[1][2] He is, as of Spring 2024, a visiting scientist and program organizer at the Simons Institute for the Theory of Computing at the University of California, Berkeley.
He is known for his work (together with Anurag Anshu and Chinmay Nirkhe) on proving the NLTS conjecture, a famous open problem in quantum information theory.
In 2023, he was awarded the James Clerk Maxwell Medal and Prize by the Institute of Physics for his "outstanding contributions to the quantum error correction field, particularly work on proving the no low-energy trivial state conjecture, a famous open problem in quantum information theory".
The conjecture was proven by Breuckmann and colleagues (Anurag Anshu and Chinmay Nirkhe) by showing that the recently discovered families of constant-rate and linear-distance low-density parity-check (LDPC) quantum codes correspond to NLTS local Hamiltonians.
[citation needed] He and his former doctoral student Oscar Higgott are inventors of a U.S. patent titled “Subsystem codes with high thresholds by gauge fixing and reduced qubit overhead”, which concerns a technique to significantly improve the performance of quantum error correction in quantum computers.