Modeling and Assessment of Qubits on Silicon – MAQSi

The modeling of qubits uses a wide range of analytical and numerical techniques. To this end, the consortium is developing a multi-physics simulation code, TB_Sim, which is able to model these qubits down to the atomic scale if needed. This code integrates various approaches for the electronic structure of qubits (effective mass and its multi-band «kp« generalizations, atomistic methods such as tight-binding) and accounts for the complexity of their environment (structural strains, phonons, electrostatics, etc. .). It also integrates time-dependent solvers for the dynamics of the qubits. TB_Sim was developed to make the most of high-performance computing infrastructures in order to be able to model systems as complex as possible.

The project focused during the first 18 months on the manipulation and readout of spin qubits. We highlight below a few results, obtained for some of them in collaboration with the experimental teams:

Manipulation of holes: We have de-embedded and modeled the different microscopic mechanisms at play during the manipulation of hole spin qubits on «silicon-on-insulator«. Modeling shows that silicon is an excellent host material for hole spin qubits when the quantum dots are oriented to take best advantage of the very high anisotropy of its valence band [B. Venitucci & Y.-M. Niquet, Phys. Rev. B 99, 115317 (2019); V. Michal, B. Venitucci & Y.-M. Niquet, accepted at Phys. Rev. B (arXiv: 2010.07787)].

Spins readout: We show that reflectometry allows not only to probe low spin states (singlet, triplet), but also high spin states (quintets, septets), and, in general, to make an extensive spectroscopy of the spin qubit states [T. Lundberg et al., Phys. Rev. X 10, 041010 (2020); R. Ezzouch et al., To be submitted].

The project is now adressing the modeling and characterization of multi-qubit gates.

1. Simple model for electrical hole spin manipulation in semiconductor quantum dots: Impact of dot material and orientation, B. Venitucci & Y.-M. Niquet, Phys. Rev. B 99, 115317 (2019).
2. Hole-phonon interactions in quantum dots: Effects of phonon confinement and encapsulation materials on spin-orbit qubits, B. Venitucci, J. Li & Y.-M. Niquet, Phys. Rev. B 102, 075415 (2020).
3. Spin quintet in a silicon double quantum dot: Spin Blockade and Relaxation, T. Lundberg et al., Phys. Rev. X 10, 041010 (2020).
4. Charge detection in an array of CMOS quantum dots, E. Chanrion et al., Phys. Rev. Applied 14, 024066 (2020).
5. Spin readout of a CMOS quantum dot by gate reflectometry and spin-dependent tunnelling, V. Ciriano-Tejel et al., submitted to Phys. Rev. X Quantum [arXiv: 2005.07764].
6. Longitudinal and transverse electric field manipulation of hole spin-orbit qubits in one-dimensional channels, V. Michal, B. Venitucci & Y.-M. Niquet, accepted for publication in Phys. Rev. B. [arXiv: 2010.07787].
7. Reflectometry of charge transitions in a silicon quadruple dot, H. Bohuslavskyi et al., submitted to Phys. Rev. Applied [arXiv: 2012.04791].

Quantum information technologies could lead to breakthroughs in computing/simulation and cryptography. France develops an original platform for quantum information, based on the "Silicon on Insulator" (SOI) technology. Yet many aspects of the physics of silicon quantum bits (qubits) remain poorly understood, which complicates the interpretation of the experiments and the optimization of the devices. The goal of the MAQSi project is to address modeling and simulation of silicon qubits in order to i) make significant progress in the understanding of the physics of these qubits, ii) sort the existing options, and make recommendations for the design of SOI qubits, iii) demonstrate ahead of the experimental work the relevance of SOI technologies for quantum information, and identify their strengths and weaknesses, in order to promote this platform. This project gathers two theoretical groups that have unique capabilities in France on the simulation of quantum silicon devices (INAC/MEM, CNRS/IEMN), with the experimental group that is leader in quantum CMOS measurements and coordinates European projects on the fabrication and measurements of SOI qubits (INAC/PHELIQS).

We will set-up tools for the microscopic and atomic scale simulation of silicon qubits and address the following challenges in MAQSi:
- Spin manipulation and readout: We intend to achieve fast, all electrical manipulation of electron and hole qubits relying as far as possible on the intrinsic spin-orbit coupling, For that purpose, we need to make progress in the understanding of spin-orbit coupling in silicon, and to optimize the design of the qubits.
- Decoherence and variability: We will characterize the disorders that limit the reproducibility (variability) and coherence of silicon qubits.
- Two qubit gates: We will investigate exchange coupling between qubits and assess the performances of two (or more) qubit gates.

The ambition of MAQSi is to solve these issues through a tight collaboration between experimental and modeling teams, These challenges can not, indeed, be efficiently addressed from an experimental only perspective due to the costs and time scales of device fabrication and characterization. As the quantum information technologies on silicon are developing very fast, it is extremely important to complement the experimental activity with state-of-the-art modeling able to give insights into the operation of silicon qubits and bring forward new ideas.