In 2022, he became Lecturer (Assistant Professor)[5] in Quantum Computing Theory at the University of Bristol.
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".[6][7]Quanta Magazine described the proof as "one of the biggest developments in theoretical computer science".[8][9][10] This result built on his introduction with Jens Eberhardt of “Balanced Product Quantum Codes”.[11][12]
The NLTS conjecture posits that there exist families of Hamiltonians with all low-energy states of non-trivial complexity. It was formulated in 2013 by Fields MedallistMichael Freedman and Matthew Hastings at Microsoft Research. 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.[13][14] This result is a step towards proving the quantum PCP conjecture, considered the most important open problem in quantum complexity theory. [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.[15] Their related work was included as a major development for computer science in 2023 by Quanta.[16][17][18]