Universal physics of quantum matter at the change of the hierarchy and the state

Ian Richard C Buckley

We survey the Origami Instruction Set Architecture (), a universal opcode language whose seven primitives---FLIP, FLOP, SPLIT, SPLAT, TWIST, LABEL, ORBIT---together with an eighth, BIND, describe every physical process at every scale from quantum gravity to metabolism. The algebraic closure of these opcodes is the Fano incidence structure = PGL(3,\GF_2), and their computational complexity hierarchy stratifies into three tiers: H^0 (tropical/classical), H^1 (Clifford/stabiliser), and H^2 (magic/topological). This hierarchy is a physical observable: the H^k tier of a process determines whether it can be simulated classically (H^0), efficiently by stabiliser circuits (H^1), or requires genuine quantum resources (H^2). We survey applications across nuclear and particle physics, quantum field theory, condensed matter, quantum chemistry, biology, mathematics, and economics, citing over forty companion papers in which each domain is developed in detail. We state nine open problems including the uniqueness conjecture and the completeness question beyond qutrits.

Karl Ferdinand Herzfeld

Xiaolei Zhang

It is shown that a coherent understanding of all quantized phenomena, including those governed by unitary evolution equations as well as those related to irreversible quantum measurements, can be achieved in a scenario of successive nonequilibrium phase transitions, with the lowest hierarchy of these phase transitions occurring in a ``resonant cavity'' formed by the entire matter and energy content of the universe. In this formalism, the physical laws themselves are resonantly-selected and ordered in the universe cavity in a hierarchical manner, and the values of fundamental constants are determined through a Generalized Mach's Principle. The existence of a preferred reference frame in this scenario is shown to be consistent with the relational nature of the origin of physical laws. Covariant unitary evolution is shown to connect smoothly with the reduction of wavefunction in the preferred frame during quantum measurement. The superluminal nature of quantum processes in the lowest hierarchy coexists with the universal speed limit obeyed by processes in higher hierarchies. A natural quantum-to-classical transition is also obtained which is stable against the diffusive tendency of the unitary quantum evolution processes. In this formalism a realistic quasi-classical ontology is established for the foundations of quantum mechanics.

Gerardo Ortíz

Gerardo Ortiz Department of Physics, Indiana University, Bloomington, Indiana 47405, U.S.A. Quantum matter often displays complex phase diagrams as a result of competing interactions, with orderings (states of matter) which are believed to be influenced by being in proximity to quantum critical points, e.g., high-Tc materials, heavy fermion compounds, and frustrated magnets. Each quantum phase is characterized by different behaviors of appropriate correlation functions, such as long-range order, or algebraic or exponential decay. Since entanglement is a property inherent in quantum states and is strongly related to quantum correlations, one would expect that the entanglement present in the ground state (GS) of the system changes substantially at a quantum phase transition (QPT), i.e., when there is a qualitative change in the behavior of the correlations between constituents. Obviously, the identification and quantification of those changes become issues of utmost relevance.

Alan V. Durrant