All you need to know about Quantum Technology part I

This is a 2-part article, and here is the link to the second part.?

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Why this paper??

Richard Feynman, one of the most brilliant physicists of the 20th century, once said: “if you think you understand quantum mechanics, you don’t understand quantum mechanics”.??

Quantum physics is everywhere. Without it, you would probably not be able to read this article; there would be no cellular phones or tablets, nor personal computers. These useful devices are made up of billions of transistors that leverage quantum physics. In fact, over the last decades, technology has made it possible to assemble such equipment as we have managed to build transistors no bigger than a few nanometers (in comparison, the size of a hydrogen atom is 0.12 nanometers).?

Fortunately, in this article we will only scratch the surface of the quantum mechanics principles that are needed to understand quantum computing and quantum technology in general.?

I wrote this article for personal and professional reasons. Personal, because before studying computer science, I took some physics classes in university, and the interest has never left me since (I still love listening to science podcasts on quantum physics). A few years after taking those classes, I studied in the operational research field, more specifically in combinatorial explosion. I was amazed to see that apparently easy problems like the Traveling Salesman Problem (TSP)* were actually difficult to solve when the number of towns to visit increases. Knowing that quantum computing can help really piqued my curiosity.?

Now from a professional perspective, considering that the biggest cloud platforms are now providing quantum services on-demand, and as a cloud specialist, this article gave me the opportunity to combine my personal interest and the chance to dive further in my professional field.??

After reading many articles and watching countless videos on the topic, I ended up in situations where the information was either too simplistic and useless or extremely detailed, which in turn made it so easy to drown in mathematical equations and lose focus. I wanted to explain quantum computing and quantum technology in my own words, without equations or complex formalism.??

Even if quantum computing does only solve specific kinds of problems (especially the ones with combinatorial explosion), it might be extremely promising in a few fields like genetics, the chemical industry, or security. As we speak, quantum technology is still facing some quantum physical issues (like decoherence) that we will discuss later in this article.?

Quantum technology is indeed a complex topic that touches a lot of domains. I will try to give you a glimpse of the potential wonders that could be achieved using the quantum world.??

1. We will begin our journey with the origin of Quantum Technology.?
2. Then we will talk about key concepts of Quantum Computing, touching on physics, electronics, data, algorithms and computability, security, and cloud.?
3. Finally, we will explore potential future applications of this extraordinary technology. (Part II of this article)?

Origin of Quantum Technology?

Quantum computing is based on quantum physics, which is a theory born at the beginning of the 20th century that describes the microscopic world.??

It all started with Max Planck (and his famous constant h) and Albert Einstein (and his photoelectric effect), but these brilliant minds were quickly followed by younger talents such as Niels Bohr (and his atom model), Erwin Schr?dinger (and his cat both dead and alive at the same time), Werner Heisenberg (and his uncertainty principle), Enrico Fermi (and his paradox**), Wolfgang Pauli (and his exclusion principle) or Paul Dirac (and his anti-matter), just to name a few.??

Together, they built a model that describes atom and subatomic particles like electrons and photons and that can be used in quantum computing. The term quantum came from the fact that energy exchanges, at a subatomic level, are discontinued, dependent on the wave frequency, and come only by packages called quanta of energy.?

In the 70s, Richard Feynman, him again, thought that a quantum computer could simulate things that a classical computer could not feasibly do. An idea was born. 25 years later, even though quantum computers still did not exist, one of his students, Peter Shor, created a famous quantum algorithm that will be discussed later in this article, that gave cybersecurity a different perspective.??

In 2019, Google claimed to have reached quantum advantage with its 54-qubits Sycamore processor (53 working), which performed operations in 200 seconds, which in comparison would take a supercomputer 10,000 years to complete.??

Today, many cloud platforms provide access to quantum computing (Amazon with AWS Braket, Microsoft with Azure Quantum, IBM Cloud etc..). You can log in to their consoles and have access in a few seconds to a quantum computer that is refrigerated at a temperature close to 0K somewhere in the cloud, as if you were launching a simple virtual machine.

Key concepts in Quantum Computing?

Bit vs Qubit?

Even if classical computers are made up of transistors that could not exist without quantum physics, they still deal with classical bits which are limited to being in one state at a given time: 0 or 1. Quantum computers, in contrast, use a quantum particle and its properties to store information. This particle could be an electron, an ion, or a photon to name a few.??

Superposition, entanglement and decoherence?

To understand how quantum computers work, we need to briefly describe 3 key principles that are counterintuitive and hence incredibly hard to understand. I will not go too much into details for 2 reasons. First, I simply won’t be able to as I am not a quantum physicist. Second, the goal here is to understand quantum computing, not quantum physics even if it is extremely connected. I could use some analogies (which might be wrong) to help understand tricky concepts though.?

