Unitary Evolutions From Interacting Quantum Memories: Closed Quantum Systems Directing Themselves Using Their State Histories

Abstract

We propose, formulate and anlyze novel closed quantum systems whose unitary time evolutions, and internal interactions, emerge out of their linking quantum memories. In a closed system of the kind, the unitary evolution operator is updated, moment by moment, using the quantum state history as a compositional resource. The 'Quantum Memory Made' Hamiltonians (QMM-Hs) generating these unitary evolutions are Hermitian operators made of arbitrarily-chosen past-until-present density operators of the closed system, or its arbitrary subsystems. The time evolution is described by novel nonlocal and nonlinear von Neumann and Schrödinger equations. We establish that nontrivial Purely-QMM unitary evolutions are 'Robustly Non-Markovian', in the sense that the largest temporal distance between the compositional quantum memories admit finite lower bounds set by their interaction couplings. After general formulation and considerations, we take on the sufficiently-complex task of classifying the phases of one-qubit pure-state evolutions generated by specific choices of QMM-Hs, combining analytical methods with extensive numerical simulations, and using QMM two-point functions as natural signature probes. Analyzing Hamiltonians which are purely QMM, and those combined with the conventional Hamiltonians, we obtain and characterize specific families of analytical solutions, and then classify generic numerical solutions. We establish that QMM phase diagrams are outstandingly rich, containing wide classes of novel unitary evolutions with physically remarkable behaviours. Moreover, we show that QMM interactions give rise to novel purely internal dynamical phase transitions. We suggest several independent fundamental and applied domains and disciplines where QMM-UEs can be utilized advantageously.