An elementary introduction to Mathematica, aimed at complete beginners, including: algebraic manipulation, solving equations, complex numbers, linear algebra, functions, plotting, derivatives, integrals, solving differential equations, flow control, interactive graphics, and much more. All you need is Mathematica to try this out for yourself. I give several simple projects, including implementing a classical random walk, and basic quantum optics using operator algebra.
This is an introductory video on quantum computing by my friend and colleague, Dominic Berry from Macquarie University.
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Boson sampling is a simple model for non-universal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single photon states is fed through a Haar-random linear optics network and sampled at the output using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an analogous procedure implements the same problem, using photon-added or -subtracted squeezed vacuum states (with arbitrary squeezing), where sampling at the output is performed via parity measurements. The equivalence is exact and independent of the squeezing parameter, and hence provides an entire class of new quantum states of light in the same complexity class as boson sampling.
Boson-sampling is a simplified model for quantum computing that may hold the key to implementing the first ever post-classical quantum computer. Boson-sampling is a non-universal quantum computer that is significantly more straightforward to build than any universal quantum computer proposed so far. We begin this chapter by motivating boson-sampling and discussing the history of linear optics quantum computing. We then summarize the boson-sampling formalism, discuss what a sampling problem is, explain why boson-sampling is easier than linear optics quantum computing, and discuss the Extended Church-Turing thesis. Next, sampling with other classes of quantum optical states is analyzed. Finally, we discuss the feasibility of building a boson-sampling device using existing technology.
This is the transcript of my speech at the recent annual Australian Libertarian Society Friedman Conference.
Today I’d like to talk to you about the role of non-monetary interests in civil society, and how they are absolutely essential for the proper functioning of society. By this, I’m referring to charity & volunteer work, donations & philanthropy, lobbying and political activism.
Your typical libertarian or fiscal conservative argues for individualism - that people should be free to pursue their own self interest, particularly when it comes to financial self-interest. And I couldn’t agree more with them on that. But having the freedom to choose to pursue financial self-interest doe not imply that we are at all times obliged to pursue financial self-interest.
I’m relatively libertarian-minded, but I also do a lot of charity work that I’ll tell you about shortly. And when I tell people about my charity work, it’s not uncommon for people to respond skeptically by saying “But Peter you’re a libertarian, don’t you believe that charity contradicts libertarianism and that all social needs can be addressed by a market comprising self-interested individuals?”. My answer to this is a resounding no.
Whilst libertarianism and fiscal conservatism argues that people should be allowed to pursue self-interest, it does not imply that they are obliged to. Libertarianism is not about forcing people to act with self-interest, it’s about allowing them to. But it’s equally about allowing them not to. And so I think that individuals engaging in charitable work without any self-interest in sight, is completely consistent with a libertarian vision for society.
The role of charities in our society is absolutely essential, both domestically and internationally. Charities are a major pillar in the proper functioning of our society, and without them, the society we live in would be a much darker place.
I’d like to tell you specifically about a charity that’s very close to my heart - Lifeline. I’ve been working for Lifeline as a telephone councillor for 2 years now. I’m sure most of you have heard of Lifeline. We’re a charity organisation that offers a free 24/7 counselling hotline to offer support to people in need of someone to talk to, for any reason whatsoever. We talk with people suffering mental illness, domestic violence, sexuality issues, rape, abuse, grief, loss, and above all else, people who are considering suicide. Lifeline takes on the order of 850,000 calls per year, many of which are people who are suffering so badly that they are on the brink of suicide. These people are typically lonely, and have no one else to turn to in life. And so, as a last resort, they turn to Lifeline. In my experience, maybe 10 or 20% of our callers are at risk of suicide. And of those, we are successful in the vast majority of cases in preventing those suicides from happening. It’s therefore safe to say that Lifeline as an organisation has saved tens of thousands of lives. Similar services exist in other countries, such as the Samaritans in the UK.
All our councillors have been subject to an intensive half year training program to train them in all the issues I mentioned, particularly in suicide intervention skills. Now, not only do our councillors work for free out of the goodness of their heart and the desire to build a better and happier society, but they actually pay $500 out of their own pocket to undergo this training program.
A Randian might argue that this is absolutely insane. Not only are these people not working for their own self-interest, but they’re actually working against their own financial self-interest, to the order of $500 and many hours per week in the investment of time, to pursue someone else’s interest.
So, how to we reconcile this apparent contradiction. Well, the answer is that a society based on the libertarian ideal of individualism does not mandate self-interest, but rather mandates personal choice. And so if someone chooses to pursue their own self-interest, that’s fine. But if someone chooses to volunteer themselves to pursue someone else’s self-interest, that’s fine too.
The example I have just given you, Lifeline, is just one single charitable organisation. Without that organisation alone, tens of thousands of Australians would have committed suicide. But there are countless other charities as well, all providing equally invaluable services. John Humphreys is with us today. Without his charity, the Human Capital Project, countless young people in Cambodia would not have had the opportunity to undertake a university education. Without Oxfam, countless people would be unnecessarily dying of malaria, missing out on basic education, or not having the resources to live a basic existence. There are literally hundreds of organisations like this in just Australia alone.
All of these organisations have a business model. They must have a business model or else they wouldn’t exist. But the point I’d like to make is that their business model is fundamentally different to the business model employed by regular companies and self-interested individuals. Their model is not about profit, but about pursuing a non-monetary interest. And having organisations with this alternate business model is as vital to our society as organisations with standard profit-driven business models.
