However, there are other types of error - such as charge leakage and propagation - that may occur in quantum dot arrays and which cannot be corrected by quantum error correction codes, making them potentially damaging even when their probability is small. High fidelity single-qubit gates exceeding the threshold of error correction codes like the surface code have been demonstrated, while two-qubit gates have reached 98% fidelity and are improving rapidly. Spin qubits in silicon quantum dots are one of the most promising building blocks for large scale quantum computers thanks to their high qubit density and compatibility with the existing semiconductor technologies. With the help of logical twirling, the undesirable coherence in the noise channel can be removed and the advantages of conjugation over twirling can persist as we go to multiple rounds of quantum error correction. Our simulations show that Pauli conjugation can be robust against gate errors. In our example noise and codes, the concatenated threshold obtained using conjugation is consistently higher than the twirling threshold and can be up to 1.5 times higher than the original threshold where no mitigation is applied. The optimal conjugation schemes show improvement in logical fidelity over twirling while the weights of the conjugation gates we need to apply are lower than the average weight of the twirling gates. We devise a way to search for the optimal Pauli conjugation scheme and apply it to Steane code, 9-qubit Shor code and distance-3 surface code under global coherent \(Z\) noise. Using the optimal Pauli conjugation, we can achieve a higher logical fidelity than using twirling and doing nothing. In this Article, we show that some of the coherence of the noise channel can actually be used to improve its logical fidelity by simply sandwiching the noise with a chosen pair of Pauli gates, which we call Pauli conjugation. One solution is to use twirling to turn coherent noise into incoherent Pauli channels. ![]() ![]() Coherent noise can be much more damaging than incoherent (probabilistic) noise in the context of quantum error correction.
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