Dead or Alive: Can you be both?

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by Jérémy Ribeiro

At the heart of Quantum Mechanics lies quantum superposition. This strange phenomenon is often described as the capacity of a quantum system to be in multiple incompatible states at the same time. The most famous example of this is Schrödinger’s cat, which would be both dead and alive at the same time. But how can this be? How can we humanly make sense of that apparent contradiction? Well… I think we cannot! More precisely, I think there is a problem of language in here. Exactly what a quantum scientist means by being “in superposition”, I think, is quite far from what the layman has in mind.

A simple analogy

To start explaining what a quantum scientist has in mind when he/she says that a state is in superposition I will use a simple analogy: Shapes.

What? How is that related to the topic?

You’ll see! How would you describe or draw a shape that is both a disk and a rectangle?

That does not make any sense! Maybe something like this:

 

 

 

 

Yeah you see, it does not make sense to you, and you struggle to draw anything because I said something that does not make sense. This is exactly what happens when someone says that Schrödinger’s cat is both dead and alive! It is not clear what he/she means, and stated like that it is non-sense. When a quantum scientist says that a physical system is in superposition of two states (dead and alive), he/she means that it is in a state that is neither the first (dead) nor the second (alive) but it is in another state that possesses some of the characteristics of both (dead and alive).

Hmm…This is quite hard to visualize for me. Don’t you have an example?

Yes! For the example of the shape it could look like this:

 

 

 

 

 

 

Oh I see!

This is a relatively good analogy. This shape is neither a rectangle nor a disk, however it has some of the properties of both. Moreover I like this analogy because in quantum mechanics you cannot “see” the quantum state the physical system is in. In other words, if someone gives you a system in a certain unknown state, you cannot learn the state. If you try to measure it, you will only see a “projection” of it…

A what?

A projection is somehow a shadow, like in the picture above. It is as if we could not see the object itself but only the shadows. And you see the shape of the shadows?

Oh! They are a rectangle and a disk!

Note that we are not obliged to project the light on the object in this manner, we could use another angle to project the light, and we would get other shadows:

 

 

 

 

 

 

It is the same in quantum mechanics: It would correspond to changing the measurement you perform on the system.

However there is a very important point that this analogy does not capture. In quantum mechanics, when we measure the system we disturb it. Therefore, in general, the state after measurement is not the same as the one before. On the contrary, the shape in the pictures does not change after we shine a light it on. Here is the limit of the analogy.

To go beyond this simple and limited analogy, we will have to learn the quantum language, which we will do…

Wait! That sounds terribly complicated!

Well, do you know what an arrow is?

Like in Robin Hood?

 

Yeah, well no. More like an arrow you can draw!

Like this?

 

 

 

 

 

Yes! You see, you already speak quantum!

I am quite skeptical…

Let’s start with the real thing. The quantum language of arrows.

The quantum language is formulated in term of arrows! More precisely, the state of a quantum system is represented by an arrow. The mathematical term for these arrows is “unitary vectors of a Hilbert space (usually of finite dimension)”.

You theorists are such Barbarians!

Well yeah… I mean… Whatever… Each of these words is important, but basically this “barbarian” expression means “arrow of length 1”. So in more precise terms, a quantum state is (represented by) an arrow of length 1. This length restriction is here because the state is related with probabilities – as we will see in a moment – and probabilities add up to 1.

To simplify I will only talk about two-level systems. These are the simplest quantum systems you can find. They correspond to systems that have at most two possible outcomes when measured. For example for the spin of an electron, when we measure it, we can only measure that the spin is up or down, nothing more. We call such systems “qubits” (short for quantum bits).

Instead of using “dead” or “alive”, “up” or “down”, I will use 0 and 1 by analogy to the values that can take a bit in computer science. To specify that I am talking about arrows I will write a state as follows: |name of the state>. For example |0\rangle is a state, |1\rangle is a state.

