Quantum Mechanics and Computing Primer

A lot of people have told me that they don't understand quantum physics that well. So, I wrote this primer.

I’ve struggled most of my life to understand quantum mechanics. I’m not alone. Trying to understand what it means, how it works, and how it will impact us going forward are questions asked by every physicist and quantum hobbyist. I’ve read at least 15 books on the subject, read at least a hundred articles, watched nearly a hundred videos, interviewed over a hundred quantum experts, and even wrote a book on the subject (https://www.amazon.com/Cryptography-Apocalypse-Preparing-Quantum-Computing/dp/1119618193). After decades of being head-hurtingly confused by the subject, I think I have a fairly good grasp of the basics. I’m not an expert by any means, but I can hold my own in nearly any conversation with experts on related subjects.

This is the primer I wish I would have read 30 years ago. It will summarize quantum mechanics and briefly cover quantum computers. I won’t be able to cover everything. In fact, this will be just the briefest of introductions to all those subjects. Any brief summary of handful of quantum subjects inherently does a disservice to the reader. But I promise to give you as much insight into these complex subjects as I can in these pages.

Quantum Mechanics

Everything in this world works using quantum physics -every particle, atom, and molecule. Quantum mechanics is what makes the Sun work, allows all living things including ourselves be alive, and makes up the actions that make everything every thing. When you look at a waterfall, see a bunny run, watch light hit the ground, or throw a rock, it’s all working on quantum mechanics.

The difference is that in order to see ONLY quantum properties and physics laws in a way to understand them, we must see and experiment with them at the sub-atomic level with as few particles as possible. By the time they get combined with a trillion other things (e.g. other particles, light, dust, etc.) and end up being something big enough to be seen by the naked eye (a size called macroscopic in the science world), the individual quantum properties and behaviors get lost among all the “noise”. So, in order for scientists to view, experiment, and figure out quantum behaviors, they use only single to a handful or so of individual quantum particles. Any elementary particle, such as an election or photon, readily displays quantum behaviors that can be seen (with the aid of scientific equipment) and experimented with.

Note: An elementary particle is any particle which cannot be subdivided into even smaller components.

If you’ve heard about the weirdness of quantum mechanics, it is because that much of behavior seems very strange and contrary to what we’ve previously believed. It’s so strange and weird that it’s hard to believe for most people hearing about it for the first (or sometimes hundredth) time. The truth is that we just don’t know how to appropriately describe it in the simplest possible terms, at least not yet. When we figure out how it works and why, it’s likely to be something that we understand as naturally as we understand gravity, the air we breathe, and the concept that the Earth evolves around the Sun (instead of the other way around).

But right now, we are having a hard time describing it using our current frame of reference and understanding. Imagine how the Aztecs felt and described Spanish troops invading their country in 1519. The Aztecs, never having seen guns or gunpowder, described the Spanish firearms as something akin “sticks which shoot fire”. It’s important to understand that why we don’t know how or why about a particular quantum behavior or attribute, quantum physics is among some of the most proven science in the world. When you understand the many incredible, wonderous things about quantum mechanics, it’s not speculation or theory. Someone didn’t just make up an imaginary story that we are still trying to prove. It’s really does exist, it’s been proven to exist, and it really does result in what we are seeing. We just don’t always know how or why it does it.

Quantum Mechanic Basics

There are dozens of quantum laws and attributes which can be used to explain quantum physics. They cannot all be covered here. In fact, none of the books on quantum physics in existence cover all quantum physics laws, so I’m not going to be able to cover them all here. In fact, I’m only going to cover three. But these three are fundamental to all the others and are central to all the quantum behavior which seems so different to our traditional understanding. There are at least a dozen other very, very important quantum behaviors which anyone interested in quantum physics should understand, but these three are a great starting point: quantum measurement, the observer effect, and entanglement.

