Alexei Kitaev
Alexei Yurievich Kitaev is a Russian-American theoretical physicist.
He is currently a professor of theoretical physics and mathematics at the California Institute of Technology.
Kitaev has received multiple awards recognizing his contributions to quantum information science and condensed matter physics, particularly in quantum computation and topological phases of matter.
Life
Kitaev was educated in Russia, graduating from the Moscow [Institute of Physics and Technology] in 1986, and with a Ph.D. from the Landau Institute for Theoretical Physics under the supervision of Valery Pokrovsky in 1989.Kitaev worked as a research associate at the Landau Institute between 1989 and 1998. Between 1999 and 2001, he served as a researcher at Microsoft Research. Since 2002, Kitaev has been a professor at Caltech.
In 2021, Kitaev was elected into the National Academy of Sciences.
Research
Quantum computing and complexity
Kitaev has made contributions to quantum algorithms, quantum complexity classes, and fault-tolerant quantum computation. He introduced the complexity class QMA (Quantum Merlin–Arthur) and proved that the k-local Hamiltonian problem is QMA-complete, linking ground-state energy problems for local Hamiltonians to questions in computational complexity.He introduced the quantum phase estimation algorithm, a general procedure for estimating eigenphases of unitary operators, and independently proved what is now known as the Solovay–Kitaev theorem, which shows that a universal finite gate set can efficiently approximate arbitrary quantum operations on qubits.
He proposed using topological phases of matter and anyons for fault-tolerant quantum computation, introducing the toric code as a paradigmatic error-correcting code. He also contributed to threshold theorems for fault-tolerant codes and co-developed protocols such as the Gottesman–Kitaev–Preskill code and Bravyi–Kitaev magic-state distillation.
Topological phases and lattice models
Kitaev introduced exactly solvable lattice Hamiltonians that realize topologically ordered phases and anyonic excitations in two spatial dimensions. His toric code and related quantum-double models provide toy models realizing anyons and long-range entanglement. His Kitaev honeycomb model is an exactly solvable spin-1/2 model that can realize non-abelian anyons; this model has become a common starting point for the study of "Kitaev quantum spin liquids" in candidate materials.He has also contributed to the classification of topological phases. He related two-dimensional lattice models of topological order to algebraic data describing the anyon types and their braiding, together with a bulk invariant specifying the chiral central charge. His "periodic table for topological insulators and superconductors" uses K-theory and Bott periodicity to classify gapped free-fermion phases in different symmetry classes and spatial dimensions, and in two dimensions he proposed the "16-fold way" classification of certain topological superconductors. The so-called state introduced by Kitaev appears as a basic nontrivial 2+1-dimensional invertible phase, and his ideas have been used in generalized-cohomology classifications of symmetry-protected topological phases with symmetry group G.
Kitaev has also contributed to the study of quantum chaos and holography through his work on the Sachdev–Ye–Kitaev (SYK) model.