In this picture we see the state |0\rangle and |1\rangle and another state in between called V. Because the set of all states is the set of arrows of length 1, to every point of the blue circle (of radius 1) corresponds the ending of an arrow, and therefore each of these points corresponds to an arrow. The states |0\rangle and |1\rangle are orthogonal, i.e. they form a right angle. Having a right angle like this means, in the language of quantum mechanics, to be “incompatible”, while being in between two “incompatible” arrows is said to be in superposition of those arrows. To understand why we need to understand how quantum measurements work.

We first need to choose a measurement, that’s to say we need to choose what we want to measure. For example, if you wanted to “measure” a person, you need to decide whether you want to measure his/her height or his/her weight. In quantum mechanics the possible measurements are determined by the pairs of orthogonal vectors, in other words to choose a measurement we need to choose two arrows that form a right angle. We then say that we measure in the basis formed by these vectors. For example one measurement is characterized by the arrows |0\rangle and |1\rangle , so let’s describe in more details this particular measurement.

Let say that we want to measure the arrow |V\rangle that is between |0\rangle and |1\rangle (see image above). What we do is that we look at the projection of |V\rangle on the two arrow that represent the measurement…

Whaaaattt?

Again, the projection is like a shadow, but let me draw it:

You see here we draw a green line parallel to the arrow |0\rangle from the tip of the arrow |V\rangle, and a red line parallel to the arrow |1\rangle from the tip of the arrow |V\rangle. This allows us to get two new but shorter arrows, the green and the red. We say that the green arrow is the projection of the arrow |V\rangle on the arrow |1\rangle , and the red arrow is the projection of |V\rangle on |0\rangle . It looks a bit like for the 3D object from the last section, where the arrow |V\rangle plays the role of the 3D object, the dashed lines are the rays of light, the projection are the shadows, and the basis of the measurement (here |0\rangle and |1\rangle ) are the walls.

One of the major characteristics of quantum mechanics is that the outcome of a measurement is random. What happens during the measurement is that the arrow |V\rangle will randomly become either the arrow |0\rangle or the arrow |1\rangle with probability given by the length of the projections (in fact the square of their length): The length of the red arrow determines the probability that the arrow |V\rangle becomes the arrow |0\rangle after the measurement, while the length of the green arrow determines the probability that the arrow |V\rangle becomes the arrow |1\rangle after the measurement. When the arrow |V\rangle becomes |0\rangle we get outcome 0, and when it becomes |1\rangle we get 1. You can also see the big difference with the shapes of the previous section, here after the measurement the state is not the same as before. When you get outcome 0, the state after measurement is the arrow |0\rangle. On the contrary if you project light on the weird 3D shape above, it does not suddenly become a circle or rectangle.

Hmm, that’s a lot to process… And why is it random?

It is true that this is a lot, but try to play with different arrows, and think about the analogy of the shadows. After a while you will get a good grasp on how to get the probability of getting outcome 0 or 1 out of a measurement. For the randomness the language of arrows does not tell us why, or how the projection process works.

Hmm, ok.
And what happens if I measure the arrow |0\rangle in the basis formed by the arrows |0\rangle and |1\rangle?

Imagine you rotate the arrow |V\rangle so that it becomes really close to the arrow |0\rangle. You see that the closer to the arrow |0\rangle the bigger the red arrow becomes. And when the arrow |V\rangle touches the arrow |0\rangle, then the red arrow becomes the arrow |0\rangle itself, and has therefore length 1. On the other the closer the arrow |V\rangle is to |0\rangle the smaller the green arrow is. When it touches the arrow |0\rangle the green arrow has length 0. This means that if you measure the arrow |0\rangle in the basis formed by the arrows |0\rangle and |1\rangle , then with probability 1 the arrow |0\rangle will stay |0\rangle and you’ll get outcome 0, and you will never get outcome 1.

