Universität zu Köln

Li, Boxi ORCID: 0000-0002-2733-7186, Calarco, Tommaso and Motzoi, Felix (2022). Nonperturbative Analytical Diagonalization of Hamiltonians with Application to Circuit QED. PRX Quantum, 3 (3). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2691-3399

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Abstract

Deriving effective Hamiltonian models plays an essential role in quantum theory, with particular emphasis in recent years on control and engineering problems. In this work, we present two symbolic methods for computing effective Hamiltonian models: the nonperturbative analytical diagonalization (NPAD) and the recursive Schrieffer-Wolff transformation (RSWT). NPAD makes use of the Jacobi iteration and works without the assumptions of perturbation theory while retaining convergence, allowing us to treat a very wide range of models. In the perturbation regime, it reduces to RSWT, which takes advantage of an in-built recursive structure where, remarkably, the number of terms increases only linearly with the perturbation order, exponentially decreasing the number of terms compared to the ubiquitous Schrieffer-Wolff method. In this regime, NPAD further gives an exponential reduction in terms, i.e., superexponential compared to the Schrieffer-Wolff transformation, relevant to high-precision expansions. Both methods consist of algebraic expressions and can be easily automated for symbolic computation. To demonstrate the application of the methods, we study the ZZ and cross-resonance interactions of superconducting qubit systems. We investigate both suppressing and engineering the coupling in near-resonant and quasidispersive regimes. With the proposed methods, the coupling strength in the effective Hamiltonians can be estimated with high precision comparable to numerical results.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Li, Boxi UNSPECIFIED orcid.org/0000-0002-2733-7186 UNSPECIFIED Calarco, Tommaso UNSPECIFIED UNSPECIFIED UNSPECIFIED Motzoi, Felix UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-670839
DOI:	10.1103/PRXQuantum.3.030313
Journal or Publication Title:	PRX Quantum
Volume:	3
Number:	3
Date:	2022
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2691-3399
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Quantum Science & Technology; Physics, Applied; Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/67083