Designing control pulses for superconducting qubit systems with local control theory

Designing control pulses for superconducting qubit systems with local control theory

 

Organizations Involved:

CECAM Centre Européen de Calcul Atomique et Moléculaire (Host beneficiary), located at the in Lausanne, is an organization devoted to the promotion of fundamental research on advanced computational methods and to their application to important problems in frontier areas of science and technology.

IBM Research Laboratory – Zurich (Industrial partner) is the European branch of IBM research, which is the research and development division of the American multinational information technology company IBM.

Challenge:

The aim of this pilot project was to develop a new method and dedicated software for designing control pulses to manipulate qubit systems (see Fig.1A) based on the local control theory (LCT) The system is composed of two fixed frequency superconducting transmon qubits (Q1 and Q2) coupled to a tunable qubit (TQ) whose frequency is controlled by an external magnetic field. Changing the frequency, the TQ behaves as a targeted quantum logic gate, effectively enabling an operation on the qubit states. The system schematizes an approach to construct real quantum universal gates currently investigated by IBM.

 Solution:

Local control theory (LCT), the main theoretical tool used, originates from physical chemistry where it is used to steer chemical reactions towards predetermined products, but it had never been used to design a quantum gate. To create the software, researchers added new functionalities to the open source QuTip program package.  Two main modules were developed during the project: LocConQubit, which implements the LCT and accompanying procedures, and OpenQubit, a patch to the first module which introduces Lindblad master equation propagation scheme into the LCT which also enables direct construction of pulses under the presence of decoherence effects. All modules were written in Python and expand the functionalities of the QuTip program package.

 Business impact for the private company:

The developed software was transferred to IBM and will be of use to engineer pulses for the experimental construction of superconducting Qubits. A paper in collaboration with the industrial partner was recently published “Local control theory for superconducting qubits” (M. Mališ, P. Kl. Barkoutsos, M. Ganzhorn, S. Filipp, D. J. Egger, S. Bonella, and I. Tavernelli, Phys. Rev. A 99, 052316).

Benefits:

  • This project introduced a new procedure for generating control pulses on-the-fly in qubit systems, which is less computationally demanding and might thus open new approaches to pulse constructions
  • LCT pulse can also serve as initial guess pulses in optimal control theory
  • With LCT it was possible to design extremely short pulses with a duration of just a few tens of nanoseconds or less with an almost full fidelity (see Figure 1B).
  • The method is highly robust and requires only qubit parameters (frequencies, coupling terms) as inputs

Figure 1: A) Schematic representation of the qubit system; B) Pulses obtained by LCT (left), by a frequency filtering LCT procedure (middle), and by analytic function fitted to LCT pulse parameters (right) with their corresponding population transferring from qubit 2 (blue) to qubit 1 (orange), and frequency spectra.