Non-Clifford Gates are Required for Long-Term Memory
Authors
Jon Nelson
Joel Rajakumar
Michael J. Gullans
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.
