Methodology for quantum logic gate constructions

TL;DR

This paper presents a general framework for fault-tolerant quantum gate construction using a simple primitive called one-bit teleportation, extending the Gottesman–Chuang teleportation approach. By restricting to CSS codes and leveraging the $C_k$ gate hierarchy, it reduces the encoded gate problem to fault-tolerant preparation of specific ancilla states and transversal $C_2$ operations, enabling systematic construction of gates in $C_3$ such as the $T$ ($\pi/8$) gate, the controlled-phase gate, and the Toffoli gate. The authors demonstrate explicit circuits and fault-tolerant ancilla states for these gates and show how one-bit teleportation can be extended to remote gate construction, including two-bit teleportation and remote CNOT. The framework offers a unified, scalable path to universal fault-tolerant quantum computation and highlights potential architectures built from modular teleportation primitives and pre-prepared standard states.

Abstract

We present a general method to construct fault-tolerant quantum logic gates with a simple primitive, which is an analog of quantum teleportation. The technique extends previous results based on traditional quantum teleportation (Gottesman and Chuang, Nature {\bf 402}, 390, 1999) and leads to straightforward and systematic construction of many fault-tolerant encoded operations, including the $π/8$ and Toffoli gates. The technique can also be applied to the construction of remote quantum operations that cannot be directly performed.