Understanding Quantum Computers with Quantum Physics

The Development of Quantum Computers
The Development of Quantum Computers

Here, inside this refrigerator, at a temperature just one click above absolute zero, is a quantum computer in isolation from the rest of the universe. This emerging technology represents the promise of the future and has the potential to revolutionize our lives with its turbocharged computing. But quantum computers aren't next-generation supercomputers, they're something else entirely. Before we start talking about its potential applications, we need to understand the fundamental physics that drives quantum computing theory. We will have to dive into another dimension that is smaller and more alien than anything we intuitively understand. To the subatomic world of quantum mechanics.

Feynman's View of the Quantum World

Feynman's Idea In the 1980s, one of the most important physicists of the 20th century faced a major roadblock. Richard Feynman opened up a window into the quantum universe. But quantum systems are inherently fragile and the information they contain is hidden from us. Since Feynman could not directly observe quantum phenomena, he wanted to design a simulation. It quickly became clear that his computer was unfit for the task.
As he added particles to the quantum systems he modeled, the cost of computation began to increase exponentially. Feynman concluded that classical computers cannot scale fast enough to keep up with the increasing complexity of quantum computing. Then he made a breakthrough.
What if he could design a vehicle made of his own quantum elements?
This instrument would work according to the laws of quantum physics, making it an excellent way to probe the mysteries of the quantum world. The idea of ​​a quantum computer was born. Feynman imagined this and began to build a bridge between quantum physics and computer science.

How Quantum Computations Work

To understand how quantum computing works, it's crucial to first start by understanding what makes it quantum.
That means we need to talk about what's at the heart of quantum physics: a concept called amplitude. Here's what the classic rules of probability for getting a coin tell us if we flip a coin 20 times. We add up the probabilities for all possible outcomes that result in the text.
It's just common sense. But common sense does not rule the quantum universe. Before you measure a subatomic particle, you can think of it as a probability wave that exists in a kind of black box - a quantum system with very different chances of being in many different places.
Quantum mechanics, in essence, is a change in the rules of probability. That's where the power of quantum computing comes from - these probability rules that are different from what we're used to. Amplitudes are closely related to probabilities. But these are not possibilities. One important difference is that probability is always a zero to one number. But the amplitudes are complex numbers. And that means they follow different rules.
So if I want to know the total amplitude of something, I need to sum up the amplitudes of all the different ways that thing can happen.
But when I add up the amplitudes, I see something new, which is that a particle can reach a certain place with a positive amplitude in one direction and a negative amplitude in another. And if that happens then these two amplitudes can cancel each other out so the total amplitude is zero and that means that thing will never happen.
So the amplitudes depend on the probability that you actually see something when you look over there. This is a central thing quantum mechanics says about the world: The way you describe a physical system is a list of amplitudes. And the way a physical system changes over time is through a linear transformation of these amplitudes and some variation in these amplitudes.

How Can Quantum Computers Use Amplitudes to Quantum Storage and Processing of Information?

This is a qubit. It is the basic unit of computation in quantum computing. Qubits are like bits in a classical computer, but with one very important difference.
A bit is binary—it stores information in strings of binary digits that can only be 0 or 1. But qubits are made of subatomic particles, so they work according to subatomic logic. Qubits can be 0, 1, or what we call a linear combination of 0 and 1.
This fluid amplitude combination is at the heart of quantum computing. Before measuring a qubit, it resides in a state called superposition. You can think of it as a quantum version of a probability distribution, where each qubit has some amplitude to be 0 and some amplitude to be 1. Superposition is why quantum computers can store and manipulate vast amounts of data compared to classical computers.
When two or more qubits are in this closed state of overlap, they relate to each other through the phenomenon of entanglement.
This means that when we measure them, their final results are mathematically related.
Quantum entanglement is the word we use for characteristic correlations between parts of a quantum system that differ in ordinary experience from the correlations we normally encounter in the classical world.
You can think of it like a book. When you look at the pages one at a time, you don't see any information – you see random gibberish as the information is encoded not in individual pages but in correlations between them. And to read the book, you must collectively observe many pages at the same time.

However, this is extremely expensive if you want to describe very complex cases using ordinary bits. Imagine you have a primitive 10-qubit computer. It can store 2^10 values ​​in parallel. You need 16 kilobytes or 16 thousand bits to describe this mixed configuration with a conventional computer. Expand it to a system of 500 qubits and you now need more classical bits than atoms in the known universe. This is exactly what Feynman meant when he said that classical computers are not scalable to simulate quantum mechanics. For a quantum computer to be of any use, you have to measure the information from the qubits to get an output. The problem is that when a quantum system is measured, it collapses into a classical state. If you look at a qubit, let's say, is it zero or one, then you collapse its state, right? You force it to decide whether it will be zero or one.

Anything carries information about whether that qubit is zero or one; for example, if this information were recorded in a radiation escaping a quantum computer, then the effect on the qubit would be as if someone had measured it to see if it was 0 or 1.
When you look at the system, the amplitudes become probabilities. To extract a response from the quantum system that is not merely the result of random probability, such as the flip of a coin, we need to use interference.

The interference can be seen in classical physics. When waves in a pond crash into each other and one wave is above the surface and the other wave is below the surface and cancel each other out. Interference is what amplitudes do when you add them in. If something can happen with half amplitude in one direction and minus half amplitude the other way, then the total amplitude for it to happen will be zero.
This is what you do in the famous double-slit experiment. You close one of the ways and then you realize that what never happened before can happen now. This is a quantum algorithm.

Scientists can exploit interference by constructing a deterministic array of qubit gates. These qubit gates cause a constructive aggregation of amplitudes. This means that they are mathematically guaranteed to increase the probability of seeing one of the correct answers.
This is a quantum algorithm. Scientists can exploit interference by constructing a deterministic array of qubit gates.
These qubit gates cause a constructive aggregation of amplitudes. This means that they are mathematically guaranteed to increase the probability of seeing one of the correct answers.

Quantum Algorithm

Scientists can exploit interference by constructing a deterministic array of qubit gates. These qubit gates cause a constructive aggregation of amplitudes. This means that they are mathematically guaranteed to increase the probability of seeing one of the correct answers.
When you don't know in advance which answer is correct, you might ask, how can you concentrate all this on the correct answer?
This is exactly why it's so difficult to design quantum algorithms, and we have a whole field of studies studying it for decades.
Since 1994, there have been several major breakthroughs in quantum algorithms with theoretical applications in areas such as cybersecurity and search optimization. But according to most experts in the field, quantum computers will likely be useful for what they were born to do – when a nosy physicist wonders about the deep structure of our world. I find quantum computing exciting as a way to explore physics. Now, whether this will save anyone money - whether there will be practical applications in the short term - is still a very open question.
But it's an exciting time, at least for physicists. The truth is I believe the most important application of quantum computers is something we don't know yet.
I'm sure once we have a quantum computer to play with, we'll find great applications that we haven't foreseen yet.

source: quantamagazine.org

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