Complex instruction set computing architecture for performing accurate quantum Z rotations with less magic

We present quantum protocols for executing arbitrarily accurate π/2ᵏ rotations of a qubit about its Z axis. Reduced instruction set computing ({risc}) architectures typically restrict the instruction set to stabilizer operations and a single non-stabilizer operation, such as preparation of a "magic" state from which $T = Z(π/4)$ gates can be teleported. Although the overhead required to distill high-fidelity copies of this magic state is high, the subsequent quantum compiling overhead to realize Z rotations in a {risc} architecture can be much greater. We develop a complex instruction set computing ({cisc}) architecture whose instruction set includes stabilizer operations and preparation of magic states from which Z(π/2ᵏ) gates can be teleported, for 2 ≤ k ≤ kₘₐₓ. This results in a substantial overall reduction in the number of gates required to achieve a desired gate accuracy for Z rotations. The key to our construction is a family of shortened quantum Reed-Muller codes of length 2ᵏ⁺²-1, whose magic-state distillation threshold shrinks with k but is greater than 0.85% for k ≤ 6.