Quantum error correction in crossbar architectures

TL;DR

This paper introduces a language for mapping quantum circuits to crossbar architectures, enabling implementation of quantum error correction codes with minimal overhead and demonstrating feasible logical error suppression in large-scale quantum systems.

Contribution

It develops a mapping language tailored for crossbar quantum architectures and shows how to implement quantum error correction codes within their control constraints.

Findings

Quantum error correction codes can be mapped with small overhead in crossbar systems.

Logical error suppression is feasible with estimated experimental parameters.

The approach enables scalable quantum computing in architectures with limited control.

Abstract

A central challenge for the scaling of quantum computing systems is the need to control all qubits in the system without a large overhead. A solution for this problem in classical computing comes in the form of so called crossbar architectures. Recently we made a proposal for a large scale quantum processor~[Li et al. arXiv:1711.03807 (2017)] to be implemented in silicon quantum dots. This system features a crossbar control architecture which limits parallel single qubit control, but allows the scheme to overcome control scaling issues that form a major hurdle to large scale quantum computing systems. In this work, we develop a language that makes it possible to easily map quantum circuits to crossbar systems, taking into account their architecture and control limitations. Using this language we show how to map well known quantum error correction codes such as the planar surface and color codes in this limited control setting with only a small overhead in time. We analyze the logical error behavior of this surface code mapping for estimated experimental parameters of the crossbar system and conclude that logical error suppression to a level useful for real quantum computation is feasible.