Quantum Measurement

Perhaps no quantum attribute has more to do with all the other quantum strangeness that we see than how quantum behaviors and outcomes are measured. And in order to do that we need to understand how “classical”, non-quantum, traditional physics is seen, predicted, and measured. With traditional physics, if you understand all involved parts and actions, you cannot only accurately describe any outcome of the involved parts at any time, but without seeing them describe what will happen and what the answer will be every single time.

For example, you might have heard that anytime you randomly flip a coin that the coin has a 50% chance of landing on its “heads” side and 50% chance of landing on its “tails” side, and that over many, many flips, say a thousand, that the outcomes from the random flips would be 500-500 for any non-biased coin and coin flip. And this is true.

But from a classical physics perspective, if you flipped the coin the exact same way every time beginning with the same side facing up and applying the exact same upward force every time (including the same environmental conditions, wind, humidity, etc.) then the coin would land the exact same way every time. If it landed heads-side up the first time, it would land heads-side up every time. It wouldn’t be a 50-50 outcome. It would be 100% the same side every flip. In fact, it would be strange if even a single flip was a different answer. Not only that, but without seeing the coin or any apparatus, if you told any physicist all the parts involved, they would do a little math and tell you exactly what the coin flip outcome would be every time. The outcome is called “deterministic”. If A + B = C, then it will every time.

At the quantum level, the outcome of any single coin flip, even when done 100% the same way is random and always will be random. And all possible answers are the answer (known as superposition in the physics world). Even if the coin flip was performed identically every time, what side it landed on would be random, and if you asked a quantum physicist to predict the answer they would correctly say the answer is heads and tails and also heads and tails at the same time. What?

Yes, at the quantum level a measurement of anything results in a random answer and the answer is all possible answers. The answer must be one of the possible answers. But which answer it will be when measured at any particular time will always be random. Over a large number of measurements of the same thing, the random answer will still fit into a probability of possible answers. For example, if flipping a coin a bunch of times randomly results in 50% of the landings being heads and 50% of the landings being tails, then even though each individual landing’s result is random, over many tries, the “random” landings will still end up being 50-50. Quantum answers are probabilistic, not deterministic.

As another macroscopic example comparison. Suppose we were trying to determine where throwing a rock would make the rock be during a particular part of the rock’s travelled pathway. Using classical physics, if you tell me everything about the parts and actions involved in throwing the rock (e.g. the rock’s weight, physical characteristics, wind direction and speed, direction and angle the rock was thrown, and with how much force), any physicist could tell you where the rock was while being thrown, and where it was and its speed during any moment in time during the rock’s traveled pathway. At the beginning it would be near the beginning. At the end it would be near the end and landing, and everywhere else somewhere along the rock’s thrown arc leaving its origination point more and more behind as it traveled through time. And to be clear, this is also true of quantum physics at the macroscopic level of seeing a thrown rock.

But at the subatomic level, the quantum level, any single measurement results in a random answer from a setting of possible probabilities. If (incorrectly) applying those same measurements at the macroscopic, rock-throwing level, the rock could be anywhere along its pathway arc during any moment in time. If you measured the rock near the beginning of its take-off time, at the quantum level, the rock’s quantum equivalent, could be near the end of its pathway, near the beginning, or anywhere along the its pathway. In an ordered series of events, any single event could be randomly measured as first, middle, or last. And if you ask a quantum physicist where the rock is, a quantum physicist will say that it is everywhere along it’s thrown arc all at the same time. And the answer of what side a coin will land on, from a quantum physics level is that it is both heads and tails at the same time. A quantum answer is always all possible answers.

Again, don’t start thinking that thrown rocks don’t act like thrown rocks at the quantum level. Quantum physics says that the random answer must still be a possible answer from a set of possible probabilities. If you throw a rock in your front yard in the United States, it’s not going to randomly appear in someone’s backyard in China. All the other laws of physics, such as those governing motion, energy, and gravity, still apply. But of any of the possible answers, controlled by physics, any single answer can be any of the possible answers. And if you throw a rock, its possible answers at the end of its traveling time (versus at the beginning of its time of being thrown) of its pathway are far higher than the possibilities of the rock still being at the beginning of its pathway. But at the quantum level, any single measurement is not guaranteed to be at the beginning, middle, or end, when you think it should be from a classical viewpoint.

