Scientists / Open questions

Alexei Y. Kitaev

Quantum computing; topological quantum matter

12 questions

Kitaev's open problems for a general theory of anyons and topological order: local degrees of freedom, 'materialized' (emergent) gauge symmetry, and rigorous fault tolerance for universal anyonic computation
Practical-scale exponential error suppression in superconducting surface-code quantum error correction: reaching suppression factors of order $\Lambda\approx10$ and mitigating rare device-wide high-energy error events
Topological entanglement entropy: rigorous control of finite-size corrections, the entanglement-Hamiltonian (CFT) derivation, microscopic realizations of non-Abelian anyon theories, and higher-dimensional extensions
Scaling and full characterization of the fully frustrated Josephson-junction ladder superinductor
Energy splitting between the $\mathbb{I}$ and $\psi$ fusion channels of quasiholes confined on an antidot in the $\nu=5/2$ fractional quantum Hall state, and reproducibility of the fusion channel upon antidot charging
Universality class and local topology of the topological multicritical point of the Z2 gauge-Higgs model and the toric code in a parallel magnetic field
Physical realization of the measurement-based primitives for universal Majorana (fermionic) quantum computation: nondestructive multi-Majorana parity measurements, ancilla and encoded-state preparation, and their fault-tolerance error models and overheads
Classification and bulk characterization of two-dimensional fermionic topological orders beyond Kitaev's free-fermion 16-fold way
Correlated-error floors and practical below-threshold scaling of superconducting surface-code logical qubits
Interaction-robust classification of gapped fermionic phases beyond one dimension (the higher-dimensional Fidkowski–Kitaev program)
Security of multiparty quantum protocols under general superselection rules beyond compact symmetry groups
Fault-tolerance thresholds for long-range correlated non-Markovian Hamiltonian noise: realistic fault-path phases, spatial layout, tailored gadgets, and the marginal decay regime $z\le D$

Back to open problems

Kitaev's open problems for a general theory of anyons and topological order: local degrees of freedom, 'materialized' (emergent) gauge symmetry, and rigorous fault tolerance for universal anyonic computation

Practical-scale exponential error suppression in superconducting surface-code quantum error correction: reaching suppression factors of order Λ≈10\Lambda\approx10Λ≈10 and mitigating rare device-wide high-energy error events

Topological entanglement entropy: rigorous control of finite-size corrections, the entanglement-Hamiltonian (CFT) derivation, microscopic realizations of non-Abelian anyon theories, and higher-dimensional extensions

Scaling and full characterization of the fully frustrated Josephson-junction ladder superinductor

Energy splitting between the I\mathbb{I}I and ψ\psiψ fusion channels of quasiholes confined on an antidot in the ν=5/2\nu=5/2ν=5/2 fractional quantum Hall state, and reproducibility of the fusion channel upon antidot charging

Universality class and local topology of the topological multicritical point of the Z2 gauge-Higgs model and the toric code in a parallel magnetic field

Physical realization of the measurement-based primitives for universal Majorana (fermionic) quantum computation: nondestructive multi-Majorana parity measurements, ancilla and encoded-state preparation, and their fault-tolerance error models and overheads

Classification and bulk characterization of two-dimensional fermionic topological orders beyond Kitaev's free-fermion 16-fold way

Correlated-error floors and practical below-threshold scaling of superconducting surface-code logical qubits

Interaction-robust classification of gapped fermionic phases beyond one dimension (the higher-dimensional Fidkowski–Kitaev program)

Security of multiparty quantum protocols under general superselection rules beyond compact symmetry groups

Fault-tolerance thresholds for long-range correlated non-Markovian Hamiltonian noise: realistic fault-path phases, spatial layout, tailored gadgets, and the marginal decay regime z≤Dz\le Dz≤D

Practical-scale exponential error suppression in superconducting surface-code quantum error correction: reaching suppression factors of order $\Lambda\approx10$ and mitigating rare device-wide high-energy error events

Energy splitting between the $\mathbb{I}$ and $\psi$ fusion channels of quasiholes confined on an antidot in the $\nu=5/2$ fractional quantum Hall state, and reproducibility of the fusion channel upon antidot charging

Fault-tolerance thresholds for long-range correlated non-Markovian Hamiltonian noise: realistic fault-path phases, spatial layout, tailored gadgets, and the marginal decay regime $z\le D$