To reset, or not to reset -- that is the question

Abstract: Whether to reset qubits, or not, during quantum error correction experiments is a question of both foundational and practical importance for quantum computing. Text-book quantum error correction demands that qubits are reset after measurement. However, fast qubit reset has proven challenging to execute at high fidelity. Consequently, many cutting-edge quantum error correction experiments are opting for the no-reset approach, where physical reset is not performed. It has recently been postulated that no-reset is functionally equivalent to reset procedures, as well as being faster and easier. For memory experiments, we confirm numerically that resetting provides no benefit. On the other hand, we identify a remarkable difference during logical operations. We find that unconditionally resetting qubits can reduce the duration of fault-tolerant logical operation by up to a factor of two as the number of measurement errors that can be tolerated is doubled. We support this with numerical simulations. However, our simulations also reveal that the no-reset performance is superior if the reset duration and infidelity exceed given thresholds. For example, with the noise model we considered, we find the no-reset performance to be superior when the reset duration is greater than approximately $100$ ns and the physical error probability is greater than approximately $10^{-2.5} \approx 0.003$. Lastly, we introduce two novel syndrome extraction circuits that can reduce the time overhead of no-reset approaches. Our findings provide guidance on how experimentalists should design future experiments.