Don’t let macroscopic allegories that are often used to try and explain quantum attributes make you think that quantum particles act one way and larger things act another. That isn’t true. Everything is quantum. Everything that happens in the observable world only happens because of what happens at the quantum level. The allegories everyone, including me, uses to demonstrate a particular quantum property aren’t truly complete. Because if we described it completely and accurately, it would also always correctly describe what we see at the macroscopic level.

I, and much of the world, used to believe that the physics world was looking for some grand, unifying theory to explain how something (seemingly so strange appearing) at the quantum level ends up behaving rather ordinary and classical at the macroscopic level. But quantum mechanics is classical physics. Quantum mechanics makes the classical macroscopic things we observe happen. And if we completely understood and described all the particles and actions and all their probabilities accurately, it would absolutely explain what we see at the macroscopic observable level.

If we flipped a coin in exactly the same way every time, it would, because of quantum properties and behaviors, land the same way every time. Each individual answer would still be random from the list of possibilities, but because the coin was flipped exactly the same way each time, the list of possible probabilities ends up with the same answer. But if, at the quantum level, you measured any particular outcome of any attribute or property, it would be random from a list of possible outcomes according to their probabilities.

(Note: I’m simplifying here. It’s actually more complex than this, actually leading anyone understanding quantum physics fairly well to question what reality means. But I’m attempting to remove complexity, not add it.)

Key to understanding superposition is to understand that everything is made up electrons. An atom is made up of electrons, protons, and neutrons. Protons and neutrons make up and are located in the atom’s centered nucleus, and electrons orbit around the nucleus. But when we go to measure any electron, where it is around the nucleus or the speed it is going (they can travel at nearly the speed of light) at any particular moment in time, it cannot be predicted. We know the electron will be around a nucleus, just not where or when in time it will be in a particular place or the speed it is going. This is not because we don’t have scientific equipment accurate enough to measure an electron’s actual position and real speed around a nucleus. We do that all the time (although not both at the same time). It’s that we cannot predict exactly where around the nucleus an electron will be when we go to look for it because it’s position and speed is always random along a list of its possible probabilities. Quantum mechanics is the reason why this is so, and it leads to every other answer and part of quantum physics. Even if you don’t understand why this is important, it is THE fundamental principle that underlies the rest.

Early on in my studies, before I began to understand quantum physics well enough that it didn’t always hurt my head, I just memorized the most important laws. I didn’t understand them, but just knowing them well enough to think of them when I was learning other quantum physics properties and laws helped me mature in my understanding of quantum physics.

Any single quantum answer is a random outcome from all possible answers along a continuum of possible probabilities.

Observer Effect

To make matters stranger, whenever any quantum measurement is taken, the act of measurement or even simply observation (which is a type of “measurement”), changes the quantum answer being measured, possibly before it was measured, and definitely forever after it was measured. Before being measured, all possible quantum answers were the answer, and would be randomly presented as the answer along a list of probabilities. The act of measurement has been shown to change the answer, and quantum particles appear (we don’t know any other way of describing it right now) to change the resulting answer in the past depending being observed versus not being observed in the future. Yes, you read that right. Observing something in the future appears to change how it behaved in the past. It is as if nature cares about being observed. This isn’t speculation. This is how quantum particles act and it’s been proven over and over. We just don’t know why or how.

And after we measure a quantum answer it becomes one single answer (say heads or tails) and will never be another answer or all possible answers along a set of possible probabilities ever again. This again is fact. Before the answer is measured or observed, it is all possible answers (i.e. superposition). And when we measure it, it is only one possible (random) answer, and will never change again. This process of moving from all possible answers to one determined answer is called decoherence. When the quantum answer is in the state of all possible answers, it is called coherence. The measurement of a quantum property/answer/state decoheres the quantum thing from superposition to a final, forever state.

