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A Hunch about Quantum Computation

Rahul Gopan Rahul Gopan Follow Jan 02, 2020 · 6 mins read
A Hunch about Quantum Computation
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A Hunch about Quantum Computation

The desire that guides me in all I do is the desire to harness the forces of nature to the service of mankind Nikola Tesla

From Photoelectric effect to theory to General Relativity, an author to shaping today’s classical physics, Albert Einstein is the most prominent name in the field of science the world has ever heard. Yet, he failed to understand the quantum weirdness and went on to call it “Spooky”. Ages after, research in this field hasn’t got us any logical answers to what, why and how things work down there.

Nevertheless, applications for quantum mechanics has only hit its peek during the last decade especially in the branch of quantum information science.

When Moore’s Law hits the dot.

The exponential growth in computation power doubling every 2 years has met its end. As the law requires to pack dense integrated circuits (ICs) in a very compact space, doubling it every two years also demands the transistors to fold down to the size of a subatomic particle. As we enter the world of subatomic particle or more preferably in the quantum scales of particles, things don’t exactly work out the way we want it to.

A classical computer works on Bits which basically boils down to a transistor acting as a switch where the off state represents a 0 and the on state being a 1. While this has been the basic methodology in classical computation, a transistor at the subatomic level is not quite capable of putting up the energy barrier to block or pass electrons at will. At these scales, we are introduced to something known as Quantum Tunneling where electrons magically jumps the energy barrier and pops up on the other side. As spooky and obscure as it is, truly understanding the phenomenon of quantum tunneling is still a challenge. And so we have the villain of this story, quantum mechanics.

Knock knock, it’s Quantum Computing!

Making general computation faster and efficient was never the ideology behind quantum computation. While for checking your Instagram feeds or browsing the web or running a power hungry game is never the cup of tea for a quantum computer, it’s rather made for more complex tasks. To know the why here, let’s look into how precisely a quantum computer works.

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As previously explained, Bits are the fundamental part for classical computation. A Bit is either 0 or 1 but never both. Back to quantum computation, here we use quantum bits or qubits which are neither 0 or 1 but both! Bits are for classical computation as qubits are for quantum computation.

Qubits are in a superposition of both 0 and 1 which means it’s neither 0 or 1 unless we measure it and break the superposition. This phenomenon of superposition gives us the ability of parallel computation which is unimaginable in a classical computer. More the qubits, the more computation power a quantum computer will hold. For a quantum computer having 2 qubits, it can have 4 different states resulting in more computation power which can be calculated by 2^n where n is the number of qubits. Where a classical computer would perform a complex problem by brute forcing each possible solution, a quantum computer would check multiple solutions to the problem at once leaving the classical approach of problem solving in the dust.

The above picture is the Bloch Sphere representation of quantum states. An up spin represents 0 or |0⟩ and down spin represents 1 or |1⟩. An up spin represents 0 or |0⟩ and down spin represents 1 or |1⟩. This representation of quantum states ( |0⟩ & |1⟩ ) is known as Ket which denotes an abstract vector. While at superposition, the quantum state of a subatomic particle could have absolutely any magnitude which is uncertain and determining its state is practically impossible unless measured. This efficiency over classical computers for performing complex problem makes quantum computing our knight in shining armor.

Quantum Gates: NOT so classical

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While it’s clear that superposition and quantum uncertainty puts quantum computation ahead of the game for solving many complex problems, taking a subatomic particle to a superposition requires to have a quantum gate. Now, quantum gates don’t exactly work the same way as the ones used in classical computers except for Pauli’s Gate (similar to a NOT Gate) which we’ll be discussing in another article. Most commonly used quantum gate is the Hadamard Gate which takes a quantum state and puts it into superposition.

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Matrix representation of Hadamard Gate is given in the above picture. |0⟩ and |1⟩ states can be represented using a column matrix. When a Hadamard Gate is applied to a qubit, it puts it into superposition which is represented by matrix multiplication of both H and qubit matrices.

When two or more qubits are passed through a Hadamard Gate, the resulting quantum states would be entangled with the other i.e., for 2 qubits, possible states are |00⟩, |01⟩, |10⟩ and |11⟩ and passing it through the Hadamard Gate would result in |00⟩ being entangled with |11⟩. Entanglement means the state of one qubit can be used to determine the state of other, in short for a subatomic particle having up spin is supposedly entangled with another qubit, the other qubit will have a down spin no matter the distance between them. Although the way quantum entanglement works is still a complete mystery to date, it is sure to hold ground breaking discoveries that’d change our communication systems forever.

Conclusion

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Quantum computing is at a stage similar to where classical computers were a few decades ago. Making a quantum computer requires its subatomic particle to be in a superconducting space so there’s minimum energy lose and preparing a superconducting space requires the temperature to be as low as 15 millikelvin which is the coldest in the universe. Quantum computers today have just a few qubits of computation power having captured the interests of companies like Google, IBM, NASA, Microsoft and many startups including a Canadian startup D-Wave.

One should understand that a quantum computer doesn’t actually compute anything. A problem is conveyed into the particle through certain frequencies and the computer observes and gives the results based on the physics that takes place. So, the challenge remains to make quantum computers more interactive so we could use it to solve any complex problems including something as complicated as simulating a chemical compound or even the universe itself.

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Rahul Gopan
Written by Rahul Gopan Follow
I'm a undergrad CS student aspiring to research on Deep Learning and its implementation on Quantum Computers. My area of interests would be Machine Learning, Quantum Computing, Geometric Deep Learning and Bayesian Deep Learning. I like to write content related to the field I’m working on with an intension of making the general public aware of what’s going on in the field.