The usual libertarian argument is that the 'invisible hand’ magically converts self-interest into the interests of society, and that therefore all societal needs may be addressed by self-interested individuals. But this is clearly not the case. Adam Smith’s invisible hand will never provide the kind of service that Lifeline provides. I cannot conceive of how a profit-driven business model could fulfil that role. It’s inconceivable to think that a user-pays service could replicate Lifeline or most other charities. There’s just no way that Lifeline could talk someone out of suicide after asking them for their credit card number or playing them a recorded advertisement over the phone.
Now I’d like to go on a slightly philosophical tangent and examine what ‘self-interest’ actually means. US-style Republicans would argue this means pursuing our own business interests. But how about we define ‘self-interest’ a little more broadly. Are people engaging in charitable activities really not self-interested? Well you could argue that they are. But they’re not acting in financial self-interest. Rather, they’re pursuing 'feel-good' self-interest - they’re doing something that makes them feel good. I’ll leave it to your own philosophical leanings to decide whether this constitutes ‘self-interest’ or not.
But for argument’s sake, if it is a form of self-interest, then people who advocate people pursuing self-interest must, by definition, support this kind of self-interest - the self-interest of feeling good by helping others. On the other hand, if it’s not self-interest, then it’s nonetheless a voluntary association. And libertarians, anarchists and conservatives alike are renowned for advocating the freedom to engage in voluntary association (albeit to different degrees). Therefore, I would argue that irrespective of your philosophy on what self-interest means, if you subscribe to a right-of-centre political viewpoint, then voluntary and charitable work must not only be accepted, but encouraged, if it is a voluntary choice, made without coercion.
The final issue I’d to talk about is the role of government in all of this. I raise this issue because social democrats and socialists will typically agree completely with what I’ve said about the need for organisations not driven by profit and the failure of Adam Smith’s invisible hand to provide all of society’s needs. They would then go a step further and argue that this is proof for the need of government to fill this gap and provide these services that self-interested individuals would be unable to provide.
We could get into a philosophical debate on this issue, and spend hours and hours going around in circles arguing the philosophical merits of government charity versus self-interest. I don’t really want to go there. So let’s instead look at this empirically.
The governments of all Western societies are social democratic to some extent or another, and they all attempt to fill the gap, the hole that is left unfilled by self-interested individuals. So let’s take an empirical look at the relative successes of governments filling this void versus charitable individuals and organisations filling this void.
Let’s start by looking at what governments do. At a domestic level, first and foremost, they provide social security, most notably in the form of unemployment benefits. This results in a massive disincentive to work, and it’s paid for by higher tax rates, which prices people out of the labour market and reduces the available capital with which to employ people. The net result is that we have higher unemployment, and a reduced incentive in society for people to make and expand businesses, seek promotion, and increase their labour productivity.
At the international level, governments hand out foreign aid, which more often than not gets spent by corrupt governments on expanding their militaries or downright cronyism.
There’s very little incentive for governments to spend so-called ‘charitable money’ in an effective way, because politicians win votes by handing money out and boasting about it, rather than by achieving goals.
On the other hand, let’s look at what charitable individuals achieve. Domestically, we prevent tens of thousands of suicides - see Lifeline. We provide soup kitchens to feed the homeless, people who are completely left out by government funded social security. We provide women’s refuges, to help women escape domestic violence and rape. And at the international level we give thousands of people the gift of sight (see the Fred Hollows Foundation), we prevent thousands of cases of malaria via charitable vaccination programs, we airlift food to starving peoples. Private sector micro-loan programs have proven incredibly successful at providing people with the capital to get an education or start a small business, with very high payback rates, enabling the money to be recycled rather than swallowed up.
It’s crystal clear that charitable individuals, associating voluntarily, can achieve things that governments never could, achieving better social outcomes than governments, because governments hand out money in an ad hoc fashion purely for the purpose of boasting about how generous they are, whereas charitable individuals are goal-oriented, and only continue to attract volunteers and donations if they demonstrate that they’re achieving their goals.
Therefore, what I’d like to leave you with today, is that non-monetary interests are essential to the fabric of our society. Not only are they essential, but they cannot be replicated by any self-interest-driven business model. And having charitable organisations that provide this service, is not contradictory to the libertarian ideals of individualism and self-interest. But actually, these kinds of charities could not exist without a society that respects individualism and encourages people to pursue their own agenda, whatever that agenda might be. And perhaps most importantly, it’s a goal that governments around the world have consistently demonstrated that they are unable to replicate.
I'm pleased to announce the call-for-papers for an upcoming Special Issue of Advances in Mathematical Physics, "The Theory of Quantum Simulation, Quantum Dynamics, and Quantum Walks", for which I am the lead editor. Find out more here.
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We present an architecture for arbitrarily scalable boson-sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson-sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies.
Full text here.
Boson-sampling is a highly simplified, but non-universal, approach to implementing optical quantum computation. It was shown by Aaronson & Arkhipov that this protocol cannot be efficiently classically simulated unless the polynomial hierarchy collapses, which would be a shocking result in computational complexity theory. Based on this, numerous authors have made the claim that experimental boson-sampling would provide evidence against, or disprove, the Extended Church-Turing thesis -- that any physically realisable system can be efficiently simulated on a Turing machine. We argue against this claim on the basis that, under a general, physically realistic independent error model, boson-sampling does not implement a provably hard computational problem in the asymptotic limit of large systems.