That is why the arrows |0\rangle and |1\rangle are “incompatible” or “mutually exclusive”, if you try to measure |0\rangle (in the |0\rangle|1\rangle basis) you will always get 0 and never 1, and on the contrary if you try to measure |1\rangle you will always get 1 and never 0. For any other arrow in the middle, like |V\rangle for example, you can get 0 or 1 with non-zero probability! That’s somehow why we say it is in superposition, it is not completely “incompatible” with either of the two basis arrows, it contains some properties of |0\rangle and some of |1\rangle , it has “both shadows”.

So remember that, while you probably cannot be both dead and alive at the same time, an arrow might be able to be somewhere in between!


Jeremy2Jérémy Ribeiro is a theorist at QuTech. He specialises in quantum cryptography: the use of quantum principles to design secure protocols for communication and other cryptographic tasks. In his free time (and sometimes during work hours) he enjoys practicing his Yo-yo skills and talking about open source software and undecidable problems.


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A Quantum Internet made of Diamonds

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How cool is that? A Quantum Internet. Made of Diamonds.

by Matteo Pompili

We are constantly connected to Internet. With our computers, our smartphones, our cars, our fridges (mine is not, yet, but you get the idea). In its very first days, the Internet was a very rudimentary, yet revolutionary, connection between computers [1]. It enabled one computer on the network to send messages to any other computer on the network, whether it was directly connected to it (that is, with a cable) or not. Some of the computers on the network acted as routing nodes for the information, so that it could get directed toward the destination. In 1969 there were four nodes on the then-called ARPANET. By 1973 there were ten times as many. In 1981 the number of connected computers was more than 200. Last year the number of devices capable of connecting to Internet was 8.4 billion (with a b!) [2].
Computers on their own are already great, but there is a whole range of applications that, without a network infrastructure, would be inaccessible. Do you see where I am going?
Continue reading A Quantum Internet made of Diamonds

A Cloud Quantum Computer Business Plan

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by Christian Dickel

Quantum computing and nuclear fusion are potential 21st century technologies based on 20th century physics and neither of them is currently market ready. But while they are sometimes bunched together as fascinating concepts that will at any time be twenty years away from being realized, some estimate the timescale for the commercialization of the quantum computer to be much shorter now. Quantum computing is currently in a hype phase: The company D-wave has already sold a few quantum annealers based on flux qubits for millions of euros. They can solve certain optimization problems, but their computational advantages are a topic of debate. Google, IBM, Intel, and Microsoft are major commercial companies investing in quantum technologies right now. Several startups such as Rigetti Computing and IonQ have been founded recently with the goal of commercializing quantum computing. A list of such companies can be found here.
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Making quantum computers with spin qubits

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In one of the previous blog posts, David DiVincenzo reviewed his criteria. Here we will follow this theme and look how these criteria translate onto a physical system. Currently, there are a few qubit implementations that look quite promising. The most prominent examples are superconducting qubits, ion traps and spin qubits. We will focus on the latter one, since that’s the one I’m working on. All the platforms mentioned above fulfill the so called DiVincenzo criteria. These criteria, defined in 2000 by David DiVincenzo, need to be fulfilled for any physical implementation of a quantum computer:

  1. A scalable physical system with well characterized qubits.
  2. The ability to initialize the states of the qubits to a simple state, such as |000⟩.
  3. Long relevant coherence times, much longer than the gate operation time.
  4. A “universal” set of quantum gates.
  5. A qubit-specific measurement capability.

In this article we will go through all these criteria and show why spin qubits fulfill these criteria, but before doing that, let’s first introduce spin qubits.

Spin qubits are qubits where the information is stored in the spin momentum of an electron. A spin of a single electron in a magnetic field can either be in the spin down (low energy) or in the spin up (high energy) state. Comparing to a classical bit, the spin down state will be the analogue to a zero and spin up to a one.

The two quantum states of an fermion.

