Large Sample Superradiance and Fault-Tolerant Quantum Computation

Abstract

We quantitatively analyze superradiance (collective emission) in a three-dimensional array of qubits without imposing any restrictions on the size of the sample. We show that even when the spacing between the qubits become arbitrarily large, superradiance produces an error rate on each qubit that scales with the total number of qubits. This is because the sum of the norms of the effective Hamiltonians that decoheres each qubit scales with the total number of qubits and is, therefore, unbounded. In three spatial dimensions, the sum of the norms scales as $N^{2/3}$ where $N$ is the total number of qubits in the computer. Because the sum of the Hamiltonian norms are unbounded, the introduced errors are outside the applicability of the threshold theorem.