Alexei Kitaev

One example is Kitaev's introduction of the complexity classes QMA and QIP,[5] and his proof that the 2-local Hamiltonian problem is QMA-complete.

Kitaev also introduced the formalism for quantum computing using local fermionic modes, which he developed with his graduate student Sergey Bravyi.

[10] Kitaev has notably introduced many toy models in the fields of solid-state physics and quantum mechanics.

[17] It is believed that all invertible topological phases in two dimensions are obtained by stacking copies of the E8 state.

[29] This model has served as a paradigmatic prototype for studying anyonic spin chains.

[34] Another classification result is conjectural description of (2+1)-dimensional bosonic topological order in terms of pairs

[17] Another classification result is Kitaev's 16-fold way, which gives a periodic description of the anyons in the Kitaev spin liquids based on their Chern numbers modulo 16, which can be rephrased in terms of a classification result for minimal fermionic topological phases.

[17] This has led to wide-ranging applications of category theory to describing topological order.

Kitaev also proposed to use of module categories to describe gapped boundaries and domain walls of topological quantum systems.

In a similar spirit, Kitaev and collaborators also studied entanglement in spin chains described by conformal field theory and demonstrated that their entanglement has universal features governed by the central charge of the relevant conformal field theory.

Along with his collaborators, Kitaev demonstrated the a full protocol for quantum memory in which error detection and correction are both implemented in a fault-tolerant fashion.

[41][42][43][44][45] One issue with the surface code is that it can only naturally implement Clifford gates fault-tolerantly.

To resolve this issue, Kitaev and Sergei Bravyi introduced magic state distillation as a method for obtaining a universal gate set.

[46] Another insight of Kitaev's was the Gottesman-Kitaev-Preskill code, discovered jointly with Daniel Gottesman and John Preskill,[47][48] which serves as a basis for a model of fault-tolerant continuous-variable quantum computing.

[39] In February–March 2022, he signed an open letter by Breakthrough Prize laureates condemning the 2022 Russian invasion of Ukraine.