Why I joined the March for Science

Last Saturday was the March for Science, and I joined millions of others in marches around the world asking our governments for more funding for science. I attended the March for Science in San Francisco, and the atmosphere could not be better (for photos of the best posters, scroll to the bottom of the post!). It was truly inspiring to join so many people that were united in the belief that science keeps us safe and makes our lives better. The world we know today would have not been possible without the scientific breakthroughs of past centuries.


Science is the organized skepticism in the reliability of expert opinion.” – Richard Feynman

The cornerstone of science is the fact that it is falsifiable, which means that any scientific theory can be proven wrong by new discoveries. Scientific theories of the natural world evolve through the ages because we learn of new facts that prove the old theories wrong and the scientific community needs to seek new answers. Examples of that are Kepler’s laws of planetary motion, quantum mechanics or general relativity. It could be easy to jump to the conclusion that there are no scientific facts or absoluts, and it’s all a matter of interpretation. This is not true, a scientific fact is measurable and verifiable observation, such as the Earth being round, the speed of light constant or the existence of subatomic particles. On the other hand, a scientific theory is an interpretation of the verifiable facts, which means that if we lack a relevant fact, we might arrive at the wrong conclusion.

Scientists use the scientific method to arrive to their scientific theories. They observe a fact of nature, they formulate a hypothesis as to why it happens, they determine the logical implications and make predictions following their hypothesis, and finally they test their predictions. This process can be preformed several times, but once all their predictions are proven correct, the theory is held as true, until a contradicting fact comes along. Any contradicting provable fact is enough to falsify a theory, and therefore scientists have to be careful and thorough in their analysis. It’s one of the things I love most about science: opinions or beliefs do not matter, only evidence. We are only explorers of the world around us, seeking understanding.

The first principle is that you must not fool yourself, and you are the easiest person to fool.” – Richard Feynman

Understanding the principles of the natural world equips us to improve our quality of life and push our technological development, however the importance of scientific progress has not always been understood. It was not until the twentieth century that science became more broadly publicly funded. In the past, scientists fell mainly into three categories:

  • Scientists that had the means to support themselves, or families who would foot the bill. Examples are Sir Isaac Newton, Charles Darwin and Tycho Brahe.
  • Scientists who sought patronage from the aristocracy, like Rene Descartes, Johannes Kepler and Galileo Galilei
  • Scientists who worked a second job to support their scientific endeavours, such as Gregor Mendel, Benjamin Franklin and Michael Faraday.

Nowadays, governments spend a sizeable portion of their GDP into Research & Development (R&D) programs. In fact, there is a correlation between the amount of funding that a country invests in R&D and their Human Develpment Index (HDI). The tables below show the 20 highest-ranking countries according to their HDI (on the left) and the 20 highest-ranking countries according to how much expenditure there is per capita. I’ve marked with a star those that appear in both lists, which is 75%. The other 5 countries that spend highly in R&D but do not appear in the top 20 according to their HDI, are ranked in the top 30.Screen Shot 2017-04-26 at 9.09.36 PM

This is the reason I attended the March for Science, because scientific progress has an unparalleled influence in our development as a society. Our ability to cure diseases, build infrastructures, mass-produce food or design electronic devices comes from basic research that seeked a deeper understanding of nature. It is in our best interest to keep funding basic research.


Here is a selection of the best posters I saw at the March for Science in San Francisco, there are more excellent posters from other marches around the world in various social media platforms.

Female scientists: not martyrs, but heroes.

Last week I attended the APS March meeting in New Orleans, and there was a session in honor of the 150th anniversary of Marie Curie, in which we had talks on Marie Curie’s life, as well as lively discussions on the challenges faced by women in physics today. Professor Emerita Ruth Howes gave an incredibly inspiring and entertaining talk about Marie Curie. With the title “Marie Curie: physicist and woman” Professor Howes showed us a side of Marie that, at least I, was not aware of. The way her story was told and the details I learned about her life made me feel closer to her, not only as the pioneer she was but as a woman: the mischievous pranks of that summer in the countryside, her horror at being underprepared for the Sorbonne, the persecution of the French media when her affair with Langevin was discovered. During that talk, somehow Marie gained a new dimension, outside the well-defined outline of her scientific life. I realized this is something I had felt missing before, in the biographies of trailblazing women in science. We usually put so much emphasis in highlighting the difficulties they overcame, their hard work, their scientific discoveries, that we end up making them so perfect that is hard for girls today to identify with them. Their brilliance is an inspiration, even more so when you consider the injustices they faced, but I believe we should remind ourselves, that they were women just like us, with their personal struggles and failures. They were not one-of-a-kind martyrs, but heroes that we can emulate today.

