Imagine u go to someone's house for dinner. The host spend a whole day cooking the lousiest food just for you. the host stare eagerly into your eyes and ask with high expectation, 'how ? how? is my food good or not?' forced by the situation u always answer : 'yes' irrespective of the taste of the food.
based on the above analogy it seems that when ppl commented 'good, good' or 'very nice' on your blog, u should be not be overly flattered as the compliment may just be a show of what in cantonese called '俾面' (face-giving).
17.11.09
14.11.09
JJA and qubit calculation
I have now talking up a numerical project to calculate superconducting flux qubit. Much basic knowledge not known to me before is required. i wish to take this opportunity to tidy up a bit on the whole idea of the project, and hopefully through this short discussion a clearer and more concrete picture could emerged.
First of all, the proposed project, let's call it the flux qubit project (FQP), comprised of two components: the theoretical and the computational one. we have to know the theoretical concept first before attacking the problem at hand computationally.
The theoretical part is as follows. The problem at hand is that we have now a new type of flux qubit system, i call it 4 x 3 JJA. This is a proposal not seen anywhere in the literature because the proposer Hans Mooij has not really published it. The geometry of the 4x3 JJA is very much similar to the one mentioned in the Master thesis by Martijn (2009, Theoretical Group, Kavli Institute of Nanoscience, TU Delf). What we have is a quantum system (which is not microscopic but a macroscopic circuit of the micron size). This is a quantum system comprised of a large number of Josephson junctions (24 to be exact). To understand what this 4x3 JJA is good for, we have to understand how a single JJ works. And this in turns requires some basic knowledge in quantum mechanics, e.g. the idea of conjugate variables (e.g., {p, x}, {E,t}). In the case of a single JJ, the conjugate quantum variables are {q,phi}, where q is related to the excess number of cooper pair stored in the JJ [via q = n*(2e)], where phi is the phase difference across the JJ. In the practical implementation of a flux qubit, one normally does make some approximation to the quantum circuit to render the fluctuation in q irrelevant, so that only the variable phi is the dominant variable. q, however, is still important as its quantum fluctuation is necessary to induce quantum mixing. phi can be taken effectively as a quantised magnetic flux flowing through the JJ loop that can be detected. Its value is extremely tiny, phi \sim Phi_0, where Phi_0 = h/(2e) is the scale of quantum of magnetisation. phi (synonym to the quantum magnetic flux, or fluxon), due to its quantum character, is the quantum degree of freedom that plays the role of qubit in flux qubit. qubit is the quantity we want to manipulate finally (in a real quantum computer), hence the knowledge of how this qubit behaves is essential.
The behaviour of a flux qubit is governed by quantum mechanics. Any qubit must display a 'two-level' behavior. Under certain circumstance, the phase psi in JJ does behave like a two-level system (but this is not true in general). Hence, I really need to understand the quantum mechanical description of a two-level system, and how a flux in a JJA can be display such a two-level behavior quantum mechanically.
To describe the 4x3 JJA the quantum mechanical equations have to be written down (which has already done by Mooij). The most important quantity is the Hamiltonian. In general, once the Hamiltonian of a quantum system is written down, the behavior of the system is completely determined. What one does is then to first find out the ground state of the system. To this end, one solves the time independent Shrodinger equation to obtain the energy spectrum of the system. Basically, what is gained from this calculation is the energy of the system as a function of the external environment variables in time independent case. The degree of freedoms here are the phases (9 of them in total) in the JJA. In a single JJ, there is only one such DOE. In a JJA, there are many, and the solution to the quantum problem becomes complicated. Referring to the statement mentioned above (that 'the system must display two level behavior), one ought to make sure that, under certain restricted conditions (e.g the external magnetic bias, the so-call frustration), the energy spectrum obtained displays a profile of two weakly coupled ground states for the dof concerned (see e.g. the energy profile in page 10, Figure 2.2 of Floor Paauw's PhD thesis, 2009, Kavli Institute of Nanoscience, TU Delft). Such ground state is in turn conveniently described by the Hamiltonian Eq. (2.4) of Paauw's thesis in page 12. Essentially this Hamiltonian (which is a reduced version of the more general Hamiltonian for the whole JJA) describes the quantum mechanics of a quantum spin that has two nearly degenerate lowest ground states which are weakly coupled via the coupling terms \Delta. This \Delta term is directly related to the fluctuation of the charge q alluded to earlier. Whereas the term \epsilon controls the energy barrier that separate the two ground states of the spin. \epsilon in practice is controllable in experiment via the external magnetic frustration. Due to the presence of the coupling term \Delta, the two approximately degenerate ground states of the flux 'mix' giving rise to superposition of states. The coupling term \Delta is the 'source' of quantum behavior in the spin, otherwise, if \delta → 0 the system is reduced to a classical Ising model. The description of mixing mechanism in quantum mechanics is very much similar in spirit to the coupled quantum oscillators or Zeeman effect in atomic physics mentioned in many standard text book.
