Measurement-free Implementations of Small-Scale Surface Codes for Quantum Dot Qubits

In quantum dot spin qubits, readout is typically much slower than gate operations, and conventional surface code implementations that rely on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum dot qubits can be achieved via tunneling to a reservoir. Here, we propose small-scale surface code implementations for which syndrome measurements are replaced by a combination of Toffoli gates and qubit reset. For quantum dot qubits, this enables much faster error correction than measurement-based schemes, but requires additional ancilla qubits and nonlocal interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of 10^-2 for a 1D architecture that only corrects bit-flip errors, and 10^-4 for a 2D architecture that corrects bit and phase-flip errors. We have also demonstrated that when the measurement time is about 10 times the gate time, our method begins producing a higher threshold than the measurement-based method.

The authors acknowledge support from the Vannevar Bush Faculty Fellowship program sponsored by the Basic Research Office of the Assistant Secretary of Defense for Research and Engineering and funded by the Office of Naval Research through grant N00014-15-1-0029.