Cellular Automata (CA) are formal models for complex systems that have been widely studied and find application in a number of disciplines. However many properties of the temporal evolution of general CA are undecidable and this can be a severe problem in applications. The undecidability issue can be tackled by imposing constraints on the model. Indeed, we equip the alphabet with a group structure and we require that the global map is additive, giving rise to Additive CA over a finite group.
First, we present the abelian situation in which easy-to-check algebraic characterizations of the main dynamical properties in terms of the CA local rule have been provided.
Then, we move to the non-abelian scenario. We will consider the dynamical behavior of Additive CA on a number of classes of specific finite groups and for each of those classes, we focus on non-abelian scenarios, providing exact characterizations for some of the dynamical properties. Some results are quite surprising because they show that the non-abelianness of the group imposes strong limitations on defining the local rule of the cellular automaton, making the class of group cellular automata very constrained.

This study demonstrates how to provide specific guarantees on the entropy produced by quantum circuits implementing Boolean functions. More specifically, we study von Neumann entropy guarantees of subsystems in such circuits. Our finding 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 propose an application and use
these findings to secure the classical communication channel of a novel multi-qubit quantum teleportation protocol. We depict a full IBM Qiskit implementation and an empirical example for the execution of a three-qubit quatum teleportation protocol. Overall, our findings 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.

Boson Sampling, a non-universal computing paradigm, has resulted in impressive claims of quantum supremacy. ORCA Computing have developed a time-bin interferometer (TBI) that claims to use the principles of boson sampling to solve a number of computational problems including optimisation and generative adversarial networks. We solve a dominating set problem with a surveillance use case on the ORCA TBI simulator to benchmark the use of these devices against classical algorithms. Simulation has been used to consider the optimal performance of the computing paradigm without having to factor in noise, errors and scaling limitations. We show that the ORCA TBI is capable of solving moderately sized (n < 250) dominating set problems with comparable success to linear programming and greedy methods. Wall clock timing shows that the simulator has worse scaling than the classical methods, but this is unlikely to carry over to the physical device where the outputs are measured rather than calculated.

Quantum hashing is a useful technique that allows us to construct memory-efficient algorithms and secure quantum protocols. First, we present a circuit that implements the phase form of quantum hashing using 2^n-1 CNOT gates, where n is the number of control qubits. Our method outperforms existing approaches and reduces the circuit depth. Second, we propose an algorithm that provides a trade-off between the number of CNOT gates (and consequently, the circuit depth) and the precision of rotation angles. This is particularly important in the context of NISQ (Noisy Intermediate-Scale Quantum) devices, where hardware-imposed angle precision limit remains a critical constraint.

Quantum Merlin-Arthur proof systems are believed to be stronger than both their classical counterparts and "stand-alone'' quantum computers when Arthur is assumed to operate in $\Omega(\log n)$ space. No hint of such an advantage over classical computation had emerged from research on smaller space bounds, which had so far concentrated on constant-space verifiers. We initiate the study of quantum Merlin-Arthur systems with space bounds in $\omega(1) \cap o(\log n)$, and exhibit a problem family $\mathcal{F}$, whose yes-instances have proofs that are verifiable by polynomial-time quantum Turing machines operating in this regime. We show that no problem in $\mathcal{F}$ has proofs that can be verified classically or is solvable by a stand-alone quantum machine in polynomial time if standard complexity assumptions hold. Unlike previous examples of small-space verifiers, our protocols require only subpolynomial-length quantum proofs.

A computational model of adiabatic evolutionary quantum system (or AEQS, pronounced ``eeh-ks'') was introduced in [Yamakami (2022)] 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 short paper reports on an early-stage investigation into the behavior of re-entry-based logic elements embedded in two-dimensional grids. Inspired by Spencer-Brown’s Laws of Form, we implement and compare three update models—Classic, Self, and Re-Entry—each extending the behavior of SR flip-flops with increasing degrees of contextual awareness. Simulations across various input patterns (impulse, sinusoidal, constant, random) reveal that most configurations converge rapidly to homogeneous states, with only minor signs of sustained activity under periodic input in the Self and Re-Entry variants. While no traveling patterns or self-organizing behavior have been observed so far, these results establish a useful reference point for the limitations of binary-state re-entry systems. We outline several planned extensions, including multivalued logic and dynamic neighbor graphs, aimed at fostering richer structural dynamics. These early results are intended to inform the design of future form-based models for unconventional computation.

There are quite a few computational problems for which a quantum algorithm is known that is substantially better than a classical algorithm. Despite this, large sums of money are being invested in the development of quantum computers around the world.
In this overview, we will compare classical and quantum computing, and present reasons to invest and not to invest in quantum computing.

Quantum decoherence is a critical issue for quantum computation as it affects qubit superposition and output fidelity and is typically due to the coupling of qubits to external fields and environmental variables (i.e., thermal fluctuations, molecular vibrations, and electromagnetic fields). In this presentation, we will discuss the nanoscopic origins of quantum decoherence by examining how atoms and qubits interact through electron interactions and entanglement. Furthermore, we will explore how external fields (magnetic and electric) and thermal fluctuations affect these interactions, leading to a breaking of quantum coherence. We will conclude by discussing potential mechanisms for enhancing qubit interactions to achieve more robust information fidelity.