Leakage detection for a transmon-based surface code

npj Quantum Information, vol. 6

Abstract

Abstract Leakage outside of the qubit computational subspace, present in many leading experimental platforms, constitutes a threatening error for quantum error correction (QEC) for qubits. We develop a leakage-detection scheme via Hidden Markov models (HMMs) for transmon-based implementations of the surface code. By performing realistic density-matrix simulations of the distance-3 surface code (Surface-17), we observe that leakage is sharply projected and leads to an increase in the surface-code defect probability of neighboring stabilizers. Together with the analog readout of the ancilla qubits, this increase enables the accurate detection of the time and location of leakage. We restore the logical error rate below the memory break-even point by post-selecting out leakage, discarding less than half of the data for the given noise parameters. Leakage detection via HMMs opens the prospect for near-term QEC demonstrations, targeted leakage reduction and leakage-aware decoding and is applicable to other experimental platforms.

Authors 7

1. Boris Varbanov corresponding

   QuTech · Delft University of Technology

   Affiliation as printed

   QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

2. Francesco Battistel

   QuTech · Delft University of Technology

   Affiliation as printed

   QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

3. Brian Tarasinski

   QuTech · Delft University of Technology

   Affiliation as printed

   Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

   QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

4. Viacheslav Ostroukh

   QuTech · Delft University of Technology

   Affiliation as printed

   Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

   QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

5. Thomas E. O’Brien Aachen Instituut-Lorentz

   Leiden University · Google (United States)

   Affiliation as printed

   Google Research, Venice, CA, 90291, United States

   Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA, Leiden, The Netherlands

6. L. DiCarlo

   QuTech · Delft University of Technology

   Affiliation as printed

   Kavli Institute of Nanoscience, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

   QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands

7. Barbara M. Terhal

   Forschungszentrum Jülich · Jülich Aachen Research Alliance · QuTech · Delft University of Technology

   Affiliation as printed

   JARA Institute for Quantum Information, Forschungszentrum Juelich, D-52425, Juelich, Germany

   QuTech, Delft University of Technology, P.O. Box 5046, 2600 GA, Delft, The Netherlands