6533b7cefe1ef96bd12572e3
RESEARCH PRODUCT
Quantum computing thanks to Bianchi groups
Michel Planatsubject
Discrete mathematics[SPI.ACOU]Engineering Sciences [physics]/Acoustics [physics.class-ph]010308 nuclear & particles physicsPhysicsQC1-999010103 numerical & computational mathematics01 natural sciencesRing of integers[SPI.MAT]Engineering Sciences [physics]/MaterialsModular group0103 physical sciencesPauli groupQuadratic field0101 mathematics[SPI.NANO]Engineering Sciences [physics]/Micro and nanotechnologies/MicroelectronicsQuantumEigenvalues and eigenvectorsTrefoil knotQuantum computerMathematicsdescription
It has been shown that the concept of a magic state (in universal quantum computing: uqc) and that of a minimal informationally complete positive operator valued measure: MIC-POVMs (in quantum measurements) are in good agreement when such a magic state is selected in the set of non-stabilizer eigenstates of permutation gates with the Pauli group acting on it [1]. Further work observed that most found low-dimensional MICs may be built from subgroups of the modular group PS L(2, Z) [2] and that this can be understood from the picture of the trefoil knot and related 3-manifolds [3]. Here one concentrates on Bianchi groups PS L(2, O10) (with O10 the integer ring over the imaginary quadratic field) whose torsion-free subgroups define the appropriate knots and links leading to MICs and the related uqc. One finds a chain of Bianchi congruence n-cusped links playing a significant role [4].
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-09-05 |