The decomposition of an arbitrary 2  × 2  unitary matrix into signed permutation matrices

Vos, Alexis De; Baerdemacker, Stijn De

doi:10.1016/j.laa.2020.07.017

Search citation statements

Order By: Relevance

Paper Sections

Select...

C) Straightforward Decomposition Method1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To decompose A in the corresponding Pauli operator basis P n the idea is to compute each coefficient separately, similarly to [6].…”

Section: C) Straightforward Decomposition Methodmentioning

confidence: 99%

A Tree-Approach Pauli Decomposition Algorithm with Application to Quantum Computing

Koska,

Baboulin,

Gazda

2024

ISC High Performance 2024 Research Paper Proceedings (39th International Conference)

View full text Add to dashboard Cite

The Pauli matrices are 2-by-2 matrices that are very useful in quantum computing. They can be used as elementary gates in quantum circuits but also to decompose any matrix of C 2 n ×2 n as a linear combination of tensor products of the Pauli matrices. However, the computational cost of this decomposition is potentially very expensive since it can be exponential in n. In this paper, we propose an algorithm with a parallel implementation that optimizes this decomposition using a tree approach to avoid redundancy in the computation while using a limited memory footprint. We also explain how some particular matrix structures can be exploited to reduce the number of operations. We provide numerical experiments to evaluate the sequential and parallel performance of our decomposition algorithm and we illustrate how this algorithm can be applied to encode matrices in a quantum memory.

show abstract

“…To decompose A in the corresponding Pauli operator basis P n the idea is to compute each coefficient separately, similarly to [6].…”

Section: C) Straightforward Decomposition Methodmentioning

confidence: 99%

A Tree-Approach Pauli Decomposition Algorithm with Application to Quantum Computing

Koska,

Baboulin,

Gazda

2024

ISC High Performance 2024 Research Paper Proceedings (39th International Conference)

View full text Add to dashboard Cite

show abstract

The decomposition of an arbitrary 2  × 2 unitary matrix into signed permutation matrices

Cited by 1 publication

References 12 publications

A Tree-Approach Pauli Decomposition Algorithm with Application to Quantum Computing

A Tree-Approach Pauli Decomposition Algorithm with Application to Quantum Computing

Contact Info

Product

Resources

About

The decomposition of an arbitrary 2 × 2 unitary matrix into signed permutation matrices

Cited by 1 publication

References 12 publications

A Tree-Approach Pauli Decomposition Algorithm with Application to Quantum Computing

A Tree-Approach Pauli Decomposition Algorithm with Application to Quantum Computing

Contact Info

Product

Resources

About

The decomposition of an arbitrary 2  × 2 unitary matrix into signed permutation matrices