This is super strange to us, because in our macroscopic observable world, measuring or viewing something does not impact it unless the measurement device literally gets in the way. If we are timing a race, the racer does not change speed or position simply because we decide to use a timer to time a lap. But at the quantum world, it absolutely and always does. This particular quantum law, along with the previous section, is one of the most frustrating in the world of quantum computing. Computing is always about finding answers to problems, and according to quantum physics the answer is always random, and measuring it changes it (in the past). Yep, and that’s why quantum computing eluded us for so long and continues to challenge us as it matures.

The act of measuring something impacts it and can change its behavior in the past.

Entanglement

The last quantum behavior I will cover is entanglement. Entanglement happens when any two quantum particles meet. When they meet and “touch” they will impact the other forever more (while in their quantum states and not decohered) no matter how far apart from each other even across the universe. This is huge and has huge implications for everything. Quantum particles are meeting and touching by the trillions in every second and inch of space. Entanglement is the most natural thing that can occur in the universe. And each meeting and subsequent entanglement entangles all particles into a new (often continuously growing) linked system. From a physics and mathematical perspective, two or more entangled particles can no longer be thought of as separate entities. What one does impacts the other; and vice-versa. It’s the “butterfly effect” to the nth degree.

Let’s go back to our coin flip allegory. Any perfect random flip of any single coin is supposed to have a 50-50 shot of being heads or tails. Suppose we pulled our coin out of a pile of (entangled) coins. Entanglement says that the coin we are now flipping will be impacted by any coins it touched while in the pile. And any individual flip’s outcome will be impacted by any entangled coin from the pile; and vice-versa. So now, instead of having a 50-50 ratio from one coin, the 50-50 ratio from any and all entangled coins now becomes the overall list of probabilities.

Suppose our coin was entangled with just one other coin and both coins have a 50-50 probability of heads or tails, and you threw both coins 1000 times. Overall, the probabilities of both flipped coins would have to even out to 1000-1000. But according to entanglement theory, instead of any coin now having an individual 500-500 outcome ratio, the outcome now in charge is the larger 1000-1000, which can be obtained many different ways when involving two coins. One coin may end up being 300-700 and the other coin might be 700-300. The overall probabilities of two coins being flipped are maintained, but the individual expected results no longer have to be 500-500. This is again, simplifying the issue, but illustrates how entanglement impacts another.

Accordingly, entanglement has profound impacts of our entire reality and in particular any experiment or calculation involving them (i.e. quantum computing). In traditional computing, we are trying to use binary digits (1’s and 0’s called bits) to solve problems. Every single thing a binary computer does comes down to math as represented by 1’s and 0’s. For example, suppose we are trying to solve a math problem of 1+1. It’s easy to solve. You put a 1 in two of a computer’s CPU registers (i.e. storage area) and then tell the CPU to ADD them. The answer will be 10 in binary, which equals 2 in decimal.

In the quantum computing world, we want to do the same thing. We want to place 0’s and 1’s (and sometimes 0’s and 1’s at the same time…but more on that later below) in registers, perform math calculations and get answers. In order to do this, we need to make sure our 1’s stay 1’s and our 0’s stay 0’s. But in the quantum computational world, if any of our 1’s and 0’s entangles with any unattended others, they are now forever intertwined with the others, slightly impacting each other in some way. So, in the quantum world, I may want to place a 1 in one quantum register and a 1 in another quantum register, but if either is entangled with any other quantum particle outside of the registers, you can’t be guaranteed that they won’t change or be impacted by the other particle (which wasn’t intended to be part of the calculation). It’s not as easy to add 1+1 when there may be another…even trillions of other things impacting them that are not easily seen or known.

Because of this, all quantum computing manufacturers struggle to create their 1’s and 0’s and keep them from entangling with any other particles. Remember, entanglement is natural and what will happen if they meet any other particles. Early on they tried placing individual 1’s and 0’s into vacuum boxes with no other particles. Turns out that the sides of the box “randomly” emit quantum particles (i.e. photons), which will entangle with the desired 1’s and 0’s. Quantum computing manufacturers use a variety of methods to prevent premature entanglement. One way is to suspend quantum particles using magnetic fields, so there are no “sides” to emit random photons. The most popular way is to supercool the quantum computing components to near -460F (aka 0 Kelvin). Turns out that under very cold conditions, less random quantum particles are running around entangling with the desired and watched quantum particles that are to be used in computations. So, you’ll see most quantum computers (at least today), being associated with supercooling refrigeration apparatus. Even then, the random quantum particles are showing up all the time and entangling before the computing can be done.

