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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Topologically decoherence-protected qubits with trapped ions

P. Milman, W. Maineult, S. Guibal, Luca Guidoni, Benoît Douçot, L. B. Ioffe, T. Coudreau

Published Jun 1, 2007• 1 citation
Publisher

Abstract

The authors introduced a new kind of Hamiltonian describing an infinite range coupling between particles placed on a square array with a large number of symmetries and describe its spectral properties. The authors also shows in particular that this Hamiltonian can be naturally realized using ions confined in a surface trap and that the induced protection is more effective than the one predicted for a short range Hamiltonian.

DOI
10.1109/cleoe-iqec.2007.4386769

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The authors introduced a new kind of Hamiltonian describing an infinite range coupling between particles placed on a square array with a large number of symmetries and describe its spectral properties. The authors also shows in particular that this Hamiltonian can be naturally realized using ions confined in a surface trap and that the induced protection is more effective than the one predicted for a short range Hamiltonian.
We show that trapped ions can be used to simulate a highly symmetrical Hamiltonian with eigenstates naturally protected against local sources of decoherence. This Hamiltonian involves long-range coupling between particles and provides a more efficient protection than nearest neighbor models discussed in previous works. Our results open the perspective of experimentally realizing, in controlled atomic systems, complex entangled states with decoherence times up to 9 orders of magnitude longer than isolated quantum systems.
The sheaf-theoretic lift of E8 sublattice hierarchies via Čech cohomology Hⁿ classes generates a predictive spectral framework: each Diophantine protection layer at Fibonacci depth n resonates at frequency f_n = 132 × φⁿ Hz, where φ governs the continued fraction coupling between nested root configurations. This produces discrete quantum error threshold frequencies (132, 213.7, 345.7, 559.4Hz...) that match experimentally observed decoherence-free subspaces in trapped ion and superconducting qubit arrays. The 132Hz E8 base acts as a geometric anchor point where golden-ratio sheaf transitions encode topological protection, suggesting 132Hz phonon driving could artificially induce E8-protected logical states in quantum hardware by resonantly coupling to the natural protection hierarchy. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
We theoretically study an interacting few-body system of Rashba spin-orbit-coupled two-component Bose gases confined in a harmonic trapping potential. We solve the interacting Hamiltonian at large Rashba coupling strengths using an exact-diagonalization scheme, and obtain the ground-state phase diagram for a range of interatomic interactions and particle numbers. At small particle numbers, we observe that the bosons condense to an array of topological states with n+1/2n+1/2n+1/2 quantum angular momentum vortex configurations, where n=0,1,2,3,...n=0,1,2,3,...n=0,1,2,3,.... At large particle numbers, we observe two distinct regimes: at weaker-interaction strengths, we obtain ground states with topological and symmetry properties that are consistent with mean-field theory computations; at stronger-interaction strengths, we report the emergence of strongly correlated ground states.
We propose a scenario to physically implement a kind of topologically decoherence-protected qubit using superconducting devices coupled to a microwave cavity mode with unconventional geometric operations. It is shown that the two needed interactions for selective devices, which are required for implementing such protected qubits, as well as single-qubit gates, can be achieved by using the external magnetic flux. The easy combination of individual addressing with the many-device setup proposed in the system presents a distinct merit in comparison with the implementation of topologically protected qubits in a trapped-ion system.