Hierarchical surface code for network quantum computing with modules of arbitrary size

Ying Li,Simon C Benjamin

doi:10.1103/physreva.94.042303

Abstract

The network paradigm for quantum computing involves interconnecting many modules to form a scalable machine. Typically it is assumed that the links between modules are prone to noise while operations within modules have significantly higher fidelity. To optimise fault tolerance in such architectures we introduce a hierarchical generalisation of the surface code: a small `patch' of the code exists within each module, and constitutes a single effective qubit of the logic-level surface code. Errors primarily occur in a two-dimensional subspace, i.e. patch perimeters extruded over time, and the resulting noise threshold for inter-module links can exceed ~ 10% even in the absence of purification. Increasing the number of qubits within each module decreases the number of qubits necessary for encoding a logical qubit. But this advantage is relatively modest, and broadly speaking a `fine grained' network of small modules containing only ~ 8 qubits is competitive in total qubit count versus a `course' network with modules containing many hundreds of qubits.

Highlights

There are two approaches to fabricating a large-scale universal quantum computer
It is interesting to ask what impact the module size has on performance characteristics such as the fault tolerance threshold and, the total number of physical qubits needed per logical qubit
We have introduced a variant of the surface code approach to fault-tolerant quantum information processing

Summary

INTRODUCTION

There are two approaches to fabricating a large-scale universal quantum computer. One is to create a single “monolithic” architecture in which each qubit is directly and deterministically connected to its neighbors. An alternative is the network architecture [1,2,3,4,5,6,7,8], where a single quantum computer is formed from numerous interlinked small devices, modules, each having only a modest number of qubits and correspondingly little computational power This approach may prove to be well suited to ion trap systems [8,9,10,11] or color centers in diamond [12], where optical activity can be directly harnessed to create a photonic link; modules comprised of superconducting qubits can be networked either via microwave links [13] or by exploiting microwave-to-optical converters.

OUTLINE OF APPROACH

SYSTEM

MODULAR SURFACE CODE AND THRESHOLDS

QUBIT COSTS

Findings

CONCLUSIONS