Consani, G;
Warburton, PA;
(2020)
Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation.
New Journal of Physics
, 22
, Article 053040. 10.1088/1367-2630/ab83d1.
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Abstract
An open question in designing superconducting quantum circuits is how best to reduce the full circuit Hamiltonian which describes their dynamics to an effective two-level qubit Hamiltonian which is appropriate for manipulation of quantum information. Despite advances in numerical methods to simulate the spectral properties of multi-element superconducting circuits (Yurke B and Denker J S 1984 Phys. Rev. A 29 1419, Reiter F and Sørensen A S 2012 Phys. Rev. A 85 032111 and Amin M H et al 2012 Phys. Rev. A 86 052314), the literature lacks a consistent and effective method of determining the effective qubit Hamiltonian. Here we address this problem by introducing a novel local basis reduction method. This method does not require any ad hoc assumption on the structure of the Hamiltonian such as its linear response to applied fields. We numerically benchmark the local basis reduction method against other Hamiltonian reduction methods in the literature and report specific examples of superconducting qubits, including the capacitively-shunted flux qubit, where the standard reduction approaches fail. By combining the local basis reduction method with the Schrieffer–Wolff transformation we further extend its applicability to systems of interacting qubits and use it to extract both non-stoquastic two-qubit Hamiltonians and three-local interaction terms in three-qubit Hamiltonians.
Type: | Article |
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Title: | Effective Hamiltonians for interacting superconducting qubits: local basis reduction and the Schrieffer–Wolff transformation |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1088/1367-2630/ab83d1 |
Publisher version: | https://doi.org/10.1088/1367-2630/ab83d1 |
Language: | English |
Additional information: | Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence (https://creativecommons.org/licenses/by/4.0). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > London Centre for Nanotechnology |
URI: | https://discovery.ucl.ac.uk/id/eprint/10099052 |
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