Professor Howes

As a woman and a physicist, it bothers me that other girls and women might not feel welcome in the field. We still need to overcome challenges until we are in a position of equality with our male colleagues, and I (as am sure many others like me) often think about what is the best way in which I can contribute. There is an ever-growing community of scientists (both men and women) who champion equal opportunities and put in place programs that help this effort. Our greatest strength is our community, the mentors who help and champion students and young scientists, the role models that increase representation in the field and encourage new generations.

We want to shine the spotlight on the achievements of female scientists, in particular, those that have had to overcome particularly dire circumstances. But I think we should be careful that we don’t portray them as superhumans who have succeeded where no other person could, as by doing so we risk intimidating the same people we want to encourage. Science should not be the field of the brave but of the interested. We want to inspire young minds, and we want all the young people interested to feel they have a place in the scientific community.

I loved watching the film “Hidden figures” and one of the things I enjoyed the most was the companionship and support the women offered each other. And I loved it not only because it was inspirational and emotive, but because this is a part of my experience as a female scientist that I don’t see highlighted often. Marie Curie, Rosalind Franklin, Emmy Noether, Lise Meitner, they all had to face challenges on their own, but nowadays we have an extraordinary community of women doing scientific research, championing each other and looking for ways of levelling the playing field in the sciences. During my research in quantum computing, I’ve met incredibly smart, kind and all-around amazing women, some of whom I’m now lucky to call my closest friends. As female scientists of 2017, we still have challenges, but we are no longer alone.

Some groups and resources for women in physics:

Emmy’s beautiful mathematics

Noether’s theorem, which links together symmetry and physics, is one of the most beautiful and elegant concepts I have ever learnt. I didn’t expect to find out that Noether was really Emmy, a woman. And yet, what took me aback was my own surprise. I had always believed that women were just as capable as men of doing anything, however, when I learnt this beautiful piece of mathematics, I believed unquestionably that it had been written by a man, that the author could be a woman had not even crossed my mind. Of course, at the time I knew about Marie Curie, a female scientist so famous that could be called a legend among the hallways of the physics department. But I had never heard of Noether, nor any other woman on my physics course, and I was in the second year! This realisation opened my eyes to my unconscious bias and made me want to learn more.


Noether was really a mathematician, one of the leading founders of abstract algebra, who approached problems in a completely novel way. Her work in physics, which had so caught my attention, was just something she did on the side, to help a poor physicist who couldn’t figure out the maths of his new theory. As a result came Noether’s theorem, described technically by the equation above, which says that for every continuous symmetry of a physical system, there exists an associated conservation law. Conservation laws are fundamental in physics, as they allow us to determine phenomena that can or cannot happen in physics. Noether theorem links them to symmetries of the systems and allows us to determine which physical quantities are conserved uniquely from the properties of the Lagrangian, a function of the energy of the system. Many conservation laws had been known, such as energy and momentum conservation of a closed system, but Noether’s theorem resolved paradoxes in those conservation laws arising in new theories of physics, such as General Relativity. To say this theorem is an important result in physics is an understatement.

Emmy Noether
Emmy grew up in a family of mathematicians, who somehow failed to notice her aptitudes and didn’t encourage her to pursue mathematics. She started training as a language teacher when she became fascinated by mathematics and started attending lectures at the university of Erlangen. As a woman, she could not officially enrol, so she would simply audit the lectures. Some years later women started to be officially allowed to take classes, but the policy on women’s rights would always have a hard time catching up with her. For some time, once she had passed her doctoral thesis, she was only allowed to teach classes at the University of Gottingen that were advertised as Hilbert’s. Years later, she was able to gain a position at the university although badly paid. She would never get to be a full professor in Germany, or even gain the wages due for her work. Being forbidden from teaching at the university of Gottingen due to her Jewish heritage in 1933, she moved to Bryn Mawr, a single-sex school in the USA. Her time at the college was accompanied by difficult circumstances, as she couldn’t teach graduate courses, find a permanent position, had health problems and the political situation of Germany was increasingly bad. However, she saw things differently and said that “the last year and a half had been the happiest in her whole life, for she was appreciated in Bryn Mawr and Princeton, as she had had never been appreciated in her own country”. Unfortunately, she was to die soon after, from complications of a surgery to remove a tumour.

