A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced "eeh-ks") was introduced in [26] as a sort of quantum annealing and its underlying input-driven Hamiltonians are generated quantum-algorithmically by various forms of quantum automata families (including 1qqaf's). We study an efficient way to accomplish certain machine learning tasks by training these AEQSs quantumly. When AEQSs are controlled by 1qqaf's, it suffices in essence to find an optimal 1qqaf that approximately solves a target relational problem. For this purpose, we develop a basic idea of approximately utilizing well-known quantum algorithms for quantum counting, quantum amplitude estimation, and quantum approximation. We then provide a rough estimation of the efficiency of our quantum learning algorithms for AEQSs.
This paper studies the effects of interactivity on molecular computation, specifically in the Step Chemical Reaction Networks model (Step CRNs), by adding the ability for a user to interact with the system by selecting which species to add at each step, or by having some control over which reactions execute. The two proposed variants are Interactive CRNs and Randomized Interactive CRNs. We show that in Interactive CRNs, even when restricted to void (deletion-only) rules of relatively small size, if a user can decide which species to add at each step based on the configuration, reachability is PSPACE-complete when bounded and EXPTIME-hard when unbounded. In Randomized Interactive CRNs, we prove that reachability with void rules is PSPACE-complete.
We introduce a framework that connects two discrete models of natural computing, cellular automata (CA) and reaction systems (RS). We define pattern graphs of a CA as one-out digraphs where vertices correspond to totally periodic configurations and edges reflect CA evolution. Using pattern graphs based on periodic configurations we show that every one-dimensional binary CA can be transformed into an RS via its zero-context graph and provide counterexamples for the converse. Modified techniques, such as increasing the number of states and subgraphs of pattern graphs, are used to transform arbitrary RS into CA.
The extraction of features from speech is the most critical process in speech signal processing. Mel Frequency Cepstral Coefficients (MFCC) are the most widely used features in the majority of the speaker and speech recognition applications, as the filtering in this feature is similar to the filtering taking place in the human ear. But the current MFCC extraction is complex and requires time-frequency translations. Through our investigation, we were able to model a reservoir as a feature extractor capable of extracting the Mel Frequency Cepstral Coefficient (MFCC) without time-frequency domain translations. We have developed a real-time audio signal processing system by simplifying audio signal processing through the utilization of reservoir computers, which are significantly easier to train. We have established an experimental framework for end-to-end audio processing utilizing the reservoir and have investigated its capability to perform end-to-end audio signal processing.
This study demonstrates how to provide specific guarantees on the entropy produced by quantum circuits implementing Boolean functions. More specifically, we study guarantees on von Neumann entropy for subsystems in such circuits. Our findings indicate that input state initialization by rotating the target qubit around the X -axis of the Bloch sphere, combined with arbitrary but fixed individual qubit rotations of the control qubits around any axis or a combination of thereof, preserves the von Neumann entropy of reduced density matrices across subsystem traces. In contrast, similar rotations around the Y -axis cause entropy variation with rotation angle. Moreover, ceteris paribus, arbitrary qubit rotations on all qubits, including the target, result similarly in variability of subsystem entropy. We apply these findings to secure the classical communication channel in a novel multi-qubit quantum teleportation protocol. We depict a full IBM Qiskit implementation and its corresponding graphical-empirical example for the execution of a three-qubit quantum teleportation protocol. Overall, our results reveal insights into system entanglement and demonstrate that Boolean functions provide a structured approach for the purposes of controlling the dynamics of quantum entropy. This has implications beyond the secure obfuscation of classical communication in quantum teleportation and warrants additional investigation of quantum Boolean functions in the broad context of quantum information scrambling and beyond.
