# Introduction to quantum computing

Have you ever heard of a computer that can do things regular computers can’t? These special computers are called quantum computers. They are different from the computer you use at home or school because they use something called “qubits” instead of regular “bits”.

A bit is like a light switch that can only be on or off, like a zero or a one. But a qubit can be both zero and one at the same time! This means quantum computers can do many things at once and work much faster than regular computers. It’s like having many helpers working on a task together instead of just one.

Scientists first thought about quantum computers a long time ago, but it wasn’t until recently that they were able to build working models. Now, companies and researchers are working on making bigger and better quantum computers.

Regular computers use bits, which are either ones or zeros, to process information. These bits are passed through logic gates, like AND, OR, NOT, and XOR, that manipulate the data and produce the desired output. These gates are made using transistors and are based on the properties of silicon semiconductors. While classical computers are efficient and fast, they struggle with problems that involve exponential complexity, such as factoring large numbers.

On the other hand, quantum computers use a unit called a qubit to process information. A qubit is similar to a bit, but it has unique quantum properties such as superposition and entanglement. This means that a qubit can exist in both the one and zero states at the same time. This allows quantum computers to perform certain calculations much faster than classical computers.

In a real quantum computer, qubits can be represented by various physical systems, such as electrons with spin, photons with polarization, trapped ions, and semiconducting circuits. With the ability to perform complex operations exponentially faster, quantum computers have the potential to revolutionize many industries and solve problems that were previously thought impossible.

Now let’s understand what exactly **Quantum Superposition **and **Quantum Entanglement **are!

1.** Quantum Superposition: **Qubits can do something really cool, they can be in two states at the same time! It’s like having two helpers working on a task instead of just one. It’s like a coin, a coin can be either heads or tails but not both at the same time, but a qubit can be both zero and one at the same time. This means quantum computers can do many things at once and work much faster than regular computers. This special ability is called quantum superposition, and it’s what makes quantum computers so powerful!

Let’s dive a little deeper!

In the context of quantum computing, this means that a qubit can represent multiple values at the same time, rather than just a single value like a classical bit.

A qubit can be described as a two-dimensional vector in a complex Hilbert space, with the two basis states being |0âŸ© and |1âŸ©. A qubit can be in any state that is a linear combination of these two basis states, also known as a superposition state. This can be written as |ÏˆâŸ© = Î±|0âŸ© + Î²|1âŸ©, where Î± and Î² are complex numbers that represent the probability amplitudes of the qubit being in the |0âŸ© and |1âŸ© states, respectively. The probabilities of measuring the qubit in the |0âŸ© and |1âŸ© states are given by the squared moduli of the coefficients, |Î±|^2 and |Î²|^2, respectively.

A qubit can exist in an infinite number of superpositions of the |0âŸ© and |1âŸ© states, each corresponding to a different probability distribution. This allows a qubit to perform multiple calculations simultaneously, greatly increasing its processing power. The ability of qubits to exist in multiple states at once enables the execution of quantum algorithms that can solve certain problems exponentially faster than classical algorithms. Eg: In regular computers, a group of 4 bits can represent 16 different values, but only one at a time. However, in a quantum computer, a group of 4 qubits can represent all 16 combinations simultaneously.

A simple example of quantum superposition is Grover’s algorithm which is a quantum search algorithm that can search an unordered database with N entries in âˆšN steps, whereas a classical algorithm would take N steps. Another example is Shor’s algorithm which is a quantum algorithm that can factorize a composite number in polynomial time, a problem that is considered to be hard for classical computers. This algorithm has important implications in the field of cryptography, as many encryption methods rely on the difficulty of factoring large numbers.

2. **Quantum Entanglement: **Let’s continue the same story from quantum superposition, the tiny helpers called qubits can be in two states at the same time? Well, sometimes those qubits can become special friends and work together even when they are far apart! This is called quantum entanglement.

Imagine you have two toys, a car, and a boat. If you put the car toy in one room and the boat toy in another room, and you make them special friends so that if you change something about one toy, the other toy will change too. Even if you’re not looking at one toy, you’ll know what’s happening with the other toy just by looking at the other one. This is what quantum entanglement is, it’s like a secret connection between qubits.

This is really important for quantum computers because it allows them to perform certain calculations much faster than regular computers and to communicate faster too. It’s a very special and powerful feature of quantum computers.

Let’s dive a little deeper!

In quantum mechanics where the properties of two or more quantum systems become correlated in such a way that the state of one system cannot be described independently of the others, even when the systems are separated by a large distance. In other words, the state of one system is dependent on the state of the other system, regardless of the distance between them.

