Quantum Error Correction with Misty States

In 2017 Terry Rudolph introduced an elementary rewriting system that can be used to accurately describe the basics of quantum circuits and quantum computation to HS and middle school students. Both the accessibility and the effectiveness of this system are remarkable: the Deutsch-Josza and Grover search algorithms, Bernstein-Vazirani and the phase kickback phenomenon, superdense coding, quantum teleportation, entanglement swapping and the GHZ game are topics we’ve been able to describe in terms accessible to HS and middle school students using this formalism. Over the last two years, with help from CSTA Indiana we’ve established a Faculty Learning Community (FLC) in QIS for HS and middle school teachers currently comprised of more than 25 teachers in 5 states (IN, GA, CA, HI and TN) with prospective members in other states. The rewriting system introduced by Terry Rudolph (that relies on a representation of quantum states as “misty states”) greatly simplifies calculations and makes them accessible to first-time learners using only simple  arithmetic and without sacrificing accuracy. Furthermore it can be effectively used to facilitate the transition to the conventional mathematical apparatus. We first show concrete examples of computational effectiveness via a new category of misty states that are in some sense irreducible yet are able to drastically simplify calculation overall. We then show how to address topics of quantum error correction (i.e., the bit flip, sign flip and Shor codes) using misty states.