Cluster preformation law for heavy and superheavy nuclei

Universal quantum computation using fractal symmetry-protected cluster phases

“…However, MBQC is only universal in 2 or higher dimensions, as one spatial dimension must play the role of time in the quantum circuit. In 2D, regions of computational usefulness have been shown numerically to coincide with the phase diagram of nontrival SPT phases 21,22,29 , and proven to persist within small perturbations about the cluster state fixed point of the square lattice cluster model 38 . Recently, this same cluster model was proven to possess universal computational power everywhere within a cluster phase, protected by rigid linelike symmetries 39 .…”

Computationally Universal Phase of Quantum Matter

“…Numerical evidence exists for deformed Affleck-Kennedy-Lieb-Tasaki Hamiltonians on the honeycomb lattice [7,8,13]. In addition, extended regions of constant computational power have also been observed in SPT phases with Z 2 -symmetry [14].…”

Quantum spin models for measurement-based quantum computation

“…In Ref. [35], it was shown that by deforming these wavefunctions away from fixed points there is a finte region such that quantum computational universality persists [35]. Moreover, its disappearance in one direction seems coincide with the phase transition to a Z 2 symmetry-breaking phase.…”

“…But the ability for the entire SPT phases for arbitrary qubit or qudit gates is only established recently by Miller and Miyake [29] and Stephen et al [30,31]. However, the status in 2D has not been explored much, with only some results on fixed-point wave functions [32][33][34], and certain result slightly beyond fixed points [35]. Future development may strengthen the notion of computational phases in SPT and other phases of matter.…”