In the realm of quantum computing, the principles that govern these powerful machines often challenge our classical understanding of logic. At the heart of this technology lies the concept of superposition, which allows quantum bits or qubits to exist in multiple states simultaneously. This property enables quantum computers to process vast amounts of information at speeds unattainable by classical computers. For instance, while a traditional bit can represent either a 0 or a 1, a qubit can represent both at the same time, resulting in parallel computations that revolutionize problem-solving capabilities.

Moreover, the phenomenon of entanglement plays a crucial role in the functionality of quantum systems. When qubits become entangled, the state of one qubit is directly linked to the state of another, regardless of the distance separating them. This non-locality defies classical logic, where information transfer appears to be bound by space and time. Consequently, quantum computers can solve complex problems in optimization and cryptography much more efficiently than their classical counterparts, paving the way for advancements in various fields including medicine, logistics, and artificial intelligence.

The paradox of quantum states primarily arises from the delicate nature of superposition and entanglement. When quantum computers process information, they leverage these quantum states to perform complex calculations at unprecedented speeds. However, due to various factors such as environmental noise and material imperfections, these states are particularly susceptible to errors. This fragility poses significant challenges, as errors can lead to decoherence, undermining the reliability and efficiency of quantum computations. Understanding how to manage and correct these errors is essential for harnessing the true potential of quantum technology.

One of the most intriguing aspects of quantum error correction involves quantum redundancy, where information is encoded in a way that allows for recovery even when some quantum bits (qubits) are compromised. Techniques such as the Shor code or the surface code represent pioneering approaches to mitigate errors and maintain coherence in quantum states. The ongoing research in this field not only seeks to improve the robustness of quantum systems but also deepens our understanding of the fundamental principles of quantum mechanics. As we delve deeper into this paradox, the future of quantum computing holds the promise of revolutionary advancements in various sectors, heralding a new era of computational power.

Quantum Entanglement represents one of the most perplexing phenomena in quantum physics, whereby particles become interconnected in such a way that the state of one instantaneously influences the state of another, regardless of the distance separating them. This principle raises compelling questions about the nature of reality and information transmission. In recent studies, the unexpected implications of quantum entanglement have been linked to computational errors in quantum computing systems. As researchers delve deeper, they have begun to uncover how entangled states may inadvertently introduce unforeseen variables that complicate computational processes, leading to errors that can derail complex calculations.

Understanding the relationship between quantum entanglement and computational errors is critical for the advancement of quantum computing technology. It is essential to recognize that as we harness the power of entangled states for computation, we must also develop robust error-correction methods. Here are some key considerations to keep in mind:

1. Analyzing how entanglement affects computational pathways can provide insights into error origins.
2. Implementing effective error-correction protocols will mitigate risks associated with entangled states.
3. Further research into quantum error mitigation techniques is essential for achieving reliable quantum computations.