This spin model of the qubit is taken from the quantum Ising Model. If I understand how quantum mechanics describes the Ising model, I can just take over the well-known results and the interpretation of the quantum Ising Model to apply it here. In a generic Ising model, the spin only takes on two values, labelled |uparrow> and |downarrow>. Hence a qubit that has only two quantum states can be 'mapped' to a spin (which also has only two states). The mathematical description of a spin can equally well be applied to a qubit. In other words, the behavior of a qubit can be imagined to be well represented by that of a quantum spin. In basic quantum mechanical text book one often read about illustrative examples on quantum mechanical calculation done on Ising Model and also on coupled harmonic oscillators. That's why I say I need basic knowledge in quantum mechanics to understand the behavior of the flux qubit.
OK. the task comes in steps. The first step is to establish the two-level behavior of the qubit so that it can be described by the spin Hamiltonian of Eq. (2.4) in Pauuw's thesis. This initial step is by no way a trivial one although it's also not that difficult to establish. Mooij has made this step for us. There are papers published by others who reported solely on the discovery of 'yet another two-level system' suitable as a potential qubit. In these paper they merely reported that they have found another JJA system which in certain limit reduced to the two-level spin Hamiltonian of Eq. (2.4), leaving the details to the others.
The time independent calculation of the GS energy is only the first step. I also need to work out the excited state energy spectrum. The GS of the JJA can be calculated using a version of quantum Monte Carlo (QMC) called Diffusion Monte Carlo (DMC), and it is not a difficulty task. Martijn has already done it in his Master thesis. The excited state is slightly difficult. It will be tackled using excited state Monte Carlo Monte Carlo (ESMC).
Once the time independent ground state energy of the JJA is solved, I will proceed further to trace out the time evolution of the qubit system starting from its stationary (i.e. time-independent) solution. Technically, if the Hamiltonian H and the solution of the quantum state at t=0 is known, then the evolution of its states can be obtained via
|state(t)> = exp(iH*t)|state(t=0)>.
The theories, methodology and other technical details of this I am still learning, but in principle it's nothing more that a routine calculation for those who know how to use quantum mechanics at their finger tips (no me though). Any basic quantum mechanics textbook will talk about this. I hope that I will be able to write to more about this part on how to trace the time evolution of qubit soon (i.e when I understand them better).
There are still one more thing i have not clarify. As mentioned in the beginning of this 'article', this project also contains a 'computational aspect'. Pragmatically, this is the real task that I have to work on. Understanding the theoretical framework and methodologies in QM calculation are only the first step. The real dirty job is to solve the quantum equations. In our case concerned, we have to use computer to solve it by writing Fortran codes. This is the kind of dirty job I am working on now. Numerical and computational strategies to solve QM system are a big field by itself. For this matter, the book by Thijssen is essentially useful. For small system, often there are standard numerical techniques/methods available to solve our problem. For example, one often heard about some jargons in computational quantum mechanics e.g. Ritz variational method, Hartree-Fock, Density functional theory, Lanczos method, Quantum Monte Carlo, generalisd eigen value problem, optimisation etc. Two years ago i am still very ignorant of all these jargon. But now i think i am now more or less (at least in principle) understand what these things are and how to implement them in my computer. These are all 'standard technical trick' that one uses in routine basis to solve quantum mechanical problems. However, i suppose that the ability to know how to use computer to solve a generalised quantum mechanical Hamiltonian is not a very common knowledge even for experienced researchers.
The main issue one often encounter is that for a quantum system having too large a number of degree of freedoms, or a complicated interactions (as described by the Hamiltonian), computer power simply becomes not enough since the Fock space in which the solution lies increases exponentially with every additional degree of freedom. The larger the Fock space is the search for the solution simply needs more step to iterate, hence longer time. One often have to use alternative or clever computational tricks to circumvent this bottle neck. One common 'master tool' is to resort to QMC method when everything else does not work.
