Back-end-aware Fault-tolerant Quantum Oracle Synthesis

Quantum oracle synthesis involves compiling arbitrary Boolean functions into quantum circuits using specific quantum gates supported by the target quantum computer. The Clifford+T gate library is particularly common in fault-tolerant quantum computing systems. Utilizing XOR-AND-inverter graphs (XAGs) as the logic representation for the target Boolean functions has received extensive attention due to the observed direct correlation between the number of AND nodes in an XAG and the T count and the helper qubit count of the quantum oracle optimally compiled from it. However, to be deployed onto fault-tolerant quantum hardware, quantum gates must be further re-expressed by logical quantum error correction (QEC) code operations, a process known as back-end compilation. This paper enhances the current XAG-based oracle synthesis techniques by establishing a link between the properties of XAGs and quality measures of back-end-compiled quantum oracles. This link unlocks more optimization opportunities - -experimental results demonstrate average reductions of 4.49% in T count, 7.00% in logical time steps, and 14.89% in helper qubit count, respectively, on benchmarks optimized by the proposed back-end-aware XAG optimization approaches.