Coded Computing Meets Quantum Circuit Simulation: Coded Parallel Tensor Network Contraction Algorithm

TL;DR

This paper introduces the first coded computing schemes for parallel tensor network contraction, enhancing fault tolerance in quantum circuit simulation and tensor computations.

Contribution

It proposes two novel coding schemes inspired by matrix multiplication codes, improving resilience and generality in tensor network contraction algorithms.

Findings

2-node code achieves significant resilience gains

Hyperedge code extends applicability beyond quantum tensor networks

Resilience improves with node failures and tensor dimensions

Abstract

Parallel tensor network contraction algorithms have emerged as the pivotal benchmarks for assessing the classical limits of computation, exemplified by Google's demonstration of quantum supremacy through random circuit sampling. However, the massive parallelization of the algorithm makes it vulnerable to computer node failures. In this work, we apply coded computing to a practical parallel tensor network contraction algorithm. To the best of our knowledge, this is the first attempt to code tensor network contractions. Inspired by matrix multiplication codes, we provide two coding schemes: 2-node code for practicality in quantum simulation and hyperedge code for generality. Our 2-node code successfully achieves significant gain for $f$-resilient number compared to naive replication, proportional to both the number of node failures and the dimension product of sliced indices. Our hyperedge code can cover tensor networks out of the scope of quantum, with degraded gain in the exchange of its generality.