Dead or Alive: Can you be both?


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…


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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The first Delft qubit


By Hans Mooij


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.

Continue reading The first Delft qubit

Inside Intel


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

How to make artificial atoms out of electrical circuits – Part II: Circuit quantum electrodynamics and the transmon


by Christian Dickel

There are different kinds of scientific papers. Some are like James Joyce’s Ulysses – you really want to read them but you have never made it through. There are the English classics – they are timeless and awe-inspiring. Like Shakespeare, some papers have changed the english language and, for example, teleported the wrong ideas into the heads of numerous journalists. In my group, we have a Harry Potter paper that we read again and again and keep discovering new insights. This is Jens Koch et al.’s 2007 classic “Charge insensitive qubit design derived from the Cooper pair box”, which introduced the transmon qubit.

Continue reading How to make artificial atoms out of electrical circuits – Part II: Circuit quantum electrodynamics and the transmon

A day in the life of a Master student


Author: Sophie Hermans

Hi! My name is Sophie Hermans and I am a Master student in the group of Ronald Hanson. I have started my MSc project about five months ago in the “cavity team”. Today I will take you along and show you what I do on a regular day.

There is no better way than to start the day with a freshly brewed, warm and strong cup of coffee.

Continue reading A day in the life of a Master student

Who simulates a quantum simulation?


by Christian Dickel

Elon Musk puts the odds of us living in a “base reality” at one in a billions. His more likely alternative: we live in a simulation running on a computer. After the Matrix movie and in the age of computer games, this might not be an absurd idea to many people anymore. I will not focus on the merits of the simulation hypothesis here. However, as a quantum scientist, I am convinced that if we were living in a simulation it would have to  be a quantum one. Here, I want to explain why that is and I’d like to share some of my recent experience with quantum simulations – maybe the most interesting-looking application for future quantum computers at this point. In the process of the quantum simulation we also simulated the simulation – a concept that is kind of hinted at in Musk’s phrase “base reality”. From the base reality there could be a whole ladder of simulations within simulations all the way down – except for the problem of diminishing computer power. To answer the question in the title, in our research group my colleagues Marios and Nathan recently simulated a quantum simulation before running it on a small scale quantum processor.
Continue reading Who simulates a quantum simulation?

The APS March meeting


By Jonas Helsen, Christian Dickel, Adriaan Rol, James Kroll and Suzanne Van Dam

The March Meeting of the American Physical Society, held every year in March (hence the name) is probably the largest meeting of physicists in the world. Held in a different city in the US every year it is a five day long whirlwind of talks, discussions, meetings, catching up with old friends and making new ones from all over the world. Since a sizeable subsection of the March meeting deals with quantum information processing (as of this year we are officially a Division!) a large group of Qutech scientists made the trek to New Orleans, both to speak about our latest developments and to learn about science going on all around the world. For this occasion we asked a few people to jot down their impressions of this weeklong carnival of physics and have bundled them in this blogpost. We will also add some pictures which hopefully convey the general scale and feel of the March meeting.

Continue reading The APS March meeting

Why turning a ket into a cat may or may not be a good idea


By Adriaan Rol

When I’m at a party people often ask me what I do.

There is a lot of things I can talk about: why is a quantum computer interesting or useful , or:  what do I actually do during my day. But quite often people end up asking a confused question about this curious story of an undead cat. In this blog post I will try to shed some light on this case as well as delve into the question of why we use these kind of stories.

Dead? Or alive? Or both?

When trying to understand a new theory we physicists love our thought experiments.  We take some mathematical model of the world, change some parameters to see how it behaves and try to extract some rules of thumb or intuition from it. Continue reading Why turning a ket into a cat may or may not be a good idea

Progression of technology for quantum control or: jumping and drifting of NV centres



Technological sophistication is a cornerstone of our society. Apart from a few outstanding examples, technology has always advanced towards a new echelon, which in turn enabled further advance. Whether one investigates the height of the tallest skyscrapers, or the timeline from the first transistor to today’s computers, the principle remains the same: inventions are being made with increasingly faster strides. Of course this trend should hold true for our favourite qubit! Along these lines I will delve into a technological aspect of my favourite qubit: the nitrogen-vacancy (NV) centre in diamond.

Continue reading Progression of technology for quantum control or: jumping and drifting of NV centres

Nanoscale Superstition


by Michiel de Moor

In our cleanroom, we use nanofabrication techniques to combine materials in a precise and controlled way in order to study the wonders of quantum physics. For a nice introduction on the topic, I recommend reading Madelaine Liddy’s blog post. This post is not about nanofabrication specifics, but more about the people involved in the process.

Doing nanofabrication takes up a significant amount of time. Often it’s very difficult to understand what the important parameters are, and outcomes can seem random. As scientists, we should be rational and analyze the problem, then test possible solutions until we understand what is happening. But as people, we are susceptible to the same kind of magical thinking that makes people believe lightning strikes are a sign of Zeus’ displeasure.

As with cooking food, every research group will have their own fabrication recipes (which are, of course, the very best in the world). Continue reading Nanoscale Superstition