Quantum computers and classical computers represent two fundamentally distinct paradigms in the world of computation, each with its own set of principles and capabilities. Understanding the differences between them requires delving into the realms of quantum mechanics, information theory, and computational science. This exploration will cover key aspects such as qubits, superposition, entanglement, and quantum gates, contrasting them with classical bits, logic gates, and classical algorithms.

At the heart of the disparity lies the basic unit of information: classical computers utilize bits, which can exist in one of two states, 0 or 1, forming the basis for classical binary logic. Quantum computers, on the other hand, leverage qubits, which exploit the principles of quantum superposition and entanglement to exist in multiple states simultaneously. This ability enables quantum computers to perform certain computations exponentially faster than their classical counterparts for specific types of problems.

A classical bit is the most basic form of information in classical computing, representing a binary state of either 0 or 1. Classical computers process information through logical operations performed on these bits using classical gates, such as AND, OR, and NOT gates. Classical algorithms are built upon these operations, employing step-by-step procedures to manipulate bits and solve problems.

In contrast, a qubit, the fundamental unit of quantum information, can exist in a superposition of states, effectively representing 0, 1, or any quantum combination of both simultaneously. This unique property arises from the principles of quantum mechanics, allowing quantum computers to process information in parallel. Superposition is a key advantage, enabling quantum computers to explore multiple solutions to a problem concurrently, potentially leading to significant speedup for certain algorithms.

Entanglement is another quantum phenomenon that distinguishes quantum computers from classical ones. When qubits become entangled, the state of one qubit becomes linked with the state of another, regardless of the physical distance between them. This interdependence allows quantum computers to exhibit correlations and dependencies beyond classical computing capabilities. Exploiting entanglement enables the creation of quantum circuits and gates that perform complex operations, contributing to the power of quantum algorithms.

Quantum gates are the building blocks of quantum circuits, analogous to classical gates in classical computing. However, quantum gates operate on qubits and take advantage of quantum phenomena. For instance, the Hadamard gate places a qubit into a superposition of states, while the CNOT gate is an entangling gate that creates entanglement between two qubits. These gates allow quantum computers to perform intricate operations and transformations on quantum states, forming the basis for quantum algorithms.

Shor's algorithm and Grover's algorithm are two prominent examples showcasing the quantum advantage. Shor's algorithm, developed by mathematician Peter Shor, efficiently factors large numbers exponentially faster than the best-known classical algorithms. This has significant implications for cryptography, as many encryption schemes rely on the difficulty of factoring large numbers. Grover's algorithm, proposed by Lov Grover, provides a quadratic speedup for unstructured search problems, impacting areas such as database searching and optimization.

Despite these quantum advantages, quantum computers face several challenges and limitations. Quantum coherence, the delicate state that allows quantum computers to maintain superposition and entanglement, is susceptible to environmental disturbances and noise. Quantum error correction, an active area of research, seeks to address these challenges by developing techniques to protect quantum information from errors.

Moreover, building and maintaining quantum computers require extremely low temperatures, typically near absolute zero, to preserve quantum coherence. This imposes significant engineering challenges and adds to the complexity and cost of developing practical quantum computers. Achieving and maintaining quantum supremacy, where a quantum computer outperforms the most advanced classical computers for a specific task, remains a milestone rather than a routine achievement.