When reading about Noether’s life, it was her personality that struck me the most. She was a fantastic woman and an incredible mathematician, whose informal lifestyle caused many jokes that she would simply ignore. Her appearance, dress and weight were usually commented upon, so was her voice, deemed “loud and disagreeable” because it was not soft and refined as other women’s. She cared enormously for her students, with whom she shared her ideas and whom she taught with passion and enthusiasm, regardless of their political position (to the point that one of her students used to come to her house to take class wearing a nazi brown SA shirt). Her students held her in high esteem as she made them feel like she was one of them, “almost as if she too were thinking about the theorems for the first time.” She applied to both mathematics and life a general principle of simplification and removal of the unnecessary. She wore comfortable men’s shoes and coats, and during a time, she would go six days a week to eat the same dinner at the same time, at the same table of the same restaurant. According to Noether’s only American graduate student, “her methods of thinking and working were simply a reflection of her way of life: that is, to recognise the unnecessary, brush it aside and enter wholeheartedly into the present”.

She was also held in high esteem by her colleagues, and it was thanks to their continuous campaigning that she was able to get her teaching positions, first at the university of Gottingen and later on in Bryn Mawr College and the Institute of Advance Studies in Princeton (although sadly she died before she could join the latter). Hermann Weyl, a professor in Gottingen before the Second World War, said that he was “ashamed to occupy a preferred position beside her, whom I knew to be my superior as a mathematician in many aspects”. After she made important contributions to Einstein’s theory of General Relativity, Einstein wrote to Hilbert: “Yesterday I received from Miss Noether a very interesting paper on invariants. I’m impressed that such things can be understood in such a general way. The old guard at Göttingen should take some lessons from Miss Noether! She seems to know her stuff.” He was later to write, in her obituary for the New York Times, “In the judgment of the most competent living mathematicians, Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began.”
Noether, unlike some of her male colleagues, did not receive much recognition during her life and was instead criticised for many unimportant things. As historians, Crease and Mann said: “Had Noether been a man, her appearance, demeanour, and classroom behaviour would have been readily recognised as one of the forms that absent-minded brilliance frequently assumes in the males of the species”. I find Noether inspiring. Inspiring because of her achievements, which are made particularly striking given the tidal forces she had to fight against to pursue her lifelong passion for mathematics. Inspiring for her drive, her attitude towards students and colleagues, her dismissal of criticism. Inspiring because of her beautiful mathematics.



Today’s post is a celebration of Ada Lovelace’s Day, international celebration day of the achievements of women in science, technology, engineering and maths (STEM)!

Most of the biographical anecdotes of this post have been obtained from the book:  Nobel Prize Women in Science: Their Lives, Struggles, and Momentous Discoveries by Sharon Bertsch McGrayne

Fault-Tolerant Quantum Technologies ’16

After some weeks’ hiatus, Quanta for Breakfast is back! Today I want to give my thoughts on the Fault-Tolerant Quantum Technologies Workshop that I attended this summer in Benasque, Spain. It was my first time visiting the beautiful town and both the location and the workshop definitely lived up to my expectations.

The conference took place at the Centro de Ciencias de Benasque Pedro Pascual, a facility for hosting workshops and scientific meetings and truly a dream come true for physicists at a conference. There were blackboards everywhere: conference theatre, meeting rooms, corridors, outside blinds… It has all the facilities needed to be a place of scientific work and discussion and there is really no excuse to not talk about physics all day long. The building itself had a very interesting design and was built with sustainability in mind. The Centre was named in honour of the Spanish physicist Pedro Pascual, whose Quantum Mechanics book, co-authored with Alberto Galindo, I thoroughly studied as an undergrad at the Universidad Complutense de Madrid. Benasque itself is charming, full of hikers, incredible scenery and good food. There were some complaints about the time it took to have lunch, but what can I say, it’s a holiday town in Spain, restaurants assume the diners want to relax and enjoy the food 🙂 . However, for the people who couldn’t wait to go back to the blackboards, there was always the option of grabbing some tapas.

The meeting was really fantastic, from the content of the talks to the atmosphere throughout the two weeks. On top of the welcome drinks and conference dinner, there were some great activities organised, such as a couple of group hikes, an ascent to Aneto (the tallest peak in the Pyrenees), canyoning and an AMA Reddit session.


