Logical-qubit operations in an error-detecting surface code
Jorge Marques (TU Delft - QCD/DiCarlo Lab, Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre)
Boris M. Varbanov (TU Delft - QCD/Terhal Group, TU Delft - QuTech Advanced Research Centre)
M.D. Moreira (Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab, TU Delft - QuTech Advanced Research Centre)
H.A.S. Ali (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab)
N. Muthusubramanian (Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab, TU Delft - QuTech Advanced Research Centre)
C. Zachariadis (TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft, TU Delft - QCD/DiCarlo Lab)
Francesco Battistel (TU Delft - QCD/Terhal Group, TU Delft - QuTech Advanced Research Centre)
M.W. Beekman (TU Delft - BUS/TNO STAFF, TU Delft - QuTech Advanced Research Centre, TNO)
N Haider (TU Delft - QuTech Advanced Research Centre, TU Delft - BUS/TNO STAFF, TNO)
W.J. Vlothuizen (TU Delft - BUS/TNO STAFF, TU Delft - QuTech Advanced Research Centre, TNO)
A Bruno (TU Delft - QCD/DiCarlo Lab, TU Delft - BUS/Quantum Delft, TU Delft - QuTech Advanced Research Centre, Kavli institute of nanoscience Delft)
Barbara M. Terhal (Quantum Computing, TU Delft - QuTech Advanced Research Centre, TU Delft - QCD/Terhal Group, Forschungszentrum Jülich)
L di Carlo (Kavli institute of nanoscience Delft, TU Delft - QuTech Advanced Research Centre, TU Delft - QN/DiCarlo Lab, TU Delft - QCD/DiCarlo Lab)
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Abstract
Future fault-tolerant quantum computers will require storing and processing quantum data in logical qubits. Here we realize a suite of logical operations on a distance-2 surface code qubit built from seven physical qubits and stabilized using repeated error-detection cycles. Logical operations include initialization into arbitrary states, measurement in the cardinal bases of the Bloch sphere and a universal set of single-qubit gates. For each type of operation, we observe higher performance for fault-tolerant variants over non-fault-tolerant variants, and quantify the difference. In particular, we demonstrate process tomography of logical gates, using the notion of a logical Pauli transfer matrix. This integration of high-fidelity logical operations with a scalable scheme for repeated stabilization is a milestone on the road to quantum error correction with higher-distance superconducting surface codes.
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