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Fault-tolerant protocols enable large and precise quantum algorithms. Manysuch protocols rely on a feed-forward processing of data, enabled by a hybridof quantum and classical logic. Representing the control structure of suchprograms can be a challenge. Here we explore two such fault-tolerantsubroutines and analyze the performance of the subroutines using QuantumIntermediate Representation (QIR) as their underlying intermediaterepresentation. First, we look at QIR's ability to leverage the LLVM compilertoolchain to unroll the quantum iteration logic required to perform magic statedistillation on the $[[5,1,3]]$ quantum error-correcting code as originallyintroduced by Bravyi and Kitaev [Phys. Rev. A 71, 022316 (2005)]. This allowsus to not only realize the first implementation of a real-time magic statedistillation protocol on quantum hardware, but also demonstrate QIR's abilityto optimize complex program structures without degrading machine performance.Next, we investigate a different fault-tolerant protocol that was firstintroduced by Paetznick and Svore [arXiv:1311.1074 (2013)], that reduces theamount of non-Clifford gates needed for a particular algorithm. We look at fourdifferent implementations of this two-stage repeat-until-success algorithm toanalyze the performance changes as the results of programming choices. We findthe QIR offers a viable representation for a compiled high-level program thatperforms nearly as well as a hand-optimized version written directly in quantumassembly. Both of these results demonstrate QIR's ability to accurately andefficiently expand the complexity of fault-tolerant protocols that can berealized today on quantum hardware.

Advances in compilation for quantum hardware -- A demonstration of magic state distillation and repeat-until-success protocols