Large Sample Superradiance and Fault-Tolerant Quantum Computation

Understand

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.