Reducing hardware requirements for fault-tolerant distributed quantum computers

Abstract

Distributed quantum computers hold great promise in the realization of scalable and fault-tolerant quantum computers. They contain multiple nodes with small quantum devices that can generate inter-node entanglement. Next to realizing distributed architectures on a single chip, these systems can be extended to large-scale quantum networks. Connecting the nodes based on the topology of a quantum error-correction code forms an intuitive path toward fault tolerance.

Performing error-detection measurements in distributed error-correction codes requires the generation and consumption of entangled states. We focus on systems that are capable of generating remote two-qubit entanglement between pairs of connected nodes—i.e., Bell pairs. Entangled states of higher weight—the so-called Greenberger-Horne-Zeilinger (GHZ) states—can be generated by fusing Bell pairs. On top of this, the quality of the generated entangled states can be increased with entanglement distillation. We implement dynamic programming to generate high-quality GHZ states by fusing and distilling Bell pairs.

The dynamic program allows us to optimize the quality of error-detection measurements for a specific distributed error-correction code: the (toric) surface code. We numerically evaluate the performance of this code with noise models based on experimental characterization of diamond color center hardware, including the typical behavior of memory decoherence in these devices. This leads to the identification of a threshold in the ratio between entanglement generation and the decoherence rates.

For a two-dimensional error-correction code like the surface code, performing error-detection over multiple time steps can be reinterpreted as measuring the qubits of a three-dimensional cluster state. This equivalence enables considering more general three-dimensional cluster states as fault-tolerant channels that transform the logical qubits of the underlying error-correction code. We use this idea to investigate distributed logical memory channels for general types of circuit-level and entanglement noise.

Our results show that efficient generation of high-quality entanglement and strategic design of error-correction channels are important aspects for developing noise-resilient distributed quantum computers.