Leveraging Different Boolean Function Decompositions to Reduce T-Count in LUT-Based Quantum Circuit Synthesis

Lookup Table (LUT) based synthesis methods have recently been proposed as a way to synthesize quantum Boolean circuits in a qubit-constrained environment. Other recent research papers have demonstrated the possibility of using relative phase quantum circuits when compute/uncompute logic is used in tandem, reducing T-count in quantum Boolean circuits in the fault-tolerant quantum computing paradigm. Because LUT-based synthesis methods use compute/uncompute pairs on ancilla qubits, this suggests that implementing the arbitrary Boolean logic that make up the individual Boolean logic network nodes in a relative phase manner could reduce the T-count. To generate such arbitrary Boolean functions, we utilize Shannon’s decomposition, Davio expansions, as well as alternating balanced and unbalanced relative phase circuits. Experimental results demonstrate that our method can reduce the T-count to an average of 24% of the existing method.