## Definition

Applied Quantum Computing, at its core, refers to the practical application of quantum computing principles to solve complex real-world problems. These principles draw from the laws of quantum mechanics, utilizing unique phenomena such as superposition and entanglement to perform calculations that surpass the capabilities of classical computers.

## The Principles of Quantum Mechanics

Quantum mechanics, the branch of physics that describes the puzzling behaviors of particles on the tiniest scales, gives birth to these fascinating principles.

**Superposition**allows quantum bits, or ‘qubits,’ to exist in multiple states simultaneously, unlike classical bits that can only be 0 or 1. This characteristic endows quantum computers with the ability to process a vast number of possibilities all at once.- In contrast,
**entanglement**, another quantum mechanical phenomenon, binds qubits so that the state of one instantaneously affects the state of another, regardless of the distance separating them. This enables powerful correlations not achievable in classical systems.

*Learn more about the principles of Quantum Computing here.*

## The Potential of Quantum Computing

This unique computational ability of quantum computers opens up new avenues of research and problem-solving in numerous fields. The potential applications of quantum computing are vast and varied. From developing efficient portfolios in finance, streamlining aircraft planning to facilitating groundbreaking research in drug discovery and artificial intelligence, the influence of quantum computing promises to be transformative.

Major tech companies such as IBM, Google, and Microsoft recognize the burgeoning potential of this technology, investing heavily in quantum research and development.

In particular, the advent of quantum computing could provide critical tools to enhance cybersecurity, with the potential to bolster the security of information sharing and online systems greatly. Furthermore, it could prove instrumental in environmental monitoring and healthcare advancements, revolutionizing how we diagnose diseases and discover new treatment modalities.

While the possibilities seem endless and the potential transformative, it is important to recognize that the road to realizing these applications is fraught with challenges. Decoherence and error correction are key problems that quantum computing must overcome. These qubits are extraordinarily delicate and sensitive to their environments, requiring specific conditions like extreme cold to function effectively.

## Fundamental Concepts in Quantum Computing

### Postulates of Quantum Mechanics

Quantum mechanics, the cornerstone of quantum computing, revolves around several fundamental postulates. To understand these, one must recognize the importance of the quantum bit or qubit, which distinguishes quantum computing from classical computing. Unlike classical bits in a definite state of 0 or 1, qubits can exist in multiple states, exploiting superposition, a key principle of quantum mechanics.

This principle is integral to understanding how quantum computations can achieve parallelism and, thus, perform complex calculations rapidly. Another critical postulate of quantum mechanics is entanglement, where qubits become intrinsically linked, causing the state of one to instantly influence the state of another, regardless of the distance between them. This unique property allows for faster and more efficient information processing.

### Quantum Errors and Error Correction

This technology faces significant challenges, one of which is the susceptibility of quantum systems to errors. Quantum systems are very delicate, influenced by environmental factors, leading to decoherence and the loss of quantum information. Quantum Error Correction (QEC) is a set of techniques designed to protect quantum information from such errors. By encoding the quantum information across multiple physical qubits, quantum systems can detect and correct errors without disturbing the delicate quantum state.

Protected qubits are a significant area of research in fault-tolerant quantum computing, playing a vital role in mitigating the errors that naturally arise in quantum computation and maintaining the integrity of quantum data.

### Quantum Gates and Circuits

In quantum computing, computations are performed by applying a sequence of quantum gates to an initial state of qubits to create a quantum circuit. Unlike classical logic gates, these quantum gates can represent probabilistic and reversible transformations, which allows for powerful computational potential. Entanglement creation and applying quantum gates and circuits are fundamental to running quantum programs on real hardware and exploring quantum algorithms.

### Quantum State and its Measurement

One of the key principles in quantum mechanics is the measurement postulate which states that measuring a quantum system results in the system collapsing from a superposition state into one of the possible eigenstates associated with the measurement, which can then be read out classically. The observer effect, another fundamental aspect of quantum mechanics, notes that the mere observation of a quantum system inevitably alters its state.

### The No-Cloning Theorem and Quantum Teleportation

The no-cloning theorem is a vital concept in quantum information theory. It stipulates that creating an identical copy of an arbitrary unknown quantum state is impossible. This attribute is especially crucial in quantum cryptography, where the inability to clone quantum states provides a robust safeguard against eavesdropping.

In contrast, quantum teleportation is a process by which the state of a qubit (or a set of qubits) can be transmitted from one location to another without physically sending the actual qubit(s) involved. It leverages the properties of entanglement and quantum measurement to achieve this seemingly paradoxical outcome. Although it may sound like a concept from science fiction, quantum teleportation is an integral part of the quantum information science landscape and a key enabler of future quantum technologies.

## Quantum Computing Models

### Gate-based Quantum Computing

Gate-based quantum computing represents the foundation of quantum computer operations. At the heart of this model is a basic building block, the quantum bit or qubit. Unlike the classical binary bit with a single value of either 0 or 1, a qubit can represent a range of states due to a fascinating principle of quantum mechanics called superposition.

Quantum gates are operations that can manipulate these qubits. They are the quantum analog of classical logic gates and can perform complex computations with extraordinary speed. The pivotal property of quantum gates is their ability to manipulate the quantum state of a single qubit or entangle multiple qubits, establishing a correlation between their states.

While highly complex, the gate-based quantum computing model harnesses the fundamental peculiarities of quantum physics to open up new avenues for processing information. It can potentially disrupt various industries, from cryptography to material science, owing to its capacity to solve complex problems that traditional computers find almost intractable.

### Adiabatic Quantum Computing

Adiabatic quantum computing (AQC) offers a unique approach to problem-solving in the quantum world. It is premised on the principle of adiabatic evolution from quantum physics, which states that if a system evolves slowly enough, it will remain in its ground state â€” the lowest energy state. This inherent nature of quantum systems allows an adiabatic quantum computer to find the minimum or “ground state” of a complex problem.

AQC works by initializing the quantum system in an easy-to-prepare ground state and then gradually transforming this state into one that represents the solution to the problem. This method can prove extremely efficient for solving optimization problems, offering a promising alternative to gate-based models, especially when dealing with noise and quantum error correction issues.

### Quantum Annealing

Quantum annealing is a type of adiabatic quantum computing. It’s a heuristic method designed to solve complex optimization problems more efficiently than classical computing. Quantum annealing uses the principles of quantum superposition and tunneling, allowing it to explore a much larger solution space than traditional methods.

A simple way to understand quantum annealing is by visualizing a landscape of peaks and valleys, with the solution to a problem being the lowest valley. While classical computing might get stuck in a high valley, quantum annealing can tunnel through peaks to find the lowest valley, providing a more optimal solution.