Group hike


On top of all these activities, there was plenty of free time for work and discussion, which is mostly missing in other conferences. This free time combined with the group discussions truly gave us the opportunity to learn new concepts and work together. Speaking for myself, not being an expert in Quantum Error Correction, I came back from the conference having a much better understanding of many concepts, in particular around the concept of cellular automata decoders, which featured in several talks (including a video demonstration by Barbara Terhal, shown in the GIF below). The concept of algorithms using cellular automata in quantum information processes is very powerful, particularly when considering cluster state computations or topological error correction, where the information is stored in global degrees of freedom and can be acted upon with local operations.


Demonstration of a cellular automata decoder


The biggest highlight of this workshop was, for me, the extensive discussion around experiments. There were several talks dedicated to the topic:

Steve Flammia: Comparing Experiments to the Fault Tolerant Threshold

– Hector Bombin: On the effect of correlated noise

James Wooton: A decoding algorithm for proof of principle experiments

Ying Li: Resource cost of fault-tolerant quantum computing in hybrid quantum computers and LOQC

Niel de Beaudrap: NQIT

– Yours truly: Fault-tolerant considerations when designing a linear-optical quantum computer

Hugo Cable: Minimised switching in linear-optical quantum computing

– James Auger: Topological Error Correction with Faulty Components

Joe O’Gorman: Realistic magic state distillation factories

Also, there were some technical discussions on experimental implementations of quantum computers, as well as which codes should be the first to be implemented  in small scale experiments.

We are currently at a very exciting point in the development of quantum computers. Experiments are starting to get large enough that some small codes can be tested on them. Proofs of principle experiments of topological codes have been implemented with superconducting qubits, as well as with photons and ion traps. However, the community is not in agreement on which codes are the most useful and what scope we have to find yet better error correction codes. On top of that, it might be the case that the different constraints of the various physical systems make it impossible for a single code to be optimal for all. Good news is that, now that the Quantum Error Correction and experimental communities are engaging so much with each other, we can expect vast improvements on the performance of small quantum computers thanks to codes tailored to the specific requirements of the physical systems.

Finally, I would like to thank the organisers – Dan Browne, Earl Campbell and Michael Kastoryano – for such a fantastic experience, I look forward to future editions of the workshop!



I don’t want to leave the post without mentioning the game Decodoku, a browser and mobile citizen-science game based on Quantum Error Correction, which was advertised at the conference. It’s presented as a series of puzzles, reminiscent of the popular sudoku, 2048 and Threes, but in which the problems solved mimic the effects of noise on a topological code. Good strategies for solving these puzzles efficiently could potentially become new decoding algorithms, it gives an excellent excuse for the time spent playing 😀 . If you find out you are really good at it, let the developer (James Wooton) know.

Be so good they can’t ignore you

The first time I read this sentence was on the cover of a notebook, I love motivational stationary and this one caught my attention. It differed from other inspirational sayings in that it didn’t encourage believing in yourself but rather working on yourself. Later, when reading Eric Barker’s blog, of which I am a long term fan, I learnt that this was advice given by Steve Martin to aspiring performers. I am, no longer, a performer, but have since made it a motto of my own work. I find that whenever I’m demotivated, it gives a tangible goal, as it forces me to ask myself what can I do to become a better physicist and whatever that is, I do. It also shows a defiant attitude toward preconceptions and restrictions imposed from outside, but one that is intended to prove them wrong. It will make you become the dark horse of your work endeavours.

Cal Newport, a Georgetown professor in Computer Science and blogger of Study Hacks, wrote a book of the same title. The book’s goal is to identify the steps one can take to build a successful career. It analyses the careers of a number of people, both successful and failed, and finds what were the steps taken in each case that determined the career’s fate. One of the first things that got me interested in the book, is the rejection of the “courage culture”- people who promote the idea that the only thing standing between you and your goal (in this case your dream career) is yourself, and all it takes is for you to believe in yourself and build up the courage to step off the expected path. I have always been suspicious of the belief that all it takes is courage, for any situation, and much more with respect to a career path. First of all, because many endeavours won’t succeed unless we have a background set of skills that can help our bid, but mostly because I don’t believe most things come easy, it’s resolve and hard work what makes them possible. I believe in research, preparation, planning and effort. It is true that in many cases, talent plays a big role, but I’ve never regarded natural ability as the ultimate deciding factor. I wouldn’t be running if that was the case 🙂

I must say, however, that some amount of believing in yourself and your abilities is necessary, as otherwise, one might fall sick with “imposter syndrome”, so common in academia. In my opinion, the motto “be so good they can’t ignore you” can be used to soothe such feelings, as a survey of one’s worked-for abilities should put at ease any feelings of inadequacy. But, we won’t speak any more of imposter syndrome here, as that deserves a whole other post by itself. Let’s turn our attention instead to Newport’s 4 rules that can help us build a fulfilling working life.

