Theoretical Constructions of Exchange-Only Entangling and Leakage Control Gates

It was first shown 22 years ago that composite sequences of exchange pulses generated by computational searching and algorithmic optimization methods allow universal control over qubits encoded in decoherence-free subsystems (DFS) [1].  It was shown 11 years ago, again via computational search, that such control may be done more efficiently and without spin-polarization [2].  In the past decade, increased theoretical understanding of these control strategies have allowed analytic understanding and minimum-resource-theorems for these sequences [3].  This understanding has also yielded tools to derive new sequences which mitigate the spread of leakage out of the DFS, with utility in facilitating quantum error correction.  Experiments in arrays of 6 Si/SiGe dots are starting to prove these constructions practical and performant [4,5].   This talk will provide theoretical constructions for exchange-gate-synthesis useful for both analytic and computational derivation of new control pathways.  I will provide logical understanding of some previous computer-generated sequences [2,6].  Finally, I will provide examples of new leakage-mitigation strategies, with brief indication of their experimental implementation and performance expectations in silicon.

[1] DiVincenzo et al., Nature 408, 339 (2000)

[2] Fong and Wandzura, Quantum. Inf. Comp. 11, 1003 (2011)

[3] Zeuch and Bonesteel, Phys. Rev. A 93, 010303 (2016)

[4] Andrews et al., Nature Nanotechnol. 14, 747 (2019)

[5] Ha et al., arXiv:2107.10916

[6] Langrock and DiVincenzo, arXiv:2012.09517