Radio-frequency (rf) reflectometry offers a fast and sensitive method for charge sensing and spin readout in gated quantum dots. We focus in this work on the implementation of rf readout in accumulation-mode gate-defined quantum dots, where the large parasitic capacitance poses a challenge. We describe and test two methods for mitigating the effect of the parasitic capacitance, one by on-chip modifications and a second by off-chip changes. We demonstrate that on-chip modifications enable high-performance charge readout in Si/SixGe1-x quantum dots, achieving a fidelity of 99.9% for a measurement time of 1μs.

Quantum error correction is of crucial importance for fault-tolerant quantum computers. As an essential step toward the implementation of quantum error-correcting codes, quantum nondemolition measurements are needed to efficiently detect the state of a logical qubit without destroying it. Here we implement quantum nondemolition measurements in a Si/SiGe two-qubit system, with one qubit serving as the logical qubit and the other serving as the ancilla. Making use of a two-qubit controlled-rotation gate, the state of the logical qubit is mapped onto the ancilla, followed by a destructive readout of the ancilla. Repeating this procedure enhances the logical readout fidelity from 75.5±0.3% to 94.5±0.2% after 15 ancilla readouts. In addition, we compare the conventional thresholding method with an improved signal processing method called soft decoding that makes use of analog information in the readout signal to better estimate the state of the logical qubit. We demonstrate that soft decoding leads to a significant reduction in the required number of repetitions when the readout errors become limited by Gaussian noise, for instance, in the case of readouts with a low signal-to-noise ratio. These results pave the way for the implementation of quantum error correction with spin qubits in silicon.

We study spatial noise correlations in a Si/SiGe two-qubit device with integrated micromagnets. Our method relies on the concept of decoherence-free subspaces, whereby we measure the coherence time for two different Bell states, designed to be sensitive only to either correlated or anticorrelated noise, respectively. From these measurements we find weak correlations in low-frequency noise acting on the two qubits, while no correlations could be detected in high-frequency noise. We expect nuclear spin noise to have an uncorrelated nature. A theoretical model and numerical simulations give further insight into the additive effect of multiple independent (anti)correlated noise sources with an asymmetric effect on the two qubits as can result from charge noise. Such a scenario in combination with nuclear spins is plausible given the data and the known decoherence mechanisms. This work is highly relevant for the design of optimized quantum error correction codes for spin qubits in quantum dot arrays, as well as for optimizing the design of future quantum dot arrays.