Quantum Computing v/s Quantum Physics

By Jai Prakash Verma, Aashna Shah, Prachita Patel, Jayneel Shah, Smiti Kothari

What is Quantum Physics?

Quantum physics, also known as quantum mechanics, is a fascinating and revolutionary branch of physics that deals with the behaviour of particles at the smallest scales. It provides a framework for understanding the fundamental nature of matter and energy and has significantly shaped our understanding of the physical world.

At its core, quantum physics challenges the classical Newtonian view of the universe, which describes the behaviour of objects based on deterministic laws. In contrast, quantum mechanics introduces the concept of probability and uncertainty into the equation. Particles like electrons are described as wave functions[Fig. 1], which are mathematical functions which contain information about the position, momentum and other properties. The wave function helps in determining the probable location for finding the particle in a different state. It suggests that particles such as electrons and photons can exist in multiple states simultaneously, known as superposition until they are observed or measured.

One of the key principles of quantum physics is wave-particle duality. It states that particles, such as electrons or photons, can exhibit both wave-like and particle-like characteristics depending on how they are observed. This concept is best exemplified by the famous double-slit experiment [Fig 2], where particles behave as both particles and waves, creating an interference pattern on a screen.

Another intriguing aspect of quantum mechanics is entanglement. It refers to the phenomenon where two or more particles become connected in such a way that the state of one particle is instantly correlated with the state of the other, regardless of the distance between them. This concept led Albert Einstein to famously refer to it as “spooky action at a distance.”

Quantum physics also introduces the notion of quantum tunneling, which allows particles to pass through potential energy barriers that would be impossible according to classical physics. This phenomenon plays a crucial role in various fields, including semiconductor devices and nuclear fusion.

The practical applications of quantum physics are wide-ranging. Quantum cryptography offers secure communication protocols based on the principles of quantum mechanics. Additionally, quantum physics has found applications in quantum teleportation, superconductivity, and precision measurements. Quantum computers hold the promise of solving complex computational problems at a much faster rate than classical computers.

What is Quantum Computing?

Quantum computing is often wrongly interpreted to be a faster and more advanced version of classical computing. This comparison is not exactly true, because while there are some similarities (both are used to advance our understanding of the sciences), quantum computing is nowhere near the spectrum of classical computing. It is something vastly different that can change our understanding of everything we can or cannot imagine. To understand what exactly quantum computing represents, we can use the analogy of a video game as shown in Figures 3 and 4. 

In the video game analogy, let’s consider classical computing as a game map that expands with each advancement in mathematics. Initially, the map starts small, representing the computing capabilities of early computers. As mathematical techniques and algorithms evolve, the map expands, revealing new areas and possibilities for computation.

Now, let’s introduce quantum computing into this analogy. Quantum computing represents the introduction of an ocean into a map that previously had no water bodies. It’s a transformative addition that brings a completely new dimension to the game.

In classical computing, the game map expands as mathematicians and computer scientists develop new algorithms and techniques, but they still operate within the same computing model and limitations. It’s like exploring new terrains on land, finding new paths and strategies, but always staying within the realm of what is already known.

On the other hand, quantum computing introduces an entirely new computational paradigm. It’s like suddenly discovering an ocean on the game map. The ocean represents the unique properties of quantum mechanics, such as superposition and entanglement, that quantum computers harness for their operations.

Quantum Computing thus will help us explore new areas of mathematics, completely out of the realm of what is already known. Revolutionary discoveries can be made in Cryptography, Algebraic Geometry, Number Theory, Quantum Simulation, Topological Quantum Computing and so much more. We shouldn’t expect our phones to have inbuilt quantum computers in the future, it’s like asking if a vehicle that’s capable of travelling in the deepest seas and the highest mountains will ever be invented. It is possible, but not exactly close to being invented or needed. 

Just as an ocean opens up vast possibilities for exploration, quantum computing opens up new horizons in computational power and problem-solving capabilities. Quantum computers can perform calculations simultaneously in parallel, thanks to superposition, and leverage entanglement to create interconnected qubits that work together. They can help us process vast amounts of data that would take years and decades by other methods, and find patterns and connections between the data that would be otherwise invisible to the human eye. 

Quantum Computing using the Laws of Quantum Physics

Quantum computing employs qubits as fundamental units of information instead of traditional bits. The distinguishing feature of this alternative system is its ability to allow for coherent superposition of ones and zeros, the fundamental digits of the binary system on which all computing is based. At the core of quantum computing lies the concept of amplitudes, which are utilized to solve computational problems. 

Amplitude amplification is used for quantum search, simulation, and machine learning. Grover’s Algorithm uses this phenomenon to search unstructured data at blinding speed. On each pass, it amplifies the amplitude of the probable solution. In the end, the item with the highest amplitude is returned with near certainty. 