Well, the above is a simplified (and maybe erroneous) description of how i understand the project. I had no rigorous training in quantum mechanics in the past. However i really find it intellectually satisfying to learn, understand and actually calculate with quantum mechanics. QM is such an important and essential subject for anyone who want to deal with the fundamental aspects of our materialistic universe. I consider it a very very important tool that every serious theoretical physicist must master. It is unfortunate that USM treats QM as an optional subject and never want to stress on this. QM is so powerful that one cannot do without when dealing with physics at their fundamental level. For example, for anyone who wishes to research in material's physics at the nanoscale (nano science), without QM one can only scratch the surface of the core problem. So is semiconductor science, magnetism or optoelectronics. Our current materialistic development all owes their success to our ability to use QM to investigate the behavior of matter at their most fundamental level. I recall that a student once mentioned enthusiastically that he wants to learn QM. Now i think i have also developed similar kind of excitement. I gradually start to realise how ESSENTIAL QM is for fundamental physics research. With it one can do many many things in physics research.
As a last remark, one feels very empowered when envisaging the scenario where one has mastered the technical details of quantum theoretical technology, and further, is able to use the computational techniques learn to solve a generic quantum Hamiltonian. Give me a Hamiltonian which is otherwise difficult to probe analytically, and i will tell u how the system behaves using the computational methods.
August 09
Particle physics and Indiana Jones
Particle physics really has this special ummph that makes its researchers to feel like being truth seekers of the deepest mystery of the universe. I was once admirer of such noble pursuit, and maybe I still am. I can imagine when one look at the particle tracks and match them with the known laws of physics, one may feel like an Indiana Jones in search of cosmic relics for truth. In my research life in Melbourne there was no contact with real experiments. I only look at experimental figures from the arXive but never directly performing any serious analysis on experimental data (though my boss did), since my research emphasis is on theoretical modeling. However out group did write many experimental data analysis and arguing for their interpretations. It seems to me that analysing experimental data involves much statistics and is quite a specialised field by itself, at least it is not taught at the undergraduate level. Anyway I was once quite interested in the statistical analysis and data interpretation (the curiosity was aroused mainly because I always see my boss and his collaborator writes papers on this). So there are some terminology were heard over the times, some of which I know a little but never entire clear about, e.g. bins, chi-squared, 2.5 sigma signal, 5 sigma signal, parameter spaces, best fit parameters, 99.9% confidence level (which is ironically not considered a sufficient criteria to established an experimental signal), etc. Sometimes ago driven by pure curiosity I took up the book by the Oxford physicist Louis Lyons to make some light reading. since I am not in the business of actually performing the data analysis (and has no data to access) I have not done any exercises on the data analysis. I then gradually digressed to learn up computational physics stuff instead of sitting down to try out some particle statistics analysis research.
Once upon a time I was amazed to know that we can actually 'simulate' an experiment using Monte Carlo before the experiment is carried out. Lyonn's book mentioned a bit about it but never go in depth. My curiosity in the technical details of how one actually do this still remains until today. I have this impression that actually anyone who are keen enough can perform his own analysis using his own computers by accessing the original data remotely into the particle physics lab freely, provided that he has the technical knowledge..
Some thoughts on quantum mechanics
Quantum mechanics is almost all about application. It's a 'known law of physics'. Quantum computation is about manipulating the known laws of QM to process information. If QM is all about 'theory' then it would be useless is the sense that it cannot be used for application at all. For example, Feynman diagram calculation is an example of application of quantum field theory. The laws governing interactions between light and atoms, i.e. QED, is also application of quantum mechanics and quantum field theory. Formulation of new theory, say, say an alternative approach for quantum mechanics, is an extremely difficult stuff to do (as far as I am concerned). Formulation of 'new theory', as a prerequisite would require it's inventor tremendous amount of experience in application of existing theory. Quantum optics is also an quantum 'application'. It makes use of quantum interactions to describe exotic behaviour between light and atoms under specific conditions to see if there is any 'exotic' phenomena can be predicted and tested experimentally. But quantum optics itself is not a new formulation of QM but merely an application.
So my opinion is that a physics student has to learn more application of quantum mechanics. Although the quantum laws are known, the effects that could result under certain exotic physical conditions could be very very interesting. In other words, the law of QM may be pretty much 'dead' but the consequences of it could be infinitely many, of which some are not known before. For example Josephson junction is a consequence of quantum mechanical laws but was not known until the 1970s when Josephson (then just a graduate student in Cambridge) 'discovered' it. If one really wants to discover exotic thing like Josephson, he/she must gone through many 'application' exercises before exploring further into the more fundamental aspect of the law of quantum mechanics.