The first principle is the superposition. You may have heard about Schr?dinger’s cat, who is both dead and alive at the same time. It is a thought experiment conducted by Schr?dinger with the help of Albert Einstein in 1935 to extend the superposition principle to the macroscopic world. Like his cat, a qubit can be in multiple states at the same time: it could be a 0, a 1 or both. This is possible because qubit states are in fact elementary particle properties (like the spin of an electron or the polarization of a photon), and those particle states can be the result of a superposition of states, each state being pondered by a certain probability.??

A direct outcome of this principle is in 1 qubit, you can store 2 states at the same time, whereas you can only store 1 with a classical bit. ?

The second principle is called entanglement. In quantum physics, each particle is described by a wave function. Schr?dinger was the first one providing the (non-relativistic) wave function of an electron. When 2 particles are entangled, it is as if they share the same quantum wave in the same ecosystem even if they are physically far from one another.??

This is where the concept of entanglement is hard to believe: no matter the distance, capturing the state of the first particle will instantly give you the state of the second one. If you are doubtful, do not worry, brilliant minds like Einstein, Podolsky and Rosen were too. In 1935, they suggested a thought experiment, known as the EPR paradox, to explain why the quantum theory must have been incomplete, as no information can travel faster than light. Einstein and his friends thought that there must have been some local hidden variables that would make the quantum model incomplete. In 1982, Alain Aspect (2022 Nobel prize winner), proved Einstein wrong with an amazing experiment leveraging mathematician Jonathan Bell’s inequalities. (https://scienceetonnante.com/2020/10/23/bell-aspect/)??

A direct outcome of this second principle is you can manipulate 2 entangled qubits as if there were one entity.?

The last principle is not really one, but more a quantum phenomenon that makes quantum technology hard to design and quantum computers hard to build. Qubits can only have a quantum behavior if they are isolated. Even the smallest interaction with another particle will cause their state to collapse. This phenomenon, called decoherence, is the loss of the quantum state of a qubit or a set of entangled qubits. Therefore, quantum computers usually need to be kept in very cold conditions (near absolute zero).?

You can manipulate your qubit (for a limited time anyway, as the decoherence is inevitable), but you will only have one chance to know if it is more likely a 0 or a 1. This last point is important: when a measurement is performed, you will have a possible result. To make sure you get the most likely result, you will have to repeat the complete process and measurement many times before being certain you have the correct answer.??

The key behind this quantum computation is to set up a quantum superposition that calculates all possible answers at once while being smartly arranged so that all wrong answers destructively interfere with each other. That way, when you measure the output of the calculation, the result of the measurement is most likely the right answer. Of course, as mentioned above, you can still measure the wrong answer, and this is why we will have to do it multiple times (which will still be faster than using a classical computer).?

The outcome of this last principle is that you cannot read the state of the qubit without losing its superposition of states.?

With these principles in mind, now imagine a system of 3 entangled qubits. The resulting system (where each qubit can have 2 states) can store 2x2x2 states. In general, N entangled qubits can store 2 power N states simultaneously, meaning that in theory, a quantum computer with 230 qubits could perform operations on 2 power 230 objects at the same time; it is probably more than the number of atoms in the Milky Way. However, building a 230 qubits computer does not necessarily mean that 230 qubits are usable due to decoherence, and some of them might be required just for error correction.?

As mentioned above, a lot of different technologies are used for qubits; among them we can mention photon polarization and the spin of electrons, but it is worth noting that Penning traps is the technology that managed to get the most entangled qubits so far.?

Quantum gates and quantum algorithms?

A quantum gate is a basic quantum circuit operating on a small number of qubits. They are the analogues for quantum computers to classical logic gates for classical computers. An algorithm can be described with quantum gates in circuit diagrams. Quantum algorithms are sometimes easier to understand in a circuit diagram than in the equivalent written matrix representation once you understand the visual conventions. For example, one the most used gates is the Hadamard gate, famously named after the French mathematician Jacques Hadamard, that operates on a single qubit and puts it equally in the 0 and 1 state i.e., if you read the qubit value, you will have a 50% chance to read a 1 and a 50% chance to read a 0. Note that unlike many classical logic gates, all quantum logic gates are reversible.?

Shor’s algorithm?

Now that we have described how the hardware works, let us look at quantum algorithms to show how we could leverage that kind of computer. It is difficult to appreciate how quantum computers can be powerful if you try to implement classical algorithms like you would do on classical computers. How can performing operations on qubits storing millions of states simultaneously help solve problems? I will take Shor’s algorithm design as an example to illustrate the relationship between quantum algorithms and quantum computers. Shor’s algorithm is used to factor huge numbers in a very efficient way.?It is famous because it was one of the first quantum algorithms, but it has serious consequences in cybersecurity.??

