In general, quantum computation models are expected to be more powerful than classical counterparts. However, sometimes this is not the case.It is known that there exists some regular language which one-way quantum finite automata and one-way quantum counter automata cannot recognize. This is due to the restriction of reversibility which quantum models must satisfy. Thus, it is an interesting question: what kinds of quantum models suffer from/overcome the restriction? To tackle this problem, we focus on (empty-stack acceptance) one-way quantum pushdown automata, and show that there exists a regular language which one-way quantum pushdown automata cannot recognize. This implies adding a stack to one-way finite automata cannot overcome the restriction of reversibility if we adopt empty-stack acceptance as the acceptance mode.
Abstract Modeling noisy discrete systems utilizing conservative reversible elementary cellular automata (CRECA) is introduced. Reversibility in the ECA evolution rule and reversibility in the ECA circuit implementation are both achieved using a new Swap-based algorithm called Swap-based CRECA (SCRECA). The new method results in adding variable redundancy to counteract the effect of noise. The problem of obtaining a reversible map from an irreversible map is important because quantum circuits are inherently reversible and thus does not consume power, while irreversible circuits (due to either an irreversible mapping or to noise within a reversible mapping) cannot exist in the quantum domain and its circuits consume power. Since noise is an integral part of any real process and since the reduction of power consumption is a main requirement for the circuit design of future technologies such as in quantum computing (QC), the main features of several future technologies will include reversibility, and thus the...
This paper proposes a novel model utilizing Quantum Cellular Automata (QCA) to simulate complex system evolution. The core idea involves transforming classical Cellular Automata (CA) into QCA, incorporating quantum phenomena such as superposition and entanglement to model intricate dynamics. This approach offers a fresh perspective on complex system modeling by leveraging the principles of quantum mechanics. The model's design incorporates key QCA mechanisms, including the Bloch sphere representation of states and the application of unitary transformations to govern cell interactions. We present a foundational framework for QCA simulation and discuss potential applications in areas such as pattern formation, reaction-diffusion processes, and emergent behavior. The focus is on demonstrating the theoretical feasibility and outlining a methodology for future research, rather than presenting empirical experimental results. This work emphasizes the conceptual shift and potential computational advantages offered by QCA in understanding complex systems.