My first week in Delft
Yesterday night my 'boss' invited three of his research guests (me and two Americans) to his house for dinner, which make a very memorable experience. The interesting part was that we began our dinner at around 7 pm, and chat until 11pm at night. Since it is summer the sky gets dark only by 10 pm. The host played some classical music in the dinning hall, and occasionally there were long quite moments where everyone was just listening to the classical. Wow, I never experience such kind of moment. In Penang, in a gathering of similar kind, I usually won't 'allow' moment of silence to happen. But the experience last night was different. its romantic and special to me.
For the last few days I managed to do something that I almost can't hardly do successfully in Penang: I manage to wake up early (typically before 8 am), and manage to do a short period of mediation after waking up. My plan is that I wish to change as much as I manage some life style or daily habit, and also to raise myself to a higher intellectual level during this sabbatical leave period. I think in Penang I was always very 'huaxin' - flowery heart-ed, and can hardly able to concentrate for long hours to do extended period of study or thinking. Here I will try to change that. I actually admire the westerners who generally has good degree of concentration and discipline. By associate myself with many such intellectual I wish to also gain more such quality.
09 June 2009 6:15
A virtual experience with OS
After i visited Jonni's home in Melbourne, Jan 09, and witnessed his XPS laptop, I decided to get one for myself. I have been using my new Dell XPS M1330 for quite a few month by now. it is shipped with a built-in Vista 32 bit home basic (cheapest possible Windows). Recently the Vista suffered a series of serious clashes after automatic updating , so much so that I am forced to do multiple times system reinstallation. Anyone had experienced the same tragedy?
I have installed a Ubuntu 9.x 64 bits in the my laptop. Ubuntu has its own problem, esp. I can't get into the wireless in my working place which requires some sort of security authentication. The wireless authentication seems to require some sort of 'radius' certificate before it can accept the login. I can log in wireless easily with Vista which has this radius, but no luck with Ubuntu.
So I am trying an alternative way to fix the problem. The policy in TU Delft has it that guest can't used the wired LAN cable with laptops. so what I am doing as an attempt to circumvent the problem is to install Vbox (from SUN) in my Ubuntu. The Vbox virtual machine was up and running in the Ubuntu. Fine. Then I put in my Vista installation disk and get the installation running inside the Vbox. The installation went on well, so now I have a Ubuntu host and a vista guest. But the problem is: The Vista guest can get wired internet connection but not the wireless one. The problem is that the wireless driver in the Dell XPS M1330 cannot be installed inside the virtual machines. When I attempted to install the missing network controller drivers from the Dell Installation CD for drivers, permission was denied, claiming that the driver is not meant for a `32 bit application'. I even tried to download the latest driver from support.dell.com , but I got the same denial: The drivers (packaged in R12345x.exe form) just can't get installed. The wireless network controller in the virtual vista just refused to work. So, how can I make the virtual Vista installed in the vbox running in my Ubuntu to detect wireless signals? I have spent quit a bit of time trying to solve this issue since the last few days, including googling in the net, including this one http://johnpaulett.com/2007/03/25/vista-on-ubuntu-using-virtualbox/ but it did not solve my problem.
So, I actually did successfully install a Vista guest in my Ubuntu 9 host's Vbox, and the guest Vista also connect to wired internet as well. Just that the virtual Vista does not detect the wireless network card, other wise it works quite OK. There is a problem to install Windows XP 64 bit in the Dell XPS M1330, as many drivers are not provided by Dell. I actually have adopted Jonni's solutions (as a matter of fact I had tried almost all possible combination, e,g, Windows 7, Windows XP, Windows Vista as guest, vbox in vista, Vbox in Ubuntu 9 etc. All didn't work out the way I want them to be. My experience confirm the rumor that Vista 32 home basic is the lousiest OS.
At this point I decide not to spend time to trouble shoot it anymore. I had spent too much time to debug the above issues. I also discovered that I can't be disciplined enough to let go of minor things that are of no importance. The virtual machine issue is a good example. It's actually not a very essential issues to settle, but I spent weeks to do it (almost uncontrollably), and left the more hard core problem of physics programming not done. I suspect this is a manifestation of my tendency to shunt difficult problem. Almost every day, after waking up, I have to look into the mirror to remind myself not to repeat the same tendency on that day. I get to feel more deeply that cultivation spirituality is a process that requires right effort, energy and constant reminder, as our intrinsic nature is dominated by the tendency to drown into laziness.
10 August 2009 2:19
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