Quantum supremacy refers to the point at which quantum computers can perform calculations that would be practically impossible for classical computers. Unlike traditional computers, which rely on bits as the smallest unit of data that encodes information as either 0 or 1, quantum computers use quantum bits (qubits). A single qubit can exist in a state of both 0 and 1 simultaneously, thanks to the principles of superposition and entanglement. This unique capability allows quantum computers to explore multiple solutions at once, leading to exponential increases in computational power.

The implications of achieving quantum supremacy are profound. For example, tasks such as factorizing large numbers or simulating complex molecular interactions could take classical computers millions of years to solve, while quantum computers can accomplish these in mere seconds. Major tech companies and research institutions are investing heavily in this field, anticipating a future where quantum computers could revolutionize industries ranging from cryptography to drug discovery. As we continue to explore the frontiers of quantum mechanics, understanding how these machines can outperform their classical counterparts will be crucial to harnessing their full potential.

Quantum entanglement is a fundamental phenomenon in quantum mechanics where pairs or groups of particles become interconnected, resulting in instantaneous changes to one particle affecting its entangled partner, regardless of the distance separating them. This non-local relationship challenges classical notions of space and time, laying the groundwork for revolutionary advancements in various fields, particularly quantum computing. By harnessing the power of entangled states, quantum computers can process information in parallel, exponentially increasing their computational capabilities compared to traditional computers.

The implications of quantum entanglement for computing are profound. Firstly, it enables the development of quantum algorithms that can solve complex problems far more efficiently than their classical counterparts. For instance, algorithms like Shor's and Grover's leverage entangled qubits to perform tasks such as factoring large numbers and searching unsorted databases with unprecedented speed. Secondly, the concept of quantum teleportation, which relies on entangled particles, could revolutionize secure communication by allowing the transmission of information without the actual movement of particles, enhancing data security in the digital age.

Quantum computers represent a significant leap forward in computational power, enabling them to tackle complex problems that are beyond the reach of classical computers. This revolutionary technology utilizes the principles of quantum mechanics, such as superposition and entanglement, to process information in fundamentally different ways. For instance, while classical computers operate with bits that can either be 0 or 1, quantum computers leverage qubits that can exist in multiple states simultaneously. As a result, quantum computers hold the potential to solve optimization problems, simulate molecular interactions, and enhance cryptographic systems at unprecedented speeds.

However, the question remains: can quantum computers solve problems that classical limits cannot? The answer is increasingly leaning towards yes. Problems categorized as NP-hard, which include various logistical and combinatorial challenges, may find feasible solutions through quantum algorithms that exploit quantum parallelism. For instance, in fields like drug discovery and material science, the ability of quantum computers to model complex systems at the molecular level could lead to breakthroughs unimaginable with classical computing. As research advances, we may witness the dawn of a new era where quantum computers redefine our approach to problem-solving.