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Before we get into quantum machine learning, we need to be familiar with the fundamentals of quantum mechanics.

The Evolution of Quantum Mechanics and Computing

To really grasp the incredible potential of quantum machine learning, we need to take a step back and look at where it all began – quantum mechanics. Back in the early 20th century, this revolutionary framework emerged, shedding light on how matter and energy behave at the tiniest scales. Incredible minds like Niels Bohr, Albert Einstein, and Richard Feynman came up with theories and carried out experiments that shook up our classical understanding of physics.

The notion of quantum computing sprouted from the realization that we could leverage quantum mechanics to process information in mind-boggling ways, far beyond what classical computers could ever do. As we moved into the late 20th century, visionaries like David Deutsch and Richard Feynman were already laying down the fundamental principles of quantum computation.

Classical Bits

In classical computing, the bit is the fundamental unit of data. It can be thought of like a light switch: it can either be in the “off” position (0) or the “on” position (1). Every operation in classical computing, from running a simple calculator to rendering graphics in the latest video games, breaks down into a series of changes in these binary states. This binary system is a foundation of all classical computation, from simple arithmetic to complex algorithms.

Quantum Bits (Qubits)

Qubits, by contrast, aren't limited to just two states. They leverage principles from quantum mechanics, the most foundational and (admittedly) strangest of physics realms.

The most crucial quantum principle here is superposition. As mentioned, it allows a qubit to exist in a combination of both the 0 and 1 states simultaneously. Imagine our light switch analogy: instead of just “on” or “off,” the light can be any level of brightness in between, depending on the probability amplitude of each state.

But there's an essential twist: when you measure a qubit that's in superposition, it collapses to one of the two states, 0 or 1, based on their probability amplitudes. Before measurement, a qubit in superposition might lean more towards 0 or more towards 1, but you won't know for sure until you observe it. So while a qubit in superposition embodies a continuum of possibilities, measurement forces a definite outcome.

A set of two classical bits can be in one of four possible configurations at any given time: 00, 01, 10, or 11. However, two qubits can exist in a superposition of all these four states at once. As the number of qubits increases, this parallelism grows exponentially.

Quantum Parallelism: The Powerhouse

At this point, you might be asking, why does superposition matter? The power of superposition is computational parallelism. Due to the superposition property of qubits, a quantum computer can process an exponentially large number of possibilities simultaneously. For instance, while 3 bits can represent any one of 8 possible combinations at a time (from 000 to 111), 3 qubits can represent all 8 combinations at once.

To get a better picture of this, here is an analogy, imagine you are responsible for managing a massive library with an unimaginably vast collection of books. Each book represents a potential solution to a complex problem, and your goal is to find the one specific book that holds the answer you're seeking.

In the classical library (classical computing), you have a team of librarians (representing bits) who search for the right book one by one. Each librarian can look at only one book at a time, and they need to examine all the books sequentially until they find the one that contains the answer.

Now, in the quantum library (quantum computing), you have a team of special librarians (representing qubits) with a unique ability. These librarians can open all the books simultaneously, thanks to the superposition property of qubits. It's like they can flip through all the pages of every book at once!

Because of this quantum parallelism, the team of quantum librarians can explore all the possible books (solutions) at the same time, vastly increasing the chances of quickly finding the one that holds the solution you need. While the classical library might take an incredibly long time to find the answer, the quantum library can accomplish the task in a fraction of the time.

This ability to search through the vast collection of solutions in parallel is what makes quantum computing highly promising, especially for problems that are beyond the capabilities of classical computers. It opens up new possibilities and accelerates the progress in various fields, including the exciting realm of machine learning, where complex optimization and pattern recognition tasks can be performed exponentially faster than classical methods.

Quantum entanglement

Another foundational principle is quantum entanglement. Quantum entanglement is a very strange, yet fundamental, phenomenon that takes place in the quantum world. It refers to the interconnectedness of quantum particles in such a way that the state of one particle cannot be described independently of the state of the other(s), no matter the distance between them.

To explain this concept, here is another analogy, imagine you and a friend have two identical mystery boxes. You both agree that, without peeking, you will each take one box and go to separate locations. The agreement is that inside the boxes are two complementary items. Let's say, a pair of shoes: one left shoe and one right shoe.

Without opening the boxes, neither of you knows which shoe you have. It's only when you open your box and find, for instance, the left shoe, that you instantly know your friend has the right one, regardless of the distance between you two. Even if you were on opposite ends of the Earth, or even in different galaxies, as soon as you open your box, the contents of your friend's box are immediately known.

In this analogy:

The mystery boxes represent the entangled qubits.

The shoes inside the boxes represent the quantum states of the particles (like spins).

The action of opening the box to reveal a shoe corresponds to measuring a qubit and collapsing it into a definite state.

The crucial point here is that the shoes (quantum states) were always complementary, but the exact nature of each shoe wasn't known until one box was opened. Similarly, in quantum entanglement, the state of one particle isn't defined until it's measured, but once it is, the state of its entangled partner becomes immediately known, even across vast distances.

But here's where the analogy deviates from quantum reality: in our shoe example, the left and right shoes were pre-determined when the boxes were separated. In quantum entanglement, the state isn't predetermined; it's only decided at the moment of measurement. This makes the instantaneous “knowledge” of the other particle's state all the more mysterious, and is why Einstein found it so “spooky.”

This property forms the backbone of many quantum algorithms and protocols. In quantum computing, it provides the basis for phenomena like quantum teleportation (the transfer of quantum states between locations) and quantum superdense coding (a method of sending two classical bits of information using only one qubit). It also forms the backbone of quantum key distribution, which could potentially provide perfectly secure communication by detecting any eavesdroppers due to changes in the entangled system.

However, it's essential to note that while entanglement can seem like it allows for faster-than-light communication, it doesn't actually violate the cosmic speed limit set by the speed of light. This is because you can't control the outcome of your measurement, and thus can't send specific information instantaneously. The correlation between entangled particles becomes apparent only when the measurement results are compared, which still requires classical communication (limited by the speed of light).

What comes next in Part 2?

In Part 2 we will explore the world of quantum algorithms and their potential to revolutionize machine learning. We will look into how researchers are harnessing quantum mechanics to achieve exponential speedups in data analysis, classification, and more. We will also discuss the challenges in developing these cutting-edge algorithms and the exciting prospects of hybrid quantum-classical models. Read AwesomeOps: Quantum Machine Learning Part 2 of 4

Quantum computing at Mentat

At Mentat, we are conducting research to discover ways to use quantum computers to train our AI models more efficiently. The goal is to train models in a matter of a few minutes, rather than hours or days. This allows us to train/update models that clients need in a reasonable amount of time.