How long can a quantum memory withstand depolarizing noise?

TL;DR

This paper explores the limits of passive Hamiltonian protection for quantum memories under depolarizing noise, showing that the lifetime can only grow logarithmically with the number of qubits, and provides an explicit Hamiltonian achieving this bound.

Contribution

It establishes a fundamental limit on passive Hamiltonian protection of quantum memories and constructs an explicit Hamiltonian that reaches this limit.

Findings

Lifetime increases at most logarithmically with qubit number

Explicit Hamiltonian constructed to saturate the protection bound

Protection exploits the noise itself for enhanced stability

Abstract

We investigate the possibilities and limitations of passive Hamiltonian protection of a quantum memory against depolarizing noise. Without protection, the lifetime of a single qubit is independent of N, the number of qubits composing the memory. In the presence of a protecting Hamiltonian, the lifetime increases at most logarithmically with N. We construct an explicit time-independent Hamiltonian which saturates this bound, exploiting the noise itself to achieve the protection.