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QI: Fachverband Quanteninformation

QI 36: Poster – Quantum Information (joint session QI/Q)

QI 36.42: Poster

Donnerstag, 13. März 2025, 17:00–19:00, Tent

Householder reflections in the Hilbert space of ions trapped in Paul trap — •Vasil Vasilev and Nikolay Vitanov — Department of Physics, Sofia University, James Bourchier 5 boulevard, 1164 Sofia, Bulgaria

This work investigates the ways of generating Householder reflections in the Hilbert space of ions trapped in Paul trap. The Householder reflection is a powerful approach for matrix manipulation in classical data analysis. Here we explore its use in quantum information processing for the creation of arbitrary unitary matrices. In previous publications, an arbitrary Householder transformation is produced either by using different couplings in an N-pod system, for which, however, the Hilbert space is non-scalable [1], or in a scalable Hilbert space but for equal couplings [2,3]. Here we discuss the more general situation of constructing Householder reflections with different couplings in a scalable Hilbert space. The ultimate objective is to construct C^n-phase gates which can be used as native implementations of Householder reflections and hence for efficient decomposition of unitary matrices. The proposed concept can also be used for physical synthesis of arbitrary random matrices. We explore their Haar measures and present a comparison with the Givens rotations method.

[1] Peter A. Ivanov and Nikolay V. Vitanov Phys. Rev. A 77, 012335

[2] Peter A. Ivanov, Nikolay V. Vitanov and Martin B. Plenio Phys. Rev. A 78, 012323

[3] S. S. Ivanov, P. A. Ivanov, I. E. Linington, and N. V. Vitanov Phys. Rev. A 81, 042328

Keywords: Householder; ions in Paul trap; C^n-phase gates; random matrices