In the context of quantum computing, entanglement is used to perform certain calculations much faster than classical computers. In a quantum computer, qubits are used to represent the state of the system, and entanglement is used to correlate the state of multiple qubits, enabling them to perform multiple calculations simultaneously.

An example of quantum entanglement is the Bell states, which are maximally entangled states of two qubits. The Bell states are a set of four quantum states that allow for fast and secure communication between two parties. These states are created by applying a specific operation called the Bell-state measurement, which allows for a fast and secure transfer of quantum information between two parties. Another example is Grover’s algorithm which utilizes the properties of entanglement to perform a search operation exponentially faster than any classical algorithm.

**Disadvantages of Quantum Computers**

Quantum computers have the potential to revolutionize the field of computing, but they also come with a number of disadvantages. Some of the main challenges and limitations of quantum computing include:

**Noise and decoherence:**One of the biggest challenges in building a quantum computer is the problem of noise and decoherence. Quantum systems are extremely sensitive to their environment, and any noise or disturbance can cause errors in the computation. This makes it difficult to maintain the delicate quantum state of the qubits and to perform accurate and reliable computations.**Scalability**: Another major challenge is scalability. Building a large-scale quantum computer with a large number of qubits is extremely difficult, as it requires the precise control of a large number of quantum systems. Currently, the number of qubits that can be controlled and manipulated in a laboratory setting is still quite small, which limits the potential of quantum computing.**Error correction**: Error correction is another major challenge in quantum computing. In classical computing, errors can be corrected using error-correcting codes, but in quantum computing, the errors are much more difficult to detect and correct, due to the nature of quantum systems.**Lack of robust quantum algorithms**: Even though some quantum algorithms have been developed, their number is still limited, and many problems that can be solved using classical computers have no known quantum algorithm.**High cost**: Building and maintaining a quantum computer is extremely expensive, due to the need for specialized equipment and highly trained personnel. The cost of building a large-scale quantum computer is also likely to be quite high, which could limit the availability of quantum computing to certain groups or organizations.**Power consumption**: Quantum computers are extremely power-hungry, due to the need to maintain the delicate quantum state of the qubits. This makes it difficult to scale up quantum computing to larger systems, as the power requirements become prohibitively high.

Quantum computers have the potential to revolutionize the field of computing, but they also come with a number of disadvantages. Some of the main challenges and limitations include *noise and decoherence, scalability, error correction, lack of robust quantum algorithms, high cost, and power consumption.*

There are several multinational companies that have built and are currently working on building quantum computers. Some examples include:

**IBM**: IBM has been working on quantum computing for several decades, and has built several generations of quantum computers. The company has made significant progress in the field, and its IBM Q quantum Experience platform allows anyone with an internet connection to access and runs experiments on its quantum computers. IBM’s most recent quantum computer, the IBM Q System One, is a 20-qubit machine that is designed for commercial use.**Google**: Google has been working on quantum computing for several years and has built several generations of quantum computers, including the 72-qubit Bristlecone quantum computer. The company claims that its quantum computer has reached “quantum supremacy,” meaning it can perform certain calculations faster than any classical computer.**Alibaba**: Alibaba has been investing heavily in quantum computing, and in 2017 it announced that it had built a quantum computer with 11 qubits. The company has also been developing its own quantum chips and is planning to release a cloud-based quantum computing service in the near future.**Rigetti Computing**: Rigetti Computing is a startup company that is building and developing superconducting qubits-based quantum computers. They offer a cloud-based quantum computing platform for researchers and developers to access their quantum computers.**Intel**: Intel has been developing its own quantum computing technology and has been building quantum processors and cryogenic control chips, which are used to control the quantum bits. In 2019, they announced the development of a 49-qubit quantum processor, one of the largest processors of its kind developed so far.**D-Wave Systems**: D-Wave Systems is a Canadian quantum computing company, founded in 1999, which is known for its development of the D-Wave One, the first commercially available quantum computer. D-Wave’s quantum computers are based on a technology called quantum annealing, which is a type of quantum optimization algorithm. They claim to have built the first commercially available quantum computer, but their system is not a fully general-purpose computer and it’s mainly used for optimization problems.**Xanadu**: Xanadu is a Canadian startup company that is building a new type of quantum computer based on a technology called photonic quantum computing. Photonic quantum computing is based on the manipulation of light particles (photons) to perform quantum computations. Xanadu’s approach is different from other companies that are building quantum computers, as it uses light instead of superconducting qubits. They are focusing on developing a general-purpose quantum computer that can run multiple algorithms.

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