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Modeling hole qubits to better unravel their secrets



We recently analyzed experiments on hole qubits using numerical simulations that describe in detail these quantum devices. Our work paves the way for the optimization of hole devices and for a detailed understanding of the effects of spin-orbit coupling in silicon

Published on 26 September 2019

Qubits are devices in which information is stored as a quantum superposition of two states "0' and "1'. The possibility of superimposing different configurations opens up many perspectives for information processing. These "0" and "1" states can be the "up" and  "down" spin states of an electron placed in a magnetic field. CEA-Grenoble manufactures such spin qubits by trapping electrons under the gates of silicon-on-insulator transistors. It is also possible to store information in the spin of a hole left after removing an electron from silicon. The physics of these holes is very original, rich and complex. Numerical simulation improve our understanding of their behavior and show their potential.

In silicon qubits, the spin is manipulated by modulating the magnetic field in which the device is immersed. However, it remains difficult to control such modulations at the single qubit scale. This is why it may be advantageous to make qubits by using 'holes' rather than electrons. These are indeed subjected to a strong "spin-orbit coupling", i.e. the spin of a hole is intimately linked to its movement in space. It thus becomes possible to act on the spin of a hole by giving it an oscillatory motion thanks to a radio-frequency electric field directly created by the gate of the transistor (and much easier to control than a radio-frequency magnetic field).
However, the physics of holes is much richer and more complex than that of electrons. We recently analyzed experiments on hole qubits [1, 2] using numerical simulations that describe in detail these quantum devices down to the atomic scale if necessary. These simulations allowed us to access many quantities that are not experimentally measurable and therefore complete the "portrait" they were able to establish of these qubits. In particular, these simulations have allowed us to better understand the mechanisms of spin manipulation at the nanoscale [3. We then were able to establish a "minimal" analytical model that incorporates the essential mechanisms highlighted by the simulation [4]. Our analytical model describes the conditions to be met to optimize hole control and demonstrates that silicon is an ideal material for hole qubits despite its low spin-orbit coupling, due to its very anisotropic electronic properties (the dynamics of holes being very strongly dependent on the direction of their movement in the crystal).
This work paves the way for the optimization of hole devices and for a detailed understanding of the effects of spin-orbit coupling in silicon.


Modeling of four qubits along a silicon wire (red), each controlled by a gate (transparent grey). The iso-surfaces of electron density under each of these gates, which indicate where the holes are located, are shown in yellow. 

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