Abstract

The leading paradigm for performing computation on quantum memories can be paraphrased as distill-then-synthesize. One performs several rounds of distillation to create high-fidelity magic states that provide one good T-gate. Gate synthesis composes many T-gates to realise a desired circuit. The gate synthesis problem has been formulated in several guises, including synthesis of single qubit gates and a restricted class of multi-qubit gates. Rather than following the standard distill-then-synthesize, one can construct exotic magic states that circumvent some the overhead of gate synthesis. I will present a unified framework that realises one round of distillation and multi-qubit gate synthesis in a single step, and some related tools for optimisation of multi-qubit circuits. I will also present a compressed protocol for efficient realisation of single qubit gates.