Quantum physics, one of the major branches of modern physics, lays the foundation for our understanding of all fundamental particles, energy, and forces (except gravity). It explains how our universe works on the tiniest scales, including the very building blocks of nature: atoms, electrons, photons, and even smaller particles. Quantum physics has significantly contributed to advancements in technology in areas such as atomic energy, integrated circuits, lasers, photonics, and even quantum computing. Today, lasers and photonics alone are a $16 trillion market!

Quantum entanglement is a core phenomenon in quantum physics that occurs when a pair or group of particles, such as electrons or photons, become entangled, creating a special connection between them, even when separated by an enormous distance. Where this phenomenon finds practical application is in quantum computing. Understanding quantum computing, which can help us find better materials and medicines, and solve complex problems exponentially faster, requires us to understand quantum entanglement. 

Understanding Quantum Entanglement

Quantum entanglement lies at the heart of quantum physics, defying our understanding of classical physics and causality. This phenomenon is shown when two or more particles become entangled, establishing a special connection or relationship between them, regardless of distance in space. Think of two objects that are connected in such a way that they are described as a single system, even when set apart by a vast distance. The state of one object cannot be described or measured without getting information about the other object's state in the system.

In 1905, Albert Einstein helped to pioneer the quantum theory, from which he proposed the existence of quantum entanglement. In 1935, Einstein, alongside Boris Podolsky and Nathan Rosen, published what became known as the Einstein-Podolsky-Rosen (EPR) paradox, which inadvertently uncovered the strange concept of “entanglement.” Because of the mysterious nature of this phenomenon, especially the fact that entangled particles tend to share an inexplicable bond despite being very far apart, Einstein termed it “spooky action at a distance.” Erwin Schrödinger, one of the founding members of quantum mechanics was the first physicist to coin the term “entanglement.”

This became the core concept that allowed scientists to speculate about the idea of a computer that would leverage these properties. 

The Principles of Quantum Computing

From being considered purely speculative to becoming a rapidly emerging technology, quantum computing is a paradigm shift from classical computing. It is an entirely different approach to computing that leverages the properties of entanglement and superposition to solve highly complex problems that classical computing finds difficult to solve. Just like classical computing relies on bits for its operations, quantum computing also relies on quantum bits (or qubits) for the same purpose.

Qubits are the fundamental units of information in quantum computing that are a linear combination of two distinct states. Unlike classical bits that can only be 0 or 1, qubits can simultaneously be 0 or 1 or in a superposition of both until their state is measured. Depending on the architecture of quantum systems, qubits can be made from trapped ions, photons, real or artificial atoms, or quasiparticles.

If you have ever wondered how quantum computers solve complex problems that are unfeasible for classical computers, then the answer lies in the property of quantum entanglement. Quantum computing uses quantum entanglement to create networks of qubits. As more and more qubits are entangled in these networks, the ability of the system to handle calculations grows exponentially. 

Quantum Entanglement in Quantum Computing

Quantum entanglement is integral to what makes quantum computing more powerful than classical computing.

Quantum circuit-level implementation of entanglement is achieved through a CNOT gate. A controlled-NOT (or CNOT) gate is used to create an entangled state for two qubits. The first qubit is usually called the control qubit, while the second qubit is called the target qubit. The CNOT gate flips the target qubit only on the condition that the control qubit is in the state |1⟩. Representing this gate can take the form of the matrix [1,0,0,0], [0,1,0,0], [0,0,0,1], [0,0,1,0]. 

Quantum entanglement has contributed immensely to our advancements and continues to make in quantum computing, including:

• Quantum algorithms: Quantum algorithms are the step-by-step procedures that harness quantum properties, such as entanglement and superposition, for complex calculations at a much faster rate than classical computing. In other words, quantum algorithms are the stepwise coded instructions that leverage quantum properties to handle the intricacies of advanced computations. 
• Error correction: Quantum error correction (QEC) is a technique that protects quantum computers from noise. When quantum information (or qubits) are exposed to this kind of noise, they get degraded. This is known as decoherence. QEC relies on quantum entanglement to handle the encoding and protection of the logical qubits. For example, the three-qubit bit-flip code, known to be one of the simplest QEC codes, uses three entangled physical qubits to encode one logical qubit. If one of the physical qubits flips due to the influence of noise, the remaining two can detect and correct the error by measuring their entanglement.
• Cryptography: Quantum cryptography is a type of encryption technique that leverages the capabilities of entangled quantum bits (qubits). This cryptographic system takes advantage of the principles of quantum entanglement, where two qubits (or particles) remain connected even when separated by a vast distance. This system promises to be more secure than existing cryptographic methods. This is because any attempt to gain access to or intercept information causes detectable changes in the entanglement, which will instantaneously alert both the sender and receiver of interference. 

Entanglement in the Next-Gen Computing Era 

Quantum entanglement is a mind-bending phenomenon that occurs when two or more particles become interconnected in such a way that their quantum states are dependent on each other, regardless of the distance that separates them. This phenomenon is the key to quantum computing and algorithms. 

Two quantum algorithms that leverage entanglement are Shor’s algorithm and Grover’s algorithm. The former (Shor’s algorithm) is used for integer factorization, that is, it finds the prime factors when given an integer N. It is exponentially faster at solving this problem than the best-known classical algorithm. Grover’s algorithm can search a large, unsorted database exponentially faster than the best-known classical algorithm for the same purpose. These algorithms demonstrate the transformative potential of quantum computing in areas such as cryptography and database search and leverage the power of quantum entanglement to open a new era of next-gen computing.