Shor’s Algorithm is used to find the prime factors of a number. It uses constructive interference [Fig. 5] and quantum parallelism to find the period of the modular exponentiation function, which is used to factorize the number.

Quantum computers harness the unique properties of quantum matter because where classical computing relies on binary bits representing 1s and 0s, quantum computing encompasses 1s, 0s, and the simultaneous presence of both states. The remarkable processing power of quantum computers stems from the ability of qubits to exist in multiple states concurrently. A qubit is represented using a Bloch sphere [Fig. 6]. It is a physical representation of all possible qubit states that can help researchers pinpoint and manipulate various such states within the sphere to their advantage.

The key concepts of quantum physics being applied here are Quantum Entanglement, superposition, quantum measurement and quantum gates. Quantum computing relies on the principles of quantum physics to process and manipulate information. Here are the key ways in which quantum computing utilizes quantum physics:

1. Entanglement: Entanglement is a peculiar property of quantum physics that allows two or more qubits to become correlated in such a way that the state of one qubit is instantly related to the state of the others, regardless of the distance between them. This means that the knowledge of the state of one qubit can tell us information about the other qubit. Entanglement enables the creation of complex relationships and dependencies between qubits. It is a crucial resource in quantum computing as it can be used to perform computations in parallel, exploit quantum parallelism, and enhance the computational capabilities of quantum algorithms.

2. Superposition: Quantum computing takes advantage of superposition, a fundamental principle of quantum mechanics. Superposition allows qubits to exist in a combination of 0 and 1 states simultaneously [Fig 7]. This means a qubit can represent both states simultaneously, rather than being limited to a single state like classical bits. By leveraging superposition, quantum computers can perform calculations on multiple potential solutions simultaneously, which significantly increases their computational power.

3. Quantum Gates: Quantum gates are analogous to classical logic gates and are used to manipulate qubits. These gates operate on the quantum states of qubits, applying transformations that change their states. Quantum gates can rotate the state of a qubit, entangle multiple qubits, or perform other operations based on the principles of quantum physics. Some commonly used quantum gates are the Hadamond gate (used to put qubits into a state of superposition), Pauli gates (rotate qubits around the x, y or z axis), Phase gate (introduce a phase shift into the state of the qubit without changing its amplitude), Controlled Not gate (flips the bit of the second qubit depending on the value of the first qubit) and the Swap gate (swaps bits of both qubits).

These operations allow for constructing quantum algorithms that can solve problems efficiently.

4. Quantum Measurement: Quantum measurement is the process of extracting information from qubits by making observations. When a qubit is measured, it collapses into a definite state (either 0 or 1) with a probability determined by its superposition. Measurement introduces randomness into the computation and extracts classical information from the quantum system.

By harnessing these quantum phenomena, quantum computers can perform computations differently from classical computers. The ability to simultaneously process multiple states, exploit entanglement, and employ quantum algorithms enables quantum computers to potentially solve certain problems more efficiently, providing advantages in specific domains such as cryptography, optimization, and simulation of quantum systems.

The applications of quantum computing are vast and never-ending. From what started as a proposal by Feynman in 1982, the advancements made in quantum computing have already changed the game for so many different fields [Fig. 8] across the world. It has revolutionized and accelerated progress and has paved the way for a new era of scientific exploration and innovation. As researchers delve deeper into quantum physics and quantum algorithms, we can expect groundbreaking discoveries and novel applications that will reshape the way we approach computational problems, scientific research, and technological innovation.

Conclusion

Quantum Physics and Quantum Computing are intricately connected. Quantum Physics provides the foundational principles and phenomena that quantum computing harnesses to achieve massive computational power. Quantum computing is not just a faster version of classical computing; it represents a paradigm shift, opening up new horizons of mathematical research and computational possibilities, challenging our understanding of the universe, and propelling us into a future of limitless potential. Though we are still in the early stages of harnessing the full power of quantum computers, facing significant challenges like hardware insufficiency and scalability, there is no doubt that the progress made is remarkable and we are closer than ever to unlocking the true potential of quantum computing. 

References –

[1] Bohr Theory Image.

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Encyclopædia Britannica

https://www.britannica.com/science/physics-science/Quantum-mechanics#/media/1/458757/53743

[as accessed 5 Aug, 2023]

[2] Physics – Scientific Figure on ResearchGate. Available from: 

A Review on Quantum Computing: Qubits, Cryogenic Electronics and Cryogenic MOSFET

https://www.researchgate.net/figure/The-Bloch-sphere-provides-a-useful-means-of-visualizing-the-state-of-a-single-qubit-and_fig1_335028508

[as accessed 5 Aug, 2023]