My science fair project was studying how entanglement functions in a quantum circuit exposed to external observers.
For more background information, I would recommend reading the post below!

In my science fair 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 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.

Those were my main findings from my science fair project this year. I hope I’m able to do something as interesting next year!