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

TL;DR

This paper introduces a complex instruction set computing architecture for quantum computers that efficiently performs accurate $Z$ rotations using specialized magic states, reducing overall gate overhead compared to traditional RISC approaches.

Contribution

The authors develop a CISC architecture with an expanded instruction set including $Z(rac{ ext{pi}}{2^k})$ gates, utilizing shortened Reed-Muller codes for improved magic state distillation.

Findings

Significant reduction in gate count for $Z$ rotations.

Magic state distillation threshold remains above 0.85% for $k \\leq 6$.

Enhanced efficiency over RISC architectures for quantum $Z$ rotations.

Abstract

We present quantum protocols for executing arbitrarily accurate $\pi/2^k$ rotations of a qubit about its $Z$ axis. Reduced instruction set computing (\textsc{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 $T = Z(\pi/4)$ 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 \textsc{risc} architecture can be much greater. We develop a complex instruction set computing (\textsc{cisc}) architecture whose instruction set includes stabilizer operations and preparation of magic states from which $Z(\pi/2^k)$ gates can be teleported, for $2 \leq k \leq k_{\text{max}}$. 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 $2^{k+2}-1$, whose magic-state distillation threshold shrinks with $k$ but is greater than 0.85% for $k \leq 6$.