Measurement-free implementations of small-scale surface codes for quantum dot qubits

TL;DR

This paper proposes measurement-free small-scale surface code implementations for quantum dot qubits, replacing syndrome measurements with Toffoli gates and qubit resets to enable faster error correction.

Contribution

It introduces novel measurement-free surface code schemes tailored for quantum dot qubits, utilizing qubit resets and non-nearest-neighbor interactions.

Findings

Error thresholds of ~10^{-2} for 1D bit-flip correction

Error thresholds of ~10^{-4} for 2D bit- and phase-flip correction

Numerical simulations demonstrate feasibility of measurement-free error correction

Abstract

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 $10^{-2}$ for a 1D architecture that only corrects bit-flip errors, and $10^{-4}$ for a 2D architecture that corrects bit- and phase-flip errors.