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

TL;DR

This paper proposes a hierarchical surface code architecture for network quantum computing, enabling fault-tolerant operation with noisy inter-module links and small module sizes, optimizing resource efficiency.

Contribution

It introduces a hierarchical surface code that allows scalable quantum computing with modules of arbitrary size, improving fault tolerance and resource efficiency in network architectures.

Findings

Inter-module link noise threshold exceeds 10% without purification.

Small modules (~8 qubits) are competitive with larger modules in total qubit count.

Hierarchical coding reduces resource requirements for scalable quantum computing.

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.