Non-Clifford Gates are Required for Long-Term Memory

Jon Nelson, Joel Rajakumar, Michael J. Gullans (Oct 10 2025).

Abstract: 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.

Arxiv: https://arxiv.org/abs/2510.08451