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IF Colloquium No.11 – Free-Fermion Subsystem Codes
July 22, 2022 @ 10:00 am - 11:00 am
IF invites you to the No.11 IF Colloquium (Online Seminar Series)——————————————————————————-

Title: ” Free-Fermion Subsystem Codes “
Speaker : Adrian Chapman, Ph.D., Postdoctoral Researcher, Department of Materials, University of Oxford, United Kingdom (UK)

Abstract :Error correction is a fundamental challenge to building a scalable and fault-tolerant quantum computer. As such, this goal motivates the exciting search for novel quantum materials that are promising as quantum error-correcting codes. In general, such materials tend to either be difficult to realize experimentally — requiring high-weight measurements — or their behavior is computationally difficult to simulate classically.
I will discuss a class of error-correcting codes on qubit many-body systems that are exactly solvable by a mapping to free fermions. These “free-fermion subsystem codes” are promising candidates for experimental realization and have many properties that can be efficiently extracted classically due to their exact solvability. Furthermore, they have a deep connection to graph theory, and this relationship informs the search for codes with favorable spectra for error suppression. To illustrate this, I will introduce the checkerboard-lattice code. This code has an exact mapping to a two-dimensional free-fermion system on a torus and encodes exact topological qubits. Inspired by this example, I will detail our numerical search for favorable free-fermion subsystem codes and describe valuable graph-theoretic heuristics, which we expect to motivate further work on the design of such codes for near-term applications.

Keywords : Free-Fermions, Quantum Error Correction, Graph Theory