Quantum Dots In Python

Ongoing development of a semiconductor quantum dot simulator.

The Quantum Dots in Python (QuDiPy) simulator is a collaborative and ongoing project that aims at simulating specific aspects of electrostatically defined quantum dots fabricated in semiconducting materials. Specifically, devices which are able to be fabricated with commercial semiconductor processes for Complementary Metal–Oxide–Semiconductor (CMOS) style quantum dot devices. The primary developers/maintainers are myself and my colleague Bohdan Krohmets. The current progress can be review on the QuDiPy webpage.

An example of such devices is a laterally defined electrostatic double quantum dot device. A two-dimensional electron gas (2DEG) can be formed at cryogenic temperatures at a hetero junction interfaces of Si and an insulator (such as SiO_2). This 2DEG can be depleted into a regime where only a few electrons are occupied in desired regions in the device. Such regions are referred to as quantum dots (QDs) and have the ability to host electron spin qubits.

(Left) Simple 3D representation of a double QD and associated electrostatic potential landscape (Middle) 2D cross section displaying how a 2DEG is formed using a combination of plunger, barrier, and screening electrodes (Right) 2D cross section displaying the potential lanscaped formed for a given voltage configuration in a double QD device.

The QuDiPy simulator leverages electrostatic potentials simulated using a finite element Poisson solver for a desired device geometry and various voltage configurations to simulate specific physics in a QD (or N-dimensional array of QDs), such as, Hubbard Hamiltonian parameters, one/two qubit gates, and electron/state shuttling.

Graphical representation showing how QuDiPy is able to simulate specific electron spin qubits using electrostatic potentials from a finute element Poisson solver.

The simulator has the ability to simulate voltage control pulses from various control methodologies for both one and two qubits.

An example single qubit Hadamard gate applied to a three qubit QD device using a control method developed by B. Krohmets.
An example two qubit SWAP gate applied to a three qubit QD device using a control method developed by B. Krohmets; performing a chain of SWAPs.
Allowed votlage ranges for voltage control pulses are deterimend from charge stability regions simulated with QuDiPy; developed by Z. Merino.

One of the aims of the simulator is to simulate voltage control pulses for a node network architecture which has the potential to implement a fault tolerant surface code for quantum computing applications.

Animationg showing how a surface code can be formed with a network of QD devices; defined as nodes.

An aspect of performing a fault tolerant surface requires the formation of a maximally entangle Bell/GHZ state.

Example of a quantum ciruit to prepare a three qubit GHZ state.

This GHZ state can be formed in a three QD system by applying the following necessary voltage pulses which cause effective parameters (such as g-factor deviation and exchange energy) to have the desired time dependence.

Voltage control pulses and resultant effective parameter evolution which generates and three qubit GHZ state in a QD device.