Don’t follow passion: We are told time and time again to follow our passion: “do what you love and you won’t have to work a day in your life”. It’s one of those inspirational sayings we see everywhere and what makes Steve Job’s  commencement address so popular that it has more than 24M views on youtube. However, it is not useful advice for someone unsure about which career is best for them. I’m sure you have experienced before surprise at enjoying something you didn’t think you would. By solely advocating to pursue the things you *know* you like, there are many other enjoyable endeavours that are left out. Moreover, there is little evidence that people have pre-existing passions and this kind of approach to finding a fulfilling work life can lead to a lot of unhappiness. “Choosing your career should not be treated as finding your true calling.

Have the mentality of a craftsman: Instead of focusing on whether the jobs fulfills any dream-job fantasies we may have, we should focus on the value that we offer, enjoy the process of the work and be proud of the output generated. This is, of course, easier said than done. When our focus shifts to what we produce, the goal becomes much clearer: improve the outcome of our work. To do that, we must engage in deliberate practice, which is the style of difficult practice that is required to improve in a task. It is the kind of practice that will involve learning new techniques, practice for hours and continually face our ignorance. It is the difference between a master and a middle of the pack. It requires that we stretch beyond what is comfortable and we are willing to accept ruthless criticism. Most of us have experienced this kind of practice when going through the educational system and trying to come to grips with the material we didn’t understand. However, once we are out of education, it becomes increasingly difficult to do so, because we are not forced to, and because it’s easier to tell ourselves we have too much email. But forcing ourselves to engage in deliberate practice will increase our abilities and help us become so good that we will get noticed.

Leverage skills to obtain more control: Some people enjoy tremendous freedom and control over their working life, while others don’t. It begs the question: why do they get those perks? In most cases, those people have rare and valuable skills, that are so priced by their employers, that they can leverage them to their advantage. That is what Newport calls “career capital”. Through deliberate practice, those people have built up career capital – a valuable set of skills that allows them to trade them for more control of their own working life. However, attaining control is tricky. If it is attained before we have enough career capital to make it sustainable, we will fail, but also, once we have built enough career capital, we might face a pushback from the very people we have become invaluable to, they might try to prevent change that benefits us and not them. So how can we decide if a bid for more control is the right step to take? Newport’s law of financial viability: “When deciding whether to follow an appealing pursuit that will introduce more control into your working life, ask yourself whether people are willing to pay you for it. If so, continue. If not, move on.”

Find a mission: “A career mission is an organising purpose to your working life”. Finding a mission can be condensed in two actions: doing a series of little bets to scout out different ideas that might succeed, and having the mindset of a marketeer, i.e. being able to identify why some ideas catch while others fall flat. True missions require a specific lifestyle: patience to build career capital as well as being constantly searching for the next big idea. These ideas tend to lie in the space just beyond the cutting edge of a field, which has been referred to as the “adjacent possible”. Identifying these big ideas requires dedication to brainstorming and exposure to new ideas. But how can we figure out if a chosen mission is likely to succeed? The answer is given by Newport’s law of remarkability: “For a mission-driven project to succeed, it should be remarkable in two different ways. First, it must compel people who encounter it to remark about it to others. Second, it must be launched in a venue that supports such remarking.

Reading this book made me have a different perspective on the career decisions that lead me to where I am now. I can see how hard work and little bets allowed me to move forward and I can also see the mistakes I made. I found the book very compelling because it gives me a framework that will help me achieve a fulfilling career, it gives me tools to achieve that desire rather than just the inspiration. Also, Newport relates his personal journey as a researcher and what deliberate practices he engages on, as well as how he develops his career mission. These are practices I can directly apply myself to grow as a physicist. While reading I felt I couldn’t wait to put this framework in practice, this blog is a result of that.

What is a quantum computer?

