LocConQubit, a module for the construction of controlled pulses on isolated qubit systems using the Local Control Theory


The LocConQubit module implements the Local Control Theory[1,2], an algorithm for on-the-fly construction of a time-dependent potential that drives the evolution of a Hamiltonian towards one of its eigenstates. The algorithm is applicable to any Hamiltonian that is separable into a time-dependent and into a time-independent part, where the first part is directly incorporated into the algorithm, while the latter defines the basis of system states from which a designated target state is selected. States with vanishing interaction elements cannot be treated with the aforementioned algorithm. The algorithm is fine-tuned by the user with a single parameter in order to assure physical range of the generated time-dependent potential. This free parameter can be time-dependent while certain constrains in pulse generation can be directly incorporated into the algorithm. The module is accompanied with subroutines for pulse frequency analysis, post-processing, fidelity calculation and visualization of pulses and system evolution. The module is written in Python 3 programming language and is an addition to the open source QuTiP software package. The module uses the OpenMP functionalities available in QuTiP to parallelize the calculation of the pulse fidelity in order to search more efficiently for an optimal control pulse.

Additional module documentation, which includes background information on the Local Control Theory, information about software installation and testing and a link to the source code, can be found in our E-CAM software Library here

Practical application and exploitation of the code

The practical application of this software module is the pilot project with IBM on “Quantum Computing” sustained by an E-CAM postdoctoral researcher at École Polytechnique Fédérale de Lausanne (EPFL).

This module enables to construct more efficient control pulses for superconducting transmon qubits coupled to a single tunable coupler whose energy is controlled with an external electromagnetic pulse. By properly modulating the energy of the tunable coupler with an external control pulse, the coupler operates as a quantum logic gate between coupled qubits. To improve gate performance and thus overall performance of quantum computers, pulses are tailored to make gate operations faster while maintaining at the same time the highest possible fidelity. The Local Control Theory was applied to these systems to generate efficient state preparation pulses which transfer populations completely from one qubit state to the other, as well as pulses for the SWAP gates which completely exchange quantum states between two qubits. A set of pulses capable of transferring populations with a full fidelity to designated target states was generated and, by post-processing this set, an optimal set of pulses for experimental implementation was obtained. This set is currently being tested at IBM. In parallel, capabilities as well as limits of the Local Control theory to manipulate such systems have been investigated in detail. Results of this work are going to be published in two scientific papers. In addition, the current OpenMP parallelization will be upgraded with a more advance parallelization scheme that will enable more efficient utilization of \acs{HPC} resources and an easier implementation of parallelized optimization techniques.


[1] B. F. E. Curchod, T. J. Penfold, U. Rothlisberger and I. Tavernelli, Local control theory in trajectory-based nonadiabatic dynamics, Phys. Rev. A, vol. 84, p. 042507, 2011. [Online]. Available: https://link.aps.org/doi/10.1103/PhysRevA.84.042507

[2] V. Engel, C. Meier, and D. J. Tannor, Local Control Theory: Recent Applications to Energy and Particle Transfer Processes in Molecules, John Wiley Sons, Inc., 2009, pp. 29–101. [Online]. Available: http: //dx.doi.org/10.1002/9780470431917.ch2