John Kubiatowicz

This work compares the overhead of quantum error correction with concatenated and topological quantum error-correcting codes. To perform a numerical analysis, we use the Quantum Resource Estimator Toolbox (QuRE) that we recently developed. We use QuRE to estimate the number of qubits, quantum gates, and amount of time needed to factor a 1024-bit number on several candidate quantum technologies that differ in their clock speed and reliability. We make several interesting observations. First, topological quantum error correction requires fewer resources when physical gate error rates are high, white concatenated codes have smaller overhead for physical gate error rates below approximately 10E-7. Consequently, we show that different error-correcting codes should be chosen for two of the studied physical quantum technologies - ion traps and superconducting qubits. Second, we observe that the composition of the elementary gate types occurring in a typical logical circuit, a fault-tolerant circuit protected by the surface code, and a fault-tolerant circuit protected by a concatenated code all differ. This also suggests that choosing the most appropriate error correction technique depends on the ability of the future technology to perform specific gates efficiently.

We analyze circuits for a number of kernels from popular quantum computing applications, characterizing the hardware resources necessary to take ancilla preparation off the critical path. The result is a chip entirely dominated by ancilla generation circuits. To address this issue, we introduce optimized ancilla factories and analyze their structure and physical layout for ion trap technology. We introduce a new quantum computing architecture with highly concentrated data-only regions surrounded by shared ancilla factories. The results are a reduced dependence on costly teleportation, more efficient distribution of generated ancillae and more than five times speedup over previous proposals.