Helmholtz Coils: Modeling Qubit Interaction with PIDs

ISBN: 979-8-89480-841-3


The hardware to produce the magnetic fields was left over from previous development on the model. Thus, our primary concern in the making of a multi-Bloch sphere model was in the following objectives: Firstly, I wanted to produce a means by which multiple Bloch Spheres could be put into a single network and addressed individually based on instructions from a single controller. Secondly, I wanted a means by which readout, in the form of the vector produced by the physical system - the orientation of the internally suspended indicator - could be reported and processed automatically. Lastly, I wanted a method by which one system would seek to mimic the state of another by means of utilizing the readout mechanic of the other system. While not a perfectly accurate representation of a related, real world, concept in quantum error correction (QEC), in implementing this feature, I sought to verify the models ability to represent interactions between states - a feature required for the multi-sphere model to be of any use.

Many tools used to drive the previous iteration of the Bloch Sphere demo -although effective for their intended purpose- were not feasible to use with these new objectives, and as such every piece of control hardware and software had to be reimagined.

With our constraints outlined, I could begin the design process. The power supply units used to drive the coils of the Bloch Spheres, up until this point, had been driven using a USB hub connected to a laptop. Considering our first objective-to have multiple Bloch Spheres addressed independently by a single control unit-We deemed this not the best way to create an expandable system. As such, I replaced the 3 port USB hub with a network switch as it allowed for each coil to be addressed independently, and for coils to have a configurable IP address - allowing for convenient testing and coding convention. This was as opposed to a larger USB hub, as that would have led to a more difficult implementation than the local network I ended up creating with the ethernet switch. The power supplies available to us, namely the Keithley 2450 Sourcemeter, were addressable over ethernet via the VISA utility from National Instruments. Thus, I chose to write the control logic for the system in Python as the PY-VISA utility allowed us to write TSP commands to the power supplies, allowing us to control them remotely and automatically.

I extended existing tools for mechanically displaying quantum states to feature a network of multiple states that use automatic data collection and processing to interact in real time, thus vastly improving their utility. By utilizing Bluetooth enabled IMU sensors I was able to glean an interpretable readout from otherwise visual-only models. This readout data could then be recorded and fed to control logic to influence the states of other qubit models. The system was constructed and went through successful test runs. I discuss the developmental process as well as potential applications of this extended demonstration model.

References

  • Bloch, F. (1946). Nuclear Induction. Physical Review, 70(7-8), 460–474. Bloch sphere. (2009). Wikipedia. Retrieved October 20, 2024, from https://en.wikipedia.org/wiki/Bloch_sphere#/media/File:Bloch_sphere.svg.
  • Helmholtz, H. (1847). Über die Erhaltung der Kraft (On the Conservation of Force). Annalen der Physik und Chemie, 72, 27–55.
  • Minorsky, N. (1922). Directional Stability of Automatically Steered Bodies. Journal of the American Society of Naval Engineers, 34(2), 280–309