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Knill demonstrated a fault-tolerant quantum computation scheme based onconcatenated error-detecting codes and postselection with a simulated errorthreshold of 3% over the depolarizing channel. %We design a two-dimensionalarchitecture for fault-tolerant quantum computation based on Knill'spostselection scheme. We show how to use Knill's postselection scheme in apractical two-dimensional quantum architecture that we designed with the goalto optimize the error correction properties, while satisfying importantarchitectural constraints. In our 2D architecture, one logical qubit isembedded in a tile consisting of $5\times 5$ physical qubits. The movement ofthese qubits is modeled as noisy SWAP gates and the only physical operationsthat are allowed are local one- and two-qubit gates. We evaluate the practicalproperties of our design, such as its error threshold, and compare it to theconcatenated Bacon-Shor code and the concatenated Steane code. Assuming thatall gates have the same error rates, we obtain a threshold of $3.06\times10^{-4}$ in a local adversarial stochastic noise model, which is the highestknown error threshold for concatenated codes in 2D. We also present a MonteCarlo simulation of the 2D architecture with depolarizing noise and wecalculate a pseudo-threshold of about 0.1%. With memory error rates one-tenthof the worst gate error rates, the threshold for the adversarial noise model,and the pseudo-threshold over depolarizing noise, are $4.06\times 10^{-4}$ and0.2%, respectively. In a hypothetical technology where memory error rates arenegligible, these thresholds can be further increased by shrinking the tilesinto a $4\times 4$ layout.

Performance and Error Analysis of Knill's Postselection Scheme in a Two-Dimensional Architecture