Quick detour by the security world??

Let us take a quick detour by the security world and especially the public key encryption area to measure the potential impact of Shor’s algorithm. Public Key cryptography is used to securely exchange information between 2 parties and is based on very simple but powerful concepts: 2 keys (one public, one private) are generated and are linked by mathematical properties.??

The public key (known by everyone) is used by the sender to encrypt secrets, and only the associated private key (only known by the receiver) can decrypt the encrypted secret. Therefore, we also refer to asymmetric keys, as it is not the same key that is used to encrypt that will be the one used to decrypt the secret.??

Thanks to Public key encryption, you can securely buy articles on your favorite online website. Your browser retrieves from the website the public key that will be used by your browser to encrypt a (symmetric this time) key that will be used to encrypt all your messages by both parties later. The website receives the encrypted symmetric key that can only be decrypted by the private key. This process called key negotiation is performed every 300 seconds.?

The most widely used public-key cryptosystem is RSA, built in 1977 and named after its creators Rivest, Shamir and Adleman. RSA key pairs generation uses the product of 2 large prime numbers which is, as we will explain, a one-way operation. This product participates in mathematical transformations to get the 2 keys. Even though it is part of the public key and is no secret, the 2 large prime numbers cannot (must not) be known as they participate in the private key generation as well (i.e., if you can retrieve from the product the 2 large prime numbers, then the private key is no longer private, and your cryptosystem is at risk).??

In computational complexity theory, factoring the product of 2 large prime numbers, also known as prime factorization, is in the class NP of problems (NP is the set of decision problems for which the problem instances where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine). In practice, prime factorization is very hard to perform. For a long time, mathematicians suspected that maybe this problem, like the TSP, belonged in the class NP-complete, which would have been very convenient as we know that if P!=NP (The P versus NP problem is a major unsolved problem in theoretical computer science), no polynomial algorithm exists to efficiently solve prime factorization. In short, RSA cryptography should be safe as we do not have an efficient way to perform prime factorization, even though it has never been proven that it is a NP-complete problem. It is scary to think that most of our cybersecurity relies on a method that is not mathematically proven to be difficult to solve, and yet it has been working all this time.??

Let us go back to Shor’s algorithm.?

Shor’s algorithm was a game changer as its complexity is polynomial and then could efficiently retrieve the 2 large prime numbers from the product. In fact, mathematicians think that it belongs to a new class of problems: Bounded-error Quantum Polynomial time (BQP), which is a class of decision problems solvable by a quantum computer in polynomial time. For now, we are still safe as no quantum computer is big enough to break RSA security, but it is just a matter of time before a big player in this industry releases such a computer and employs Shor’s algorithm for prime factorization.?

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?Shor’s algorithm leverages a bunch of arithmetic rules and mathematical tools to get the result. With a mix of basic algebra, arithmetic (Euclid algorithm) and the Quantum Fourier Transform (QFT), Shor managed to efficiently solve the prime factorization problem.??

What is interesting though is the link between arithmetic properties and qubits properties. With a quantum computer, you can store a bunch of guesses, all at once, you may want to try to satisfy your arithmetic rules. From all those guesses, you choose one that hopefully highlights a certain period that is crucial in the factorization process. To extract this period from the qubits, you use the QFT that will be applied to the different wave functions that describe the superpositions of states. Because of the mathematical properties of the QFT, the wrong answers will destructively interfere with each other, leaving the resulting wave function as the answer to most likely be right.?

The takeaway here is that mathematical transformations are applied to physical waves, and the resulting wave is the most likely correct answer. Obviously, the measurement (hence the complete process as you can measure only once) must be repeated many times to make sure you get the correct answer (keep in mind the resulting wave function gives you a distribution of possible qubits states, pondered with different coefficients).?

We now conclude the first part of this article that was meant to give you an overview of quantum computers, and how they differ from classical computers. In the second part, we will focus more on quantum technology in general, diving into quantum key distribution, quantum teleportation and other exciting quantum magic. Here is the link to part II where references are available.?

Notes?

* Traveling Salesman Problem (TSP) is a problem where a salesman is asked to find a way to visit a list of towns each only once and to come back home, knowing that the length of his travel must be less than a given number. This problem, as simple as it may appear, gets harder to solve as the number of towns grows. TSP is widely used in the industry to optimize the manufacturing of integrated circuits.??

** Fermi’s paradox has nothing to do with quantum mechanics, but I found it funny to refer to it. Fermi won the Nobel Prize in physics in 1938 for his work on radioactivity induced by neutron bombardment.