This is a question you might get asked fairly often if you ever mention that you do research in quantum physics. You might even be asked if you are a Prime Minister visiting a research facility on the topic. So among all the questions I would expect to be asked, this is not a particularly surprising one. Except on my PhD viva exam, when I really did not expect it. Particularly in the form it was phrased: “How can you tell if a machine is a quantum computer? If aliens came to Earth and tried to sell you a quantum computer, what could you do to be certain they were not fooling you?”. I didn’t expect alien sales to be part of my viva, that’s for sure! Fortunately for me, some conversations I had previously had with experimentalists at the Centre for Quantum Photonics helped me give an answer that satisfied my examiners. However, I came out from the exam with the nagging feeling that that should have been a much easier question to answer.

In any standard course on quantum computing and its implementations, usually one learns about the DiVincenzo criteria, which states that a quantum computer should have:

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

These criteria were formulated in the year 2000 with a specific computational model in mind, the circuit model. Since then, other ways of implementing quantum computing have sprung out, from computational models (such as cluster state and adiabatic models) to physical implementations that don’t deal with qubits but rather with continuous variable systems. Many of these new developments don’t quite fit the DiVincenzo criteria, so are there any better definitions of what quantum computers are?

Searching through the scientific literature, and through statements of experts to the media, we can find five distinct ways in which to specify what a quantum computer is:

  1. Abstract theoretical definitions: Such is Deutsch’s definition in his 1984 paper where he formulates a physical version of the Church-Turing thesis that is compatible with quantum theory: “a quantum computer is a […] quantum generalization of the class of Turing machines”. Or Feynman’s: “It’s not a Turing machine, but a machine of a different kind”. These definitions are very abstract and lack details and specifications on the structural components, making them not very useful in practical scenarios.
  2. Implicit definitions: A quantum computer is not defined necessarily by its components but rather by stating that it uses the laws of quantum mechanics to perform computation. As true as this definition is, it is no help when trying to decide whether a computer is quantum or not. How can we assert from outside which laws govern the logical operations inside?
  3. Comparative definitions: A quantum computer is a device that can outperform classical computers. While we certainly expect them to be able to solve problems that would otherwise be outside our reach if we only had access to classical computers, relying on the classification of problems in complexity theory is uncertain business, as this classification is not written in stone and evolves as the field develops.
  4. Constructive definitions: These definitions specify what a quantum computer is by stating their components or the way information is processed. For example, defining the quantum computer as a machine that fulfils the DiVincenzo criteria falls in this category. This kind of definitions share the characteristic of being narrow and tied to a specific implementation, and therefore not general enough to apply to all architectures, physical implementations and computational models.
  5. Operational definitions: The quantum computer is fully defined by what it does, if a machine acts like a quantum computer, it is a quantum computer. The definition makes no assumptions about the theory of computation or the nature of physical reality, and therefore different interpretations of quantum mechanics should agree that the machine is a quantum computer.

There is an excellent paper which intends to figure out a useful operational definition for quantum computers that will stand the test of time, and by making no reference to how the computer exactly works, it should still hold in years to come when new techniques have been developed. As end users we care mainly about performance, and not necessarily about the nitty-gritty details of how that performance is achieved. As an example, how many of you understand all the complexity of the device you are using to read this blogpost? I certainly don’t.

The proposed operational definition of a quantum computer in this paper is as follows:

“We define a quantum computer as a device that can run a quantum algorithm efficiently, where a quantum algorithm is a classical bit string that encodes a series of quantum operations. The quantum computer should be able to take this string as input and produce another one as output. The probability distribution of the output should be consistent with the predictions of quantum theory. Finally, the time it takes the computer to produce the output should be in agreement with the difficulty of the algorithm.”

Note that this definition makes no mention of the way in which the quantum operations are performed, and therefore is open to different models of computation. The time constraint in this definition is crucial, as it excludes classical computers, because, for example, if we ran Shor’s factoring algorithm in a quantum computer we would expect an answer in polynomial time and a classical computer would require exponential time. But also this definition doesn’t depend on the current classification of complexity problems, as “the difficulty of the algorithm” mentioned in the definition would refer to the difficulty of a particular problem at the time of the test.

It is also worth noting that both the input and output are classical bit strings. After all, the input and output are the interactions of the machine with the controller, which lives in a classical world. The quantum program will be the encoding of the operations of a particular quantum algorithm, which will be part of the input string along with the initial state of the quantum computer. The instructions for generating the initial state on the quantum computer must have an efficient classical representation, this is the case for all computational models. It is worth noting that for all the current proposals of quantum computers, some classical pre and post-processing are assumed, which agrees with the above definition as long as this classical processing takes only polynomial time in the problem size.