Continue reading Making quantum computers with spin qubits

Science on the beach

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by Jonas Helsen

A few weeks ago I found myself boarding a series of planes that would take me from the Netherlands to pretty much the furthest point reachable from this starting point that still includes dry land: Sydney, Australia. I wasn’t going there entirely of my own accord. Rather I had been invited to speak at a quantum information theory workshop called Coogee. For those knowledgeable of the Sydney region, it is indeed named after a beach and yes the conference takes place less than a stone’s throw away from said beach.

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Looking back at the DiVincenzo criteria

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by David DiVincenzo

The first time that I heard that there were “DiVincenzo criteria” was when Richard Hughes of Los Alamos contacted me in the fall of 2001, telling me that ARDA (predecessor of IARPA – a funding agency of the US intelligence services) had commissioned him to form a roadmap committee to forecast the future of quantum information technology [1]. Before that, I just thought of them as a list that I showed in various talks and wrote down in a few essays. So the fact that they have become a “thing” is basically because some government bureaucrats found them a handy way to draw up metrics for the progress of their quantum computing programs.

Continue reading Looking back at the DiVincenzo criteria

A Quantum Carol

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by Helsen, Kroll, Rol and van Dam

The phone was ringing in the lab, Sophie let it ring a few times before looking up from her experiment. She was a bit annoyed until she realized what time it was, almost midnight and she had only just got the experiment running. She picked up the phone, half expecting to hear her advisor when she heard her mother’s voice:

“Sophie, we were worried about you, you didn’t pick up your phone and it has been almost four hours!”.

“Don’t worry Mom, I’ll be right there, I just have to set up a measurement run overnight, otherwise the experiment will be doing nothing over Christmas!”

“But dear, like you said, it’s Christmas, you promised you’d be here! You know how Granny has been looking forward to seeing you.”

“OK, OK I’ll just start what I have now, but I still have to refill the traps. I’ll be there in 10 minutes”, she said as she hung up the phone.

As the nitrogen traps overflowed, a haze covered the floor and she started to feel a bit dizzy…

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Towards paving the way for signatures of quantum physics

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by Michiel de Moor

Even if you’re in a niche research field, it seems almost impossible to keep up with all the scientific literature that has been coming out in the past couple of years. There are estimations that the global scientific output doubles every 9 years, so it’s not going to get any easier. If you want people to read about your results, you’ll have to stand out. An important part of standing out is having a good abstract.

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The first Delft qubit

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By Hans Mooij

Introduction

When did we have our first quantum bit? To answer, one needs to agree on the definition. When does a two-level system become a qubit? In my view, only when coherent quantum dynamics is demonstrated. In the summer of 2002, Rabi oscillations of a superconducting flux qubit were observed in our laboratory. They were published in Science [1]; the primary authors were Irinel Chiorescu (postdoc, now professor at Florida State University) and Yasunobu Nakamura (on sabbatical from NEC Japan, now professor at University of Tokyo). As we all know, much has happened in the years after. Here I want to describe what happened before. How did we come to this point? I concentrate on my personal story and on superconducting circuits. In our Quantum Transport group we had the parallel research line on semiconductor quantum dots by Leo Kouwenhoven and his people that led to our first spin qubit in 2006.

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Inside Intel

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By Jelmer Boter

In the fall of 2015 QuTech and Intel Corporation joined forces in an active collaboration working on the realisation of a quantum computer. The collaboration comprises comprises Edoardo Charbon’s control electronics, Koen Bertels’ architecture work, Leo DiCarlo’s superconducting qubits and Lieven Vandersypen’s silicon spin qubits. After having worked on the Delft side of the spin qubit part of that collaboration for almost two years, I spent three months this summer in Hillsboro, Oregon to be on the other side of the phone in our weekly Skype meetings. In this blogpost, I will share some of my experiences with you.

The writer at the entrance of an Intel building

Continue reading Inside Intel