Quasi-lattice of qubits and its mesoscopic features

Jacob M. Taylor, Mikhail D. Lukin

Hou Ian

Unlike atoms in a lattice, the spacings between neighboring qubits in a superconducting quantum circuit are mesoscopic and non-uniform. The strength of interaction between this quasi-lattice chain of qubits and a resonator mode in circuit transmission lines is inhomogeneous and geometrically dependent on the circuit layout. We propose a projection-deformation method to give analytically the eigenstates of the quasi-particle excitation that arise in the quasi-lattice. We further show that, during the quasi-particle excitation, the distribution of multi-photon resonances between the resonator photon and the quasi-lattice is determined by the degree the quasi-lattice is deformed from a normal lattice. The multi-photon resonances lead to simultaneous generation of GHZ-type and W-type of multipartite entanglement states of the qubits, which is enhanced by the inhomogeneous interaction. Comparing the concurrence and the 3-tangle generated, we find that the totally non-separable GHZ entanglement is specifically increased, up to two orders of magnitude.

Gianluigi Catelani

Hou Ian

The mesoscopic scale of superconducting qubits makes their inter-spacings comparable to the scale of wavelength of a circuit cavity field to which they commonly couple. This comparability results in inhomogeneous coupling strengthes for each qubit and hence asynchronous Rabi excitation cycles among the qubits that form a quasi-lattice. We find that such inhomogeneous coupling benefits the formation of multi-photon resonances between the single-mode cavity field and the quasi-lattice. The multi-photon resonances lead, in turn, to the simultaneous generation of inequivalent GHZ and W types of multipartite entanglement states, which are not transformable to each other through local operations with classical communications. Applying the model on the 3-qubit quasi-lattice and using the entanglement measures of both concurrence and 3-tangle, we verify that the inhomogeneous coupling specifically promotes the generation of the totally inseparable GHZ state.

Anonymous

Gang Liu

This paper lays out the philosophical foundation of mesoscopic information theory. Taking S4 modal logic and the M₃ diamond modular lattice as its mathematical skeleton, this work puts forward four modal‑probability bridging axioms which form a minimally‑sufficient axiom set: the modal necessity axiom, the modal‑probability consistency axiom, the modal‑probability regularity axiom, and the distributive‑law breaking axiom. This constraint system realizes a controlled transition from the Boolean base of S4 to the non‑Boolean M₃ lattice, embedding modal operators and probability measures within one unified formal framework. Global completeness is not pursued; only internal self‑consistency and traceable reasoning are required. This axiomatic apparatus yields a unified philosophical account of mesoscopic‑level features including modal tension, quasi‑quantum‑like behaviors and informational phase transitions. Empirical adequacy and real‑world case studies are reserved for future versions.