Fault-Tolerant Postselected Quantum Computation: Schemes

TL;DR

The paper develops fault-tolerant postselected quantum computation schemes based on a four-qubit error-detecting code, purification, and teleportation to realize a universal, constant-depth gate set. By concatenating encoded, error-detecting blocks and purifying resource states such as $|\pi/8\rangle$ and $|i\pi/4\rangle$, it enables accurate, encoded operations and bottom-up decoding to produce arbitrary stabilizer states with bounded local errors; the encoded error rate is expected to scale as $O(e^2)$ with the base error rate $e$. While the approach yields a structured path to universal quantum computation under postselection, it remains inefficient in general and requires further quantitative analysis of error thresholds and resource overhead. The methods highlight a practical framework for preparing high-fidelity stabilizer and non-stabilizer states via Bell-state resources and teleportation, with potential implications for improving the robustness of non-postselected quantum computation through postselected primitives and purified state preparation.

Abstract

Postselected quantum computation is distinguished from regular quantum computation by accepting the output only if measurement outcomes satisfy predetermined conditions. The output must be accepted with nonzero probability. Methods for implementing postselected quantum computation with noisy gates are proposed. These methods are based on error-detecting codes. Conditionally on detecting no errors, it is expected that the encoded computation can be made to be arbitrarily accurate. Although the probability of success of the encoded computation decreases dramatically with accuracy, it is possible to apply the proposed methods to the problem of preparing arbitrary stabilizer states in large error-correcting codes with local residual errors. Together with teleported error-correction, this may improve the error tolerance of non-postselected quantum computation.