Measurement-free implementations of small-scale surface codes for quantum-dot qubits
Hamdi Ercan, Joydip Ghosh, Daniel Crow, Vickram N. Premakumar, Robert Joynt, Mark G. Friesen, S. N. Coppersmith · Physical Review A · 2018
The performance of quantum-error-correction schemes depends sensitively on the physical realizations of the qubits and the implementations of various operations. For example, in quantum-dot spin qubits, readout is typically much slower than gate operations, and conventional surface-code implementations that rely heavily on syndrome measurements could therefore be challenging. However, fast and accurate reset of quantum-dot qubits, without readout, 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 non-nearest-neighbor interactions. We have performed numerical simulations of two different coding schemes, obtaining error thresholds on the orders of ${10}^{\ensuremath{-}2}$ for a one-dimensional architecture that only corrects bit-flip errors and ${10}^{\ensuremath{-}4}$ for a two-dimensional architecture that corrects bit- and phase-flip errors.