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Quantum Computing
- 1. Quantum Computing Quantum Computing is the use of quantum-mechanical(Quantum mechanics-including quantum field theory, is a fundamental theory in physics which describes nature at the smallest – including atomic and subatomic – scales.) phenomenon to perform computation. According to Moore's law, the size of computer chips is reduced by half every 6 months. If this is the case, then the various components of the computer chip that are constantly being miniaturized will start to behave under the rules of quantum mechanics instead of the usual physics. This fundamental change of hardware has in many cases also redefined the boundaries of theoretical computer science.
- 2. •Moore’s Law: We hit the quantum level 2010~2020.
- 3. It’s fascinating to think about the power in our pocket—today’s smartphones have the computing power of a military computer from 50 years ago that was the size of an entire room. However, even with the phenomenal strides we made in technology and classical computers since the onset of the computer revolution, there remain problems that classical computers just can’t solve. Many believe quantum computers are the answer.
- 4. Forget Moore's Law — Quantum Computers Are Improving According to a Spooky 'Doubly Exponential Rate' According to Neven's Law,Named after Hartmut Neven, the director of the Quantum Artificial Intelligence Lab at Google who first noticed the phenomenon, the law dictates how quickly quantum processors are improving, or getting faster at processing calculations, relative to regular computers. And it turns out, they're gaining on ordinary computers at a spookily fast, "doubly exponential rate." That means that processing power grows by a factor of 2^2^1 (4), then 2^2^2 (16), then 2^2^3 (256), then 2^2^4 (65,536), and so on. Doubly-exponential growth is so huge, it's hard to find anything that grows so quickly in the natural world, according to Quanta. "It looks like nothing is happening, nothing is happening, and then whoops, suddenly you're in a different world,"
- 5. Quantum Properties Three quantum mechanical properties — superposition — entanglement — and interference are used in quantum computing to manipulate the state of a qubit.
- 6. Superposition It states that- any two (or more) quantum states can be added together ("superposed") and the result will be another valid quantum state ; and conversely, that every quantum state can be represented as a sum of two or more other distinct states. The principle of quantum superposition states simply that a quantum particle can exists in 2 distinct locations at the same time. According to this theory, an quantum particle can exist simultaneously in multiple states, unless the operation of measurement is made.
- 7. To drive what quantum superposition means, closely observe the short video above. The video depicts through animation, what is known as Qubits in Quantum computing. A Qubit is the basic unit of quantum information, a parallel to the Bit as the basic unit of classical information. As shown in the video, a Qubit can be both 0 and 1 at the same time, till the time it is observed. This property of the Qubit to be in a superposition of 2 states at the same time is what provides the Quantum Computers with exponential speedup when compared to Classical Computers.
- 8. Let’s take a step back from talking about Qubits and Quantum Computers. Quantum superposition is something that happens throughout nature. let me take the example of the most commonly know element on earth, water. I hope all readers have a fair idea about how the water molecules are formed. Oxygen shares it’s 2 electrons with each of the Hydrogen molecule and forms a bond with them. According to classical chemistry, this sharing means that the shared electrons reside in the vacant space between the Hydrogen and Oxygen molecules. According to Quantum scientists, this is not exactly true. The shared electrons actually exists in superposition between the Oxygen and Hydrogen molecules. This means that the shared electrons are simultaneously present in both Oxygen and Hydrogen molecules and the position of these electrons need not always be in between the 2.
- 10. Exponential speedup in Computation power One of the most studied applications of quantum superposition is the possible speedup in computation.
- 11. Consider that a quantum particle is going through this maze. Remember that a quantum particle have the unique property of being at 2 places at the same time, due to the principle of quantum superposition. So, when a quantum particle encounters various paths to take within the maze, it can decide to take all of those paths at the same time using superposition. If you think about it, this process closely resembles the paradigm of parallel computing. Due to quantum superposition, the quantum particle is able to navigate the maze in exponentially less time than the classical bit.
- 12. A classical bit, on the other hand, does not posses this magical ability of superposition. A classical bit is easier to imagine, as we can just imagine our self going through a maze. At a time, we can explore only one of the paths in the maze at a time. If the path the classical particle takes ends up in a dead end, we have to backtrack all the way back and start again by choosing a different path. As you can see, this is a time consuming process and we would lose horribly if we were to race against the quantum particle.
- 13. Entanglement Entanglement describes the relationship that exists between two or more particles that interact in a way that makes it impossible to describe each particle independently, even when the particles are separated by a large distance. Rather, measurements of the particles reveal correlations, and as such the particles must always be described as a quantum state of the whole system. Entangled particles behave together as a system in ways that cannot be explained using classical logic.
- 15. The advantages is that all qubits work together with entangled therefore we can solve any problem easily, as many combination is possible.
- 16. Interference Finally, quantum states can undergo interference due to a phenomenon known as phase. Quantum interference can be understood similarly to wave interference; when two waves are in phase, their amplitudes add, and when they are out of phase, their amplitudes cancel.
- 17. qubit qubit or quantum bit (sometimes qbit) is the basic unit of information and fundamental building block in quantum computing.
- 19. • Let N=50 that is with 50 QBITS
- 20. Quantum computing fundamentals All computing systems rely on a fundamental ability to store and manipulate information. Current computers manipulate individual bits, which store information as binary 0 and 1 states. Quantum computers leverage quantum mechanical phenomena to manipulate information. To do this, they rely on quantum bits, or qubits. qubits consists with two level they are written in the conventional Dirac—or “bra-ket’’—notation
- 21. When we say the spin of a particle is in a superposition of states, it simply means it is in a linear combination of up spin and down spin. Here is the equation in the Dirac notation. The coefficient α is called the amplitude.
- 22. Here, the up spin and the down spin states are just the basis vectors. The concept is similar to the x, y basis vectors in the law of motion in Physics. The Dirac notation |ψ⟩ is just a short form for a matrix.
- 23. |0⟩ and |1⟩ are the two orthogonal basis vectors that are encoded as: It also has a dual form written as: The math is simply matrix multiplication and linear algebra. We just shorten it with Dirac notation.
- 24. We can visualize the superposition as a point lying on the surface of a unit sphere.
- 25. • 1 qubit: a|0> + b|1> • 2 qubits: a|00> + b|01> + c|10> + d|11> • 3 qubits: a|000> + b|001> + c|010> + d|100> + e|011> + f|101> +g|110> + h|111>
- 26. Due to the nature of quantum physics, the destruction of information in a gate will cause heat to be evolved which can destroy the superposition of qubits.
- 27. Quantum Gates Quantum Gates are similar to classical gates, but do not have a degenerate output. i.e. their original input state can be derived from their output state, uniquely. They must be reversible. This means that a deterministic computation can be performed on a quantum computer only if it is reversible. Luckily, it has been shown that any deterministic computation can be made reversible.(Charles Bennet, 1973)
- 28. Simplest gate involves one qubit and is called a Hadamard Gate (also known as a square-root of NOT gate.) Used to put qubits into superposition. Quantum Gates - Hadamard
- 29. A gate which operates on two qubits is called a Controlled-NOT (CN) Gate. If the bit on the control line is 1, invert the bit on the target line. Quantum Gates - Controlled NOT
- 30. We can build a reversible logic circuit to calculate multiplication by 2 using CN gates arranged in the following manner:
- 31. A gate which operates on three qubits is called a Controlled Controlled NOT (CCN) Gate. If the bits on both of the control lines is 1,then the target bit is inverted.
- 32. Applications of Quantum Computing • Parallel computations • Artificial Intelligence • Molecular Modeling • Cryptography • Financial Modeling • Weather Forecasting • Particle Physics