each of those modules hosts a subset of qubits, e.g. multiple logical qubits, and provides quantum operations on them. In this work, we implement for the first time all logical operations required for modular fault-tolerant universal quantum computing with a non-Calderbank-Shor-Steane (CSS) code, the perfect $[[5, 1, 3]]$ code, on a trapped-ion quantum computer. This code is the smallest quantum error-correcting (QEC) code capable of correcting any single-qubit error, making it a compact alternative to larger CSS codes. We demonstrate logical state teleportation and a full suite of fault-tolerant operations required for universal logical control, including logical state preparation, QEC with real-time feedback, logical measurements, magic-state preparation, logical entangling operations, and magic-state injection. Moreover, we characterize the logical spectator error picked up by idling logical qubits during quantum operations on distinct qubit registers and demonstrate a logical Pauli quantum process tomography that minimizes required sampling resources for logical tomography.

Authors 9

1. Robert Freund

   Universität Innsbruck

   Affiliation as printed

   Universität Innsbruck , Institut für Experimentalphysik , Innsbruck , Austria

2. Friederike Butt Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information , RWTH Aachen University , Aachen , Germany

   Institute for Theoretical Nanoelectronics (PGI-2) , Forschungszentrum Jülich , Jülich , Germany

3. César Benito

   Instituto de Física Teórica

   Affiliation as printed

   Instituto de Fisica Teorica UAM-CSIC , Universidad Autonoma de Madrid , Cantoblanco , Madrid , Spain

4. Ivan Pogorelov

   Universität Innsbruck

   Affiliation as printed

   Universität Innsbruck , Institut für Experimentalphysik , Innsbruck , Austria

5. Marcel Meyer

   Universität Innsbruck

   Affiliation as printed

   Universität Innsbruck , Institut für Experimentalphysik , Innsbruck , Austria

6. Alex Steiner

   Universität Innsbruck

   Affiliation as printed

   Universität Innsbruck , Institut für Experimentalphysik , Innsbruck , Austria

7. A. Bermúdez

   Instituto de Física Teórica

   Affiliation as printed

   Instituto de Fisica Teorica UAM-CSIC , Universidad Autonoma de Madrid , Cantoblanco , Madrid , Spain

8. Markus Müller Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Institute for Quantum Information , RWTH Aachen University , Aachen , Germany

   Institute for Theoretical Nanoelectronics (PGI-2) , Forschungszentrum Jülich , Jülich , Germany

9. Thomas Monz

   Universität Innsbruck · Alpine Quantum Technologies (Austria)

   Affiliation as printed

   Alpine Quantum Technologies GmbH , Innsbruck , Austria

   Universität Innsbruck , Institut für Experimentalphysik , Innsbruck , Austria