Before the desired 1’s and 0’s gets prematurely entangled with any other non-desired quantum particles, the quantum computer and its bits are considered in a state of coherence. After any random entanglements start to happen, it gets very difficult to disassociate the effects of the additional random quantum particles away from the original intended to be watched quantum particles. Imagine you drop a drop of dyed, colored, water into an ocean. You might be able to follow it for a few seconds, but pretty quickly that single drop is going to disperse across a very large oceans and the ability for your eye (or any scientific machine) to follow it will become impossible quickly.

Once this happens, and the measurers lose measurement control over the original quantum particles, the quantum computer is said to be in a state of decoherence. Decoherence is the point in time in which individually watched quantum particles are lost to the “noise” of a bunch of unwanted quantum particle effects. The quantum particle didn’t change physical states from cohered to decohered or go from entangled to unentangled. We humans and all our machines simple could not keep track of the original quantum particle we were trying to track.

Decoherence happens anytime we measure any quantum particle. The particle itself ends up getting entangled with the measurement device, even if that “measurement device” is your eye. In order for you to see something (even the value of a reading on a scientific measuring machine that is doing the actual measuring), billions of photons have to hit the object or near the object and bounce into your eyeball. In your eye the photon hits photoreceptors, both chemical and electrical, and the photon (and its energy) is absorbed into your body.

And quantum physics says anything that measures a quantum particle changes the quantum object being observed or measured, and sometimes (if not all the time) in what looks like the past. Yes, quantum mechanics seems very strange, and what I’ve shared is only 3 of the many dozens of laws. There are many others just as strange seeming, but the three I’ve shared here are the most important for understanding quantum computers. In the future we are likely to better figure out the why and how of quantum physics, to go along with the what. And when we do, what we discover will explain everything. It won’t seem strange anymore. It will be natural. The only thing that will seem strange is our previous (incorrect) understandings of how we thought the world worked.

Quantum Computers

The first quantum computer was created in 1998. Since then we’ve made over a hundred different quantum computers, using dozens of different methods. Most have less power than your wristwatch or cell phone. Most cannot solve math that your child could solve using a pencil and paper. But that’s all getting ready to change soon.

Quantum computers work using quantum particles and properties. So, too, do traditional, classical computers (everything works using quantum), but they don’t use quantum particles and properties to compute and store information. Traditional computers use binary digits (bits), 1’s or 0’s, to compute. Each bit can only be two possible things (a 1 or a 0), but only one thing at one time.

Quantum computers use quantum bits (abbreviated as qubits or qbits). A qubit is an attribute of a quantum particle (usually an electron or photon) that can be used to represent a 1 or a 0. That attribute can be any quantum attribute, but in practice, so far, it tends to be spin, charges, and polarization (these won’t be covered here). But let’s suppose a qubit is represented by a “up spin” or “down spin” of an electron, equating to a 1 or a 0, respectively.

Because of quantum superposition, although a single qubit can still only be measured as a 0 or a 1 (decohered state), while it is in its quantum cohered state, it can be a 1 and a 0. It can be both things at once. This gives a qubit a distinct advantage over a bit. For example, a 8-bit byte can represent 256 different bytes, but it can only represent 8 individual characters at any one time. 8-qubits can represent 256 different bytes at one time during calculations. Superposition and qubits add up fast.

A few thousand qubits (4000 to 9000) can break almost any cryptographic secret protected by today’s modern public key encryption. It has been stated that less than 100 stable qubits could store all the information about the universe from the Big Bang until today. That’s the power of superposition. And we are likely to have millions of stable qubits within the next decade.

There are dozens of vendors, including D-Wave, Google, IBM, Microsoft, and entire countries (e.g. China, UK, Russia, etc.) creating quantum computers and devices. We have had commercially sold quantum devices, like key distribution devices and random number generators, sold since the early 2000’s. They are fairly plentiful and fairly cheap. Working quantum computers are a different matter. Most are fairly rudimentary, expensive, require extreme environmental conditions, and not that powerful. But as previously stated, that’s getting ready to change soon.

Most quantum computers require super cold temperatures, just above -460F, so that their qubits will stay cohered long enough to do the needed calculations before decohering into the final result. And most computing qubits only last a few milliseconds before decohering, but several vendors are working on quantum technologies, such as ion traps and majorana fermions, which seem to work just fine in near normal conditions and can hold coherence for many minutes (if not longer). There is a race and tens of billions of dollars being spent by the US and China to see who gets to the most powerful supercomputer first. There after over a 100 different teams all using different quantum computers and techniques to make them into something very useful. All that competition will only serve to get us to better quantum computers faster.

Quantum Supremacy

Quantum supremacy is the moment in time when a quantum computer can do something that a traditional binary computer cannot. It can be achieved in terms of raw computational speed or performing even an otherwise “ordinary” math problem that a classical computer simply isn’t capable of (i.e. it doesn’t have to be speed related). Several companies (including Google and IBM) and China who claim they will reach quantum supremacy before the end of 2019 (https://www.wired.com/story/google-alibaba-spar-over-timeline-for-quantum-supremacy/). Google even released a report on 9/20/19 and then retracted it claiming they had already reached quantum supremacy. (https://gizmodo.com/google-says-its-achieved-quantum-supremacy-a-world-fir-1838299829 and https://fortune.com/2019/09/20/google-claims-quantum-supremacy). There is great speculation about why the report was released and suddenly retracted. So, we (the royal we as in humanity) have already reached quantum supremacy or will so reach it.

Once we reach quantum supremacy, the computing world will never be the same again. What we can do with them is both good and bad. We will get better modeling of nature, weather, chemicals, medicine, and traffic management. We will get things we cannot even imagine right now. It’s like trying to wonder what incredible things we will get from the Internet back in the early 1980’s when all we had was dial-up modems and local bulletin board systems (BBS). Back then, we got amazed when you sent an email (wonderous by itself) to someone around the world and it returned by the next day! Back then I used to set up entire company networks on 30 MB hard drives. It took a full day to format them (look up what that means if you don’t know), and I subdivided those huge, expensive drives into three separate 10 MB partitions: 10 MB for the network operating system, 10 MB for applications, and 10 MB for user’s data. We fit an entire company’s everything onto 20 MBs. Yeah, and modems cost $1000, sent data at only 9600 characters a second, and to use a modem line to a college computer system cost $60/minute. What we are going to see from quantum computing just can’t be imagined completely right now.

On the computer security side, quantum computers will crack or weaken most existing traditional cryptography solutions. And it will also give us harder to break and eavesdrop on encryption.

Now for the blatant plug. Nothing is free. <grin> I cover all of this and more, in far more detail, in my latest book (my 11th), called Cryptography Apocalypse (https://www.amazon.com/Cryptography-Apocalypse-Preparing-Quantum-Computing/dp/1119618193).

The chapter list is:

Part I – Quantum Computing Primer

Chap. 1- What is Quantum?

Chap. 2 – Quantum Computers

Chap. 3- How Can Quantum Computing Break Today’s Cryptography?

Chap. 4- When Will the Quantum Break Happen?

Chap. 5- What Will A Post-Quantum World Look Like

Part II - Preparing for the Quantum Break

Chap. 6- Quantum Resistant Cryptography

Chap. 7 - Quantum Cryptography

Chap. 8- Quantum Networking

Chap. 9- Preparing Now

Appendix of Quantum Information Sources

If you want to know more about any of these subjects, consider purchasing my book.

If you have any questions or comments, feel free to email me at [email protected] or [email protected].