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

Alireza Tavanfar1,2, Aliasghar Parvizi3,4, and Marco Pezzutto5

1Champalimaud Research, Champalimaud Center for the Unknown, 1400-038 Lisboa, Portugal
2Institute of Neuroscience, University of Oregon, Eugene, OR 97403, USA
3Department of Physics, University of Tehran, 14395-547, Tehran, Iran
4School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5531 Tehran, Iran
5Complex Systems and Statistical Mechanics, Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg

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We propose, formulate and examine novel quantum systems and behavioral phases in which momentary choices of the system's memories interact in order to source the internal interactions and unitary time evolutions of the system. In a closed system of the kind, the unitary evolution operator is updated, moment by moment, by being remade out of the system's `experience', that is, its quantum state history. The `Quantum Memory Made' Hamiltonians (QMM-Hs) which generate these unitary evolutions are Hermitian nonlocal-in-time operators composed of arbitrarily-chosen past-until-present density operators of the closed system or its arbitrary subsystems. The time evolutions of the kind are described by novel nonlocal nonlinear von Neumann and Schrödinger equations. We establish that nontrivial Purely-QMM unitary evolutions are `Robustly Non-Markovian', meaning that the maximum temporal distances between the chosen quantum memories must exceed finite lower bounds which are set by the interaction couplings. After general formulation and considerations, we focus on the sufficiently-involved task of obtaining and classifying behavioral phases of one-qubit pure-state evolutions generated by first-to-third order polynomial QMM-Hs made out of one, two and three quantum memories. The behavioral attractors resulted from QMM-Hs are characterized and classified using QMM two-point-function observables as the natural probes, upon combining analytical methods with extensive numerical analyses. The QMM phase diagrams are shown to be outstandingly rich, having diverse classes of unprecedented unitary evolutions with physically remarkable behaviors. Moreover, we show that QMM interactions cause novel purely-internal dynamical phase transitions. Finally, we suggest independent fundamental and applied domains where the proposed `Experience Centric' Unitary Evolutions can be applied natuarlly and advantageously.

Consider a closed quantum system, S, and all possible subsystems that it contains. For a window of the history stretched from an initial moment up until now, the inclusive 'Experience' of this closed system is definable naturally as an indexed archive consisting of all the states that S itself has developed unitarily, together with all the states (which are accordingly) formed by all those subsystems. The central idea of the present paper is the conjectured natural possibility of novel quantum behaviors in which it is this accumulating experience itself which plays a key role in sourcing, and updating moment by moment, the internal interactions and the Hamiltonian of S.

In other words, the defining theme of the work is suggesting, formulating and investigating deep structural and behavioral interactions between Non-Markovianity, namely dependencies on the state history, and the fundamental principle of Unitarity. We present a general formulation of the aforementioned synergy which is followed by extensive analytical and numerical analyses of the structures and the consistent solutions of the resulted novel nonlocal-in-time nonlinear Schrödinger and von Neumann equations in general contexts and in the simplest models. As clearly manifested by these explorations, the behavioral effects of the proposed interactions between experience centricity and evolution unitarity are indeed enormous: the merge leads to a wide spectrum of unprecedented distinctive classes of quantum behaviors which are remarkable qualitatively.

Concluding the work as a first step towards the complete disclosure of the proposed 'Experience-Centric Quantum Theory', namely the theory of (emergent or fundamental) Experience-Centric Unitary Evolutions, we envision and indicate how it can be naturally applied in various independent domains such as (especially `Wheelerian' frameworks of) quantum gravity, and quantum general intelligence.

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