We show that all Clifford circuits under interspersed depolarizing noise lose memory of their input exponentially quickly, even when given access to a constant supply of fresh qubits in arbitrary states. This is somewhat surprising given the result of Aharonov et al. [STOC1997] which gives a fault-tolerant protocol for general quantum circuits using a supply of fresh qubits. Our result shows that such a protocol is impossible using only Clifford gates demonstrating that non-Clifford gates are fundamentally required to store information for long periods of time.
@article{arxiv.2510.08451,
title = {Non-Clifford Gates are Required for Long-Term Memory},
author = {Jon Nelson and Joel Rajakumar and Michael J. Gullans},
journal= {arXiv preprint arXiv:2510.08451},
year = {2025}
}