In this paper they also have a set of criteria for building a quantum computer, that is general enough to fit all computational models (currently known) and all physical implementations proposed. It is based on 4 statements:

  1. Any quantum computer should have a quantum memory. Quantum memory is the broad term used to state that the quantum computer must have the capability of efficiently representing any computable pure quantum state (of a size accordant with the size of the computer) in its internal degrees of freedom. This quantum state will not have, in general, an efficient classical representation.
  2. Any quantum computer must facilitate a controlled quantum evolution of the quantum memory, which allows for universal quantum computation. By controlled quantum evolution, the authors mean that the evolution of the internal state of the quantum computer must follow the laws of quantum mechanics, and will ultimately be controlled by the end user.
  3. Any quantum computer must have a method for cooling the quantum memory. Entropy is accumulated in the quantum memory as a product of a previous computation or because of the presence of errors due to noise from the environment. Cooling refers to information-theoretic cooling, where the entropy is extracted from the quantum memory. It encompasses the process of initialisation of the quantum memory as well as the error correction procedure.
  4. Any quantum computer must provide a readout mechanism for subsets of the quantum memory. The computer must have a mechanism to translate the outcome of the computation to classical bits for the controller to obtain the result of the computation. The authors refer to subsets of measurements as during most error correcting procedures, there are intermediate measurements used to assess the presence of errors, and this kind of measurements are not of much use to the end user.

There are two other essential characteristics for a quantum computer the authors require:

  • Fault-tolerance: Fluctuations from the environment can cause stochastic errors to appear in the quantum computer. If a quantum computer still works according to its definition in the presence of such errors, it will be deemed fault-tolerant. This will be the case if the computer uses some form of error correction that has an error threshold (maximum size of individual errors) higher than the errors caused by the environment.
  • Scalability: Currently any claims of scalability in any particular physical implementation of a quantum computer are predictions, as no reasonably large quantum computer exists. Theoretically, a quantum computer is scalable if the resources required to run the same polynomial time algorithm on a larger input scaled polynomially on the size of the input. What makes a particular architecture scalable depends heavily on the architecture and technological prediction and it is difficult to make general statements without getting into the detail any given implementation. An excellent read on this subject can be found in the Quantum Pontiff blog post “Climbing Mount Scalable”.

It is perhaps because we don’t have a functioning large-scale quantum computer that it is difficult to give accurate definitions without hiding behind the “spooky” laws of quantum mechanics. At the end of the day definitions are not the most important thing, and proof of that is that Nielsen & Chuang, the must-read book for any quantum information scientist, does not define what a quantum computer is and rather lets the reader build up an intuition. But it is important to know what we talk about when we talk about quantum computers, for us to be able to make informed decisions about whether a machine is a quantum computer or not, in case aliens or someone else came to us with sales pitch.

Welcome to my blog

Hello Internet and welcome to my blog!

The idea for starting this blog comes from the group meetings we had at the Controlled Quantum Dynamics Theory Group at Imperial College, where I did my PhD. Every Wednesday morning, we’d gather in a meeting room with beautiful views over London, had breakfast and talked about physics… most of the time. Every week a member of the group would prepare a talk on a subject of their choice, it could be about their own work, an interesting paper they had read, something they had recently learnt about or anything else they thought was interesting. We had fascinating talks on art, bike physics, coffee, songbirds and many other topics.

I took the approach of using my allotted talks as an opportunity to learn about some new physics, what better incentive to get your facts straight than a room full of physicists ready to argue? Jokes aside, preparing an hour of spoken material on a new subject allowed me to grasp the basic concepts of the new topic, and I don’t think I would have tried so hard to learn about something which had (most of the time) not much to do with my PhD work, had it not been for these talks. Also, the questions raised by some members of the audience, made me look at a topic in a different or find out connexions I didn’t know about. Overall, I think those talks were one of the most formative experiences I’ve ever had.

This blog will be my online replacement for those group meetings. Topic-wise, I think it’s reasonable to say that most posts will be quantum-related, but I also hope to include some posts on computer science, outreach and other miscellaneous topics. I will sometimes post about things I know about, but my intention is to learn new things for each post. So if I ever get something wrong in a post, please point it out in the comments!  Hopefully, with time I will get the chance to learn from the comments on my posts as well.