Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Koch, Mark, Yeung, Richie, Wang, Quanlong
Natura: Preprint
Pubblicazione: 2023
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866912597278720000
author Koch, Mark
Yeung, Richie
Wang, Quanlong
author_facet Koch, Mark
Yeung, Richie
Wang, Quanlong
contents Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX diagrams involving the triangle operation. We show that this technique greatly speeds up the simulation of quantum circuits involving multi-controlled gates which can be naturally represented using triangles. We implement our approach in the QuiZX library and demonstrate a significant simulation speed-up (up to multiple orders of magnitude) for random circuits and a variation of previously used benchmarking circuits. Furthermore, we use our software to contract diagrams representing the gradient variance of parametrised quantum circuits, which yields a tool for the automatic numerical detection of the barren plateau phenomenon in ansätze used for quantum machine learning. Compared to traditional statistical approaches, our method yields exact values for gradient variances and only requires contracting a single diagram. The performance of this tool is competitive with tensor network approaches, as demonstrated with benchmarks against the quimb library.
format Preprint
id arxiv_https___arxiv_org_abs_2307_01803
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions
Koch, Mark
Yeung, Richie
Wang, Quanlong
Quantum Physics
Recent advances in classical simulation of Clifford+T circuits make use of the ZX calculus to iteratively decompose and simplify magic states into stabiliser terms. We improve on this method by studying stabiliser decompositions of ZX diagrams involving the triangle operation. We show that this technique greatly speeds up the simulation of quantum circuits involving multi-controlled gates which can be naturally represented using triangles. We implement our approach in the QuiZX library and demonstrate a significant simulation speed-up (up to multiple orders of magnitude) for random circuits and a variation of previously used benchmarking circuits. Furthermore, we use our software to contract diagrams representing the gradient variance of parametrised quantum circuits, which yields a tool for the automatic numerical detection of the barren plateau phenomenon in ansätze used for quantum machine learning. Compared to traditional statistical approaches, our method yields exact values for gradient variances and only requires contracting a single diagram. The performance of this tool is competitive with tensor network approaches, as demonstrated with benchmarks against the quimb library.
title Speedy Contraction of ZX Diagrams with Triangles via Stabiliser Decompositions
topic Quantum Physics
url https://arxiv.org/abs/2307.01803