Hi everybody! Sorry for the late post, I have been super busy with AP exams and finals :’). I’m finally back, though!

This post is about my experience with Science Fair this year. I was fortunate enough to be nominated to participate in the International Science and engineering fair in Phoenix, Arizona! It was super fun getting to meet loads of new people from all around the world 🙂

Here is some information about my project, if you are interested!
My science fair project focused on how entanglement functions in a quantum circuit exposed to external observers. In my project, I simulated the creation of a quantum circuit in Python via the Qiskit package. I implemented sites at which entanglement was created (gates) and destroyed (measurements). I ran 50 trials for a specific measurement rate (10%, 50%, 90%, etc.) at different system sizes (2, 4, 6, 8, 10 qubits) and plotted the entanglement in the system as a function of the time step.

From this, I found that the entanglement saturated at a value of n/2 * ln(2) for a system with n qubits. After this, I plotted the variance of the entanglement as a function of the measurement rate.

I also found that the variance peaked at a measurement rate of around 0.2. Variance is the fluctuation of entanglement; because the fluctuation was maximized at a measurement rate of 0.2, then this means that a phase transition occurred (specifically from a volume-law obeying system to an area-law obeying system). A volume-law obeying system is a qubit system in which the entanglement scales with system size linearly. Meanwhile, in an area-law obeying system, the entanglement increases at a much smaller scale, saturating at a lower entanglement value.

That’s the gist of my project! I hope you found it interesting 🙂