Measurement-Free Quantum Error Correction Optimized for Biased Noise

PRX Quantum, vol. 6

Abstract

In this paper, we derive optimized measurement-free protocols for quantum error correction and the implementation of a universal gate set optimized for an error model that is noise biased. The noise bias is adapted for neutral-atom platforms, where two- and multi-qubit gates are realized with Rydberg interactions and are thus expected to be the dominant source of noise. Careful design of the gates allows us to further reduce the noise model to Pauli- Z errors. In addition, the presented circuits are robust to arbitrary single-qubit gate errors, and we demonstrate that the break-even point can be significantly improved compared to fully fault-tolerant measurement-free schemes. The obtained logical qubits with their suppressed error rates on logical gate operations can then be used as building blocks in a first step of error correction in order to push the effective error rates below the threshold of a fully fault-tolerant and scalable quantum error-correction scheme.

Authors 7

1. Katharina Brechtelsbauer corresponding

   University of Stuttgart · Center for Integrated Quantum Science and Technology

   Affiliation as printed

   University of Stuttgart

   Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

2. Friederike Butt Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

   Institute for Quantum Information, RWTH Aachen University, 52074 Aachen, Germany

3. David F. Locher Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

   Institute for Quantum Information, RWTH Aachen University, 52074 Aachen, Germany

4. Santiago Higuera-Quintero

   University of Stuttgart · Center for Integrated Quantum Science and Technology

   Affiliation as printed

   University of Stuttgart

   Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

5. Sebastian Weber

   University of Stuttgart · Center for Integrated Quantum Science and Technology

   Affiliation as printed

   University of Stuttgart

   Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany

6. Markus Michael Müller Aachen Institute for Quantum Information

   Forschungszentrum Jülich · RWTH Aachen University

   Affiliation as printed

   Forschungszentrum Jülich

   RWTH Aachen University

   Institute for Quantum Information, RWTH Aachen University, 52074 Aachen, Germany

7. Hans Peter Büchler

   University of Stuttgart · Center for Integrated Quantum Science and Technology

   Affiliation as printed

   University of Stuttgart

   Institute for Theoretical Physics III and Center for Integrated Quantum Science and Technology, University of Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany