## Quantum Entanglement for Toddlers

I wrote a book a while back called Quantum Entanglement for Babies. But, now all those babies are grown into toddlers! I’ve been asked what is next on their journey to quantum enlightenment. Surely they have iPads now and know how to scroll, and so I give you Quantum Entanglement for Toddlers, the infographic!

Below is a lower-res version. Here is a high-res version (5MB). Contact me for the SVG.

## My Speech to 500 Australian Teenage Schoolboys About Mathematics

I suppose I should start with who I am and what I do and perhaps why I am here in front of you. But I’m not going to do that, at least not yet. I don’t want to stand here and list all my accomplishments so that you may be impressed and that would convince you to listen to me. No. I don’t want to do that because I know it wouldn’t work. I know that because it wouldn’t have worked on me when I was in your place and someone else was up here.

Now, of course you can tell by my accent that I wasn’t literally down there. I was in Canada. And I sure as hell wasn’t wearing a tie. But I imagine our priorities were fairly similar: friends, getting away parents, maybe sports (in my case hockey of course and yours maybe footy), but most importantly… mathematics! No. Video games.

I don’t think there is such a thing as being innately gifted in anything. Though, I am pretty good at video games. People become very good at things they practice. A little practice leads to a small advantage, which leads to opportunities for better practice, and things snowball. The snowball effect. Is that a term you guys use in Australia? I mean, it seems like an obvious analogy for a Canadian. It’s how you make a snowman after all. You start with a small handful of snow and you start to roll it on the ground. The snow on the ground sticks to the ball and it gets bigger and bigger until you have a ball as tall as you!

Practice leads to a snowball effect. After a while, it looks like you are gifted at the thing you practiced, but it was really just the practice. Success then follows from an added sprinkling of luck and determination. That’s what I want to talk to you about today: practice.

I don’t want to use determination in the sense that I was stubbornly defiant in the face of adversity. Though, from the outside it might look that way. You can either be determined to avoid failure or determined to achieve some objective. Being determined to win is different from being determined not to lose.

There is something psychologically different between winning and not losing. You see, losing implies a winner, which is not you. But winning does not require a loser, because you can play against yourself. This was the beauty of disconnected video games of 80’s and 90’s. You played against yourself, or maybe “the computer”. That doesn’t mean it was easy. I’ll given anyone here my Nintendo if they can beat Super Mario Bros. in one go. (I’m not joking. I gave my children the same offer and they barely made it past the first level). It was hard and frustrating, but no one was calling you a loser on the other end. And when you finally beat the game, you could be proud. Proud of yourself and for yourself. Not for the fake internet points you get on social media, but for you.

I actually really did want to talk to you today about mathematics. What I want to tell you is that, when I was your age, I treated mathematics like a video game. I wanted to win. I wanted to prove to myself that I could solve every problem. Some nights I stayed up all night trying to solve a single problem. You know how they say you can’t have success without failure? This is a perfect example. The more you fail at trying to solve a maths problem, the more you understand when you finally do solve it. And what came along with failing and eventually succeeding in all those maths problems? Practice.

Well I don’t know much about the Australian education system and culture. But I’m guessing from Hollywood you know a bit about highschool in North America. I’m sure you know about prom, and of course about Prom King and Prom Queen. What you may not know is that the King and Queen’s court always has a jester. That is, along with King and Queen, each year has a Class Clown — the joker, the funny guy. I wasn’t the prom king, or queen. But I did win the honour of class clown.

When I finished highschool, I was really good at three things: video games, making people laugh, and mathematics. I promise you, there is no better combination. If there was a nutrition guide for the mind, it would contain these three things. Indeed, now more than ever before, you need to be three types of smart. You need to be quick, reactive, and adaptive — the skills needed to beat a hard video game. You need emotional intelligence, you need to know what others are thinking and feeling — how to make them laugh. And finally you need to be able to solve problems, and all real problems require maths to solve them.

There are people in the world, lots of people — billions, perhaps — who look in awe at the ever increasing complexity of systems business, government, schools, and technology, including video games. They look, and they feel lost. Perhaps you know someone that can’t stand new technology, or change in general. Perhaps they don’t even use a piece of technology because they believe they will never understand how to use it.

You all are young. But you know about driving, voting, and paying taxes, for example. Perhaps it looks complicated, but at least you believe that you can and will be able to do it when the time comes. Imagine feeling that such things were just impossible. That would be a weird feeling. You brain can’t handle such dissonance. So you would need to rationalise it in one way or another. You’d say it’s just not necessary, or worse, it’s something some “other” people do. At that point, for your brain to maintain a consistent story, it will start to reject new information and facts that aren’t consistent with your new story.

This is all sounds far fetched, but I guarantee you know many people with such attitudes. To make them sound less harmful, they call them “traditional”. How do otherwise “normal” people come to hold these views? It’s actually quite simple: they fear, not what they don’t understand, but what they have convinced themselves is unnecessarily complicated. I implore you, start today, start right now. Study maths. It is the only way to intellectually survive in a constantly changing world.

Phew that was a bit depressing. Let me give you a more fun and trivial example. Just this weekend I flew from Sydney to Bendigo. The flight was scheduled to be exactly 2 hours. I was listening to an audiobook and I wondered if I would finish it during the flight. Seems obvious right? If there was less than 2 hours left in the audiobook, then I would finish. If not, then I would not finish. But here’s the thing, audiobooks are read soooo slow. So, I listen to them at 1.25x speed. There was 3 hours left. Does anyone know the answer?

Before I tell you, let me remind you, not many people would ask themselves this question. I couldn’t say exactly why, but in some cases it’s because the person has implicitly convinced themselves that such a question is just impossible to answer. It’s too complicated. So their brain shuts that part of inquiry off. Never ask complicated questions it says. Then this happens: an entire world — no most of the entire universe — is closed off. Don’t close yourself off from the universe. Study maths.

By the way, the answer. It’s not the exact answer but here was my quick logic based on the calculation I could do in my head. If I had been listening at 1.5x speed, then every hour of flight time would get through 1.5 hours of audiobook. That’s 1 hour 30 minutes. So two hours of flight time would double that, 3 hours of audiobook. Great. Except I wasn’t listening at 1.5x speed. I was listening at a slower speed and so I would definitely get through less than 3 hours. The answer was no.

In fact, by knowing what to multiple or divide by what, I could know that I would have exactly 36 minutes left of the audiobook. Luckily or unluckily, the flight was delayed and I finished the book anyway. Was thinking about maths pointless all along? Maybe. But since flights are scheduled by mathematical algorithms, maths saved the day in the end. Maths always wins.

How about another. Who has seen a rainbow? I feel like that should be a trick question just to see who is paying attention. Of course, you have all seen a rainbow. As you are trying to think about the last time you saw a rainbow, you might also be thinking that they are rare — maybe even completely random things. But now you probably see the punchline — maths can tell you exactly where to find a rainbow.

Here is how a rainbow is formed. Notice that number there. That angle never changes. So you can use this geometric diagram to always find the rainbow. The most obvious aspect is that the rainbow exits the same general direction that the sunlight entered the raindrop. So to see a rainbow, the sun has to be behind you.

And there’s more. If the sun is low in the sky, the rainbow will be high in the sky. And if the sun is high, you might not be able to see a rainbow at all. But if you take out the garden hose to find it, make sure you are looking down. Let me tell you my favourite rainbow story. I was driving the family to Canberra. We were driving into the sunset at some point when I drove through a brief sun shower. Since the sun was shining and it was raining, one of my children said, “Maybe we’ll see a rainbow!”

Maybe. Ha. A mathematician knows no maybes. As they looked out their windows, I knew — yes — we would see a rainbow. I said, after passing through the shower, “Everyone look out the back window and look up.” Because the sun was so low, it was apparently the most wonderful rainbow ever seen. I say apparently because I couldn’t see it, on account of me driving. But no matter. I was content in knowing I could conjure such beauty with the power of mathematics.

I could have ended there, since I’m sure you are all highly convinced to catch up on all your maths lessons and homework. However, since I have time, I will tell you a little bit about what maths has enabled me to get paid to do. Namely, quantum physics and computation. Maybe you’ve heard about quantum physics? Maybe you’ve heard about uncertainty (the world is chaotic and random), or superposition (things can be in two places at once and cats can be dead and alive at the same time), or entanglement (what Einstein called spooky action at a distance).

But I couldn’t tell you more about quantum physics than that without maths. This is not meant to make it sound difficult. It should make it sound beautiful. This is quantum physics. It’s called the Schrodinger Equation. That’s about all there is to it. All that stuff about uncertainty, superposition, entanglement, multiple universes, and so on—it’s all contained in this equation. Without maths, we would not have quantum physics. And without quantum physics, we would not have GPS, lasers, MRI, or computers — no computers to play video games and no computers to look at Instagram. Thank a quantum physicist for these things.

Quantum physics also helps us understand the entire cosmos. From the very first instant of the Big Bang born out of a quantum fluctuation to the fusing of Hydrogen into Helium inside stars giving us all energy and life on Earth to the most exotic things in our universe: black holes. These all cannot be understood without quantum physics. And that can’t be understood without mathematics.

And now I use the maths of quantum physics to help create new computing devices that may allow us to create new materials and drugs. This quantum computer has nothing mysterious or special about it. It obeys an equation just as the computers you carry around in your pockets do. But the equations are different and different maths leads to different capabilities.

I don’t want to put up those equations, because if I showed them to even my 25 year-old self, I would run away screaming. But then again, I didn’t know then what I know now, and what I’m telling you today. Anyone can do this. It just takes time. Every mathematician has put in the time. There is no secret recipe beyond this. Start now.

## The minimal effort explanation of quantum computing

Quantum computing is really complicated, right? Far more complicated than conventional computing, surely. But, wait. Do I even understand how my laptop works? Probably not. I don’t even understand how a doorknob works. I mean, I can use a doorknob. But don’t ask me to design one, or even draw a picture of the inner mechanism.

We have this illusion (it has the technical name in the illusion of explanatory depth) that we understand things we know how to use. We don’t. Think about it. Do you know how a toilet works? A freezer? A goddamn doorknob? If you think you do, try to explain it. Try to explain how you would build it. Use pictures if you like. Change your mind about understanding it yet?

We don’t use quantum computers so we don’t have the illusion we understand how they work. This has two side effects: (1) we think conventional computing is generally well-understood or needs no explanation, and (2) we accept the idea that quantum computing is hard to explain. This, in turn, causes us to try way too hard at explaining it.

Perhaps by now you are thinking maybe I don’t know how my own computer works. Don’t worry, I googled it for you. This was the first hit.

Imagine if a computer were a person. Suppose you have a friend who’s really good at math. She is so good that everyone she knows posts their math problems to her. Each morning, she goes to her letterbox and finds a pile of new math problems waiting for her attention. She piles them up on her desk until she gets around to looking at them. Each afternoon, she takes a letter off the top of the pile, studies the problem, works out the solution, and scribbles the answer on the back. She puts this in an envelope addressed to the person who sent her the original problem and sticks it in her out tray, ready to post. Then she moves to the next letter in the pile. You can see that your friend is working just like a computer. Her letterbox is her input; the pile on her desk is her memory; her brain is the processor that works out the solutions to the problems; and the out tray on her desk is her output.

That’s all. That’s the basic first layer understanding of how this device you use everyday works. Now google “how does a quantum computer work” and you are met right out of the gate with an explanation of theoretical computer science, Moore’s law, the physical limits of simulation, and so on. And we haven’t even gotten to the quantum part yet. There we find qubits and parallel universes, spooky action at a distance, exponential growth, and, wow, holy shit, no wonder people are confused.

What is going on here? Why do we try so hard to explain every detail of quantum physics as if it is the only path to understanding quantum computation? I don’t know the answer to that question. Maybe we should ask a sociologist. But let me try something else. Let’s answer the question how does a quantum computer work at the same level as the answer above to how does a computer work. Here we go.

How does a quantum computer work?

Imagine if a quantum computer were a person. Suppose you have a friend who’s really good at developing film. She is so good that everyone she knows posts their undeveloped photos to her. Each morning, she goes to her letterbox and finds a pile of new film waiting for her attention. She piles them up on her desk until she gets around to looking at them. Each afternoon, she takes a photo off the top of the pile, enters a dark room where she works at her perfected craft of film development. She returns with the developed photo and puts this in an envelope addressed to the person who sent her the original film and sticks it in her out tray, ready to post. Then she moves to the next photo in the pile. You can’t watch your friend developing the photos because the light would spoil the process. Your friend is working just like a quantum computer. Her letterbox is her input; the pile on her desk is her classical memory; while the film is with her in the dark room it is her quantum memory; her brain and hands are the quantum processor that develops the film; and the out tray on her desk is her output.

## ⟨B|raket|S⟩

Welcome to ⟨B|raket|S⟩! The object is to close brakets, the tools of the quantum mechanic!

Created by Me, Chris Ferrie!

2 PLAYERS | AGES 10+ | 15 MINUTES

Welcome to ⟨B|raket|S⟩! The object is to close brakets, the tools of the quantum mechanic! You’ll need to create these quantum brakets to maximize your probability of winning. But, just like quantum physics, there is no complete certainty of the winner until the measurement is made!

No knowledge of quantum mechanics is require to play the game, but you will learn the calculus of the quantum as you play. Later in the rules, you’ll find out how your moves line up with the laws of quantum physics.

## What you need

A deck of ⟨B|raket|S⟩ cards, a coin, and a way to keep score.

The instructions are here.

I suggest getting the cards printed professionally. All the cards images are in the cards folder. I printed the cards pictured above in Canada using https://printerstudio.ca. However, they also have a worldwide site (https://printerstudio.com).

You can print your own cards using a desktop printer with this file.

You can laser cut your own pieces using this file.

## Open Source

Oh, and this game is free and open source. You can find out more at the GitHub repository: https://github.com/csferrie/Brakets/.

## New papers dance!

Two new papers were recently posted on the arXiv with my first two official PhD students since becoming a faculty member! The earlier paper is titled Efficient online quantum state estimation using a matrix-exponentiated gradient method by Akram Youssry and the more recent paper is Minimax quantum state estimation under Bregman divergence by Maria Quadeer. Both papers are co-authored by Marco Tomamichel and are on the topic of quantum tomography. If you want an expert’s summary of each, look no further than the abstracts. Here, I want to give a slightly more popular summary of the work.

Efficient online quantum state estimation using a matrix-exponentiated gradient method

This work is about a practical algorithm for online quantum tomography. Let’s unpack that. First, the term work. Akram did most of that. Algorithm can be understood to be synonymous with method or approach. It’s just a way, among many possibilities, to do a thing. The thing is called quantum tomography. It’s online because it works on-the-fly as opposed to after-the-fact.

Quantum tomography refers to the problem of assigning a description to physical system that is consistent with the laws of quantum physics. The context of the problem is one of data analysis. It is assumed that experiments on this to-be-determine physical system will be made and the results of measurements are all that will be available. From those measurement results, one needs to assign a mathematical object to the physical system, called the quantum state. So, another phrase for quantum tomography is quantum state estimation.

The laws of quantum physics are painfully abstract and tricky to deal with. Usually, then, quantum state estimation proceeds in two steps: first, get a crude idea of what’s going on, and then find something nearby which satisfies the quantum constraints. The new method we propose automatically satisfies the quantum constraints and is thus more efficient. Akram proved this and performed many simulations of the algorithm doing its thing.

Minimax quantum state estimation under Bregman divergence

This work is more theoretical. You might call it mathematical quantum statistics… quantum mathematical statistics? It doesn’t yet have a name. Anyway, it definitely has those three things in it. The topic is quantum tomography again, but the focus is different. Whereas for the above paper the problem was to devise an algorithm that works fast, the goal here was to understand what the best algorithm can achieve (independent of how fast it might be).

Work along these lines in the past considered a single figure of merit, the thing the defines what “best” means. In this work Maria looked at general figures of merit called Bregman divergences. She proved several theorems about the optimal algorithm and the optimal measurement strategy. For the smallest quantum system, a qubit, a complete answer was worked out in concrete detail.

Both Maria and Akram are presenting their work next week at AQIS 2018 in Nagoya, Japan.

## Estimation… with quantum technology… using machine learning… on the blockchain

A snarky academic joke which might actually be interesting (but still a snarky joke).

## Abstract

A device verification protocol using quantum technology, machine learning, and blockchain is outlined. The self-learning protocol, SKYNET, uses quantum resources to adaptively come to know itself. The data integrity is guaranteed with blockchain technology using the FelixBlochChain.

## Introduction

You may have a problem. Maybe you’re interested in leveraging the new economy to maximize your B2B ROI in the mission-critical logistic sector. Maybe, like some of the administration at an unnamed university, you like to annoy your faculty with bullshit about innovation mindshare in the enterprise market. Or, maybe like me, you’d like to solve the problem of verifying the operation of a physical device. Whatever your problem, you know about the new tech hype: quantum, machine learning, and blockchain. Could one of these solve your problem? Could you really impress your boss by suggesting the use of one of these buzzwords? Yes. Yes, you can.

Here I will solve my problem using all the hype. This is the ultimate evolution of disruptive tech. Synergy of quantum and machine learning is already a hot topic1. But this is all in-the-box. Now maybe you thought I was going outside-the-box to quantum agent-based learning or quantum artificial intelligence—but, no! We go even deeper, looking into the box that was outside the box—the meta-box, as it were. This is where quantum self-learning sits. Self-learning is protocol wherein the quantum device itself comes to learn its own description. The protocol is called Self Knowing Yielding Nearly Extremal Targets (SKYNET). If that was hard to follow, it is depicted below.

Blockchain is the technology behind bitcoin2 and many internet scams. The core protocol was quickly realised to be applicable beyond digital currency and has been suggested to solve problems in health, logistics, bananas, and more. Here I introduce FelixBlochChain—a data ledger which stores runs of experimental outcomes (transactions) in blocks. The data chain is an immutable database and can easily be delocalised. As a way to solve the data integrity problem, this could be one of the few legitimate, non-scammy uses of blockchain. So, if you want to give me money for that, consider this the whitepaper.

## Problem

The problem is succinctly described above. Naively, it seems we desire a description of an unknown process. A complete description of such a process using traditional means is known as quantum process tomography in the physics community3. However, by applying some higher-order thinking, the envelope can be pushed and a quantum solution can be sought. Quantum process tomography is data-intensive and not scalable afterall.

The solution proposed is shown below. The paradigm shift is a reverse-datafication which breaks through the clutter of the data-overloaded quantum process tomography.

It might seem like performing a measurement of $\{|\psi\rangle\!\langle \psi|, \mathbb I - |\psi\rangle\!\langle \psi|\}$ is the correct choice since this would certainly produce a deterministic outcome when $V = U$. However, there are many other unitaries which would do the same for a fixed choice of $|\psi\rangle$. One solution is to turn to repeating the experiment many times with a complete set of input states. However, this gets us nearly back to quantum process tomography—killing any advantage that might have been had with our quantum resource.

## Solution

This is addressed by drawing inspiration from ancilla-assisted quantum process tomography4. This is depicted above. Now the naive looking measurement, $\{|\mathbb I\rangle\!\langle\mathbb I |, \mathbb I - |\mathbb I\rangle\!\langle \mathbb I|\}$, is a viable choice as

$|\langle\mathbb I |V^\dagger U \otimes \mathbb I |\mathbb I\rangle|^2 = |\langle V | U\rangle|^2,$

where $|U\rangle = U\otimes \mathbb I |\mathbb I\rangle$. This is exactly the entanglement fidelity or channel fidelity5. Now, we have $|\langle V | U\rangle| = 1 \Leftrightarrow U = V$, and we’re in business.

Though $|\langle V | U\rangle|$ is not accessible directly, it can be approximated with the estimator $P(V) = \frac{n}{N}$, where $N$ is the number of trials and $n$ is the number of successes. Clearly, $\mathbb E[P(V)] = |\langle V | U\rangle|^2.$

Thus, we are left with the following optimisation problem:
$\min_{V} \mathbb E[P(V)] \label{eq:opt},$

subject to $V^\dagger V= \mathbb I$. This is exactly the type of problem suitable for the gradient-free cousin of stochastic gradient ascent (of deep learning fame), called simultaneous perturbation stochastic approximation6. I’ll skip to the conclusion and give you the protocol. Each epoch consists of two experiments and a update rule:

$V_{k+1} = V_{k} + \frac12\alpha_k \beta_k^{-1} (P(V+\beta_k \triangle_k) - P(V-\beta_k \triangle_k))\triangle_k.$

Here $V_0$ is some arbitrary starting unitary (I chose $\mathbb I$). The gain sequences $\alpha_k, \beta_k$ are chosen as prescribed by Spall6. The main advantage of this protocol is $\triangle_k$, which is a random direction in unitary-space. Each epoch, a random direction is chosen which guarantees an unbiased estimation of the gradient and avoids all the measurements necessary to estimation the exact gradient. As applied to the estimation of quantum gates, this can be seen as a generalisation of Self-guided quantum tomography7 beyond pure quantum states.

To ensure integrity of the data—to make sure I’m not lying, fudging the data, p-hacking, or post-selecting—a blochchain-based solution is implemented. In analogy with the original bitcoin proposal, each experimental datum is a transaction. After a set number of epochs, a block is added to the datachain. Since this is not implemented in a peer-to-peer network, I have the datachain—called FelixBlochChain—tweet the block hashes at @FelixBlochChain. This provides a timestamp and validation that the data taken was that used to produce the final result.

## Results

Speaking of final result, it seems SKYNET works quite well, as shown above. There is still much to do—but now that SKYNET is online, maybe that’s the least of our worries. In any case, go download the source8 and have fun!

Acknowledgements

The author thanks the quantum technology start-up community for inspiring this work. I probably shouldn’t say this was financially supported by ARC DE170100421.

1. V. Dunjko and H. J. Briegel, Machine learning and artificial intelligence in the quantum domain, arXiv:1709.02779 (2017)
2. N. Satoshi, Bitcoin: A peer-to-peer electronic cash system, (2008), bitcoin.org.
3. I. L. Chuang and M. A. Nielsen, Prescription for experimental determination of the dynamics of a quantum black box, Journal of Modern Optics 44, 2455 (1997)
4. J. B. Altepeter, D. Branning, E. Jerey, T. C. Wei, P. G. Kwiat, R. T. Thew, J. L. O’Brien, M. A. Nielsen, and A. G. White, Ancilla-assisted quantum process tomography, Phys. Rev. Lett. 90, 193601 (2003)
5. B. Schumacher, Sending quantum entanglement through noisy channels, arXiv:quant-ph/9604023 (1996)
6. J. C. Spall, Multivariate stochastic approximation using a simultaneous perturbation gradient approximation, IEEE Transactions on Automatic Control 37, 332 (1992)
7. C. Ferrie, Self-guided quantum tomography, Physical Review Letters 113, 190404 (2014)
8. The source code for this work is available at https://gist.github.com/csferrie/1414515793de359744712c07584c6990

## David Wolfe doesn’t want you to share these answers debunking quantum avocados

Everyone knows you need to microwave your avocados to release their quantum memory effects.

Recently, I joined Byrne and Wade on Scigasm Podcast to talk about misconceptions of quantum physics. Apparently, people are wrong about quantum physics on the internet! Now, since the vast majority of people don’t listen to Scigasm Podcast [burn emoji], I thought I’d expand a bit on dispelling some of the mysticism surrounding the quantum.

### Would it be fair to say quantum physics is a new field in the applied sciences, though it has been around for a while in the theoretical world?

No. That couldn’t be further from the truth. There are two ways to answer this question.

The super pedantic way: all is quantum. And so all technology is based on quantum physics. Electricity is the flow of electrons. Electrons are fundamental quantum particles. However, you could rightfully say that knowledge of quantum physics was not necessary to develop the technology.

In reality, though, all the technology around us today would not exist without understanding quantum physics. Obvious examples are lasers, MRI and atomic clocks. Then there are technologies such as GPS, for example, that rely on the precision timing afforded by atomic clocks. Probably most importantly is the develop of the modern transistor, which required the understanding of semiconductors. Transistors exist, and are necessary, for the probably of electronic devices surrounding you right now.

However, all of that is based on an understanding of bulk quantum properties—lots of quantum systems behaving the same way. You could say this is quantum technology 1.0.

Today, we are developing quantum technology 2.0. This is built on the ability to control individual quantum systems and get them to interact with each other. Different properties emerge with this capability.

### Does the human brain operate using properties of the quantum world?

There are two things this could mean. One is legit and other is not. There is a real field of study called quantum biology. This is basically material physics, where the material is biological. People want to know if we need more than classical physics to explain, say, energy transfer in ever more microscopic biochemical interactions.

The other thing is called quantum consciousness, or something equally grandiose. Now, some well-known physicists have written about this. I’ll note that this is usually long after tenure. These are mostly metaphysical musings, at best.

In either case, and this is true for anything scientific, it all depends on what you mean by properties of the quantum world. Of course, everything is quantum—we are all made of fundamental particles. So one has to be clear what is meant by the “true” quantum effects.

Then… there are the crackpots. There the flawed logic is as follows: consciousness is mysterious, quantum is mysterious, therefore consciousness is quantum. This is like saying: dogs have four legs, this chair has four legs, therefore this chair is a dog. It’s a logical fallacy.

### Quantum healing is the idea that quantum phenomena are responsible for our health. Can we blame quantum mechanics for cancer? Or can we heal cancer with the power of thought alone?

Sure, you can blame physics for cancer. The universe wants to kill us after all. I mean, on the whole, it is pretty inhospitable to life. We are fighting it back. I guess scientists are like jujitsu masters—we use the universe against itself for our benefit.

But, there is a sense in which diseases are cured by thought. It is the collective thoughts and intentional actions of scientists which cure disease. The thoughts of an individual alone are useless without a community.

### Is it true that subatomic particles such as electrons can be in multiple places at once?

If you think of the particles has tiny billiard balls, then no, almost by definition. A thing, that is defined by its singular location, cannot be two places at once. That’s like asking if you can make a square circle. The question doesn’t even make sense.

Metaphors and analogies always have their limitations. It is useful to think this way about particles sometimes. For example, think of a laser. You likely are not going too far astray if you think of the light in a laser as a huge number of little balls flying straight at the speed of light. I mean that is how we draw it for students. But a physicist could quickly drum up a situation under which that picture would lead to wrong conclusions even microscopically.

### Does quantum mechanics only apply to the subatomic?

Not quite. If you believe that quantum mechanics applies to fundamental particles and that fundamental particles make up you and me, then quantum mechanics also applies to you and me.

This is mostly true, but building a description of each of my particles and the way they interact using the rules of quantum mechanics would be impossible. Besides, Newtonian mechanics works perfectly fine for large objects and is much simpler. So we don’t use quantum mechanics to describe large objects.

Not yet, anyway. The idea of quantum engineering is to carefully design and build a large arrangement of atoms that behaves in fundamentally new ways. There is nothing in the rules of quantum mechanics that forbids it, just like there was nothing in the rules of Newtonian mechanics that forbade going to the moon. It’s just a hard problem that will take a lot of hard work.

### Do quantum computers really assess every possible outcome at once?

No. If it could, it would be able to solve every possible problem instantaneously. In fact, we have found only a few classes of problems that we think a quantum computer could speed up. These are problems that have a mathematical structure that looks similar to quantum mechanics. So, we exploit that similarity to come up with easier solutions. There is nothing magical going on.

### Can we use entanglement to send information at speeds faster than the speed of light?

No. Using entanglement to send information faster than light is like a perpetual motion machine. Each proposal looks detailed and intricate. But some non-physical thing is always hidden under the rug.

### Could I use tachyons to become The Flash? And if so, where do I get tachyons?

This is described in my books. Go buy them.