31 January 2005

Jack Frost Designs

One of my fascinations in life is with snow and ice. This morning, I came across a New York Times video about a man who takes pictures of ice formations on his greenhouse windows.

29 January 2005


I've moved the blog from qmengineer.blogspot.com to qmechanic.blogspot.com.

I originally wanted qmechanic when I started this blog. Now it's available so I'm making the switch.

Parental blogging

The New York Times today has an article describing parents who blog about their infant children.

Of all the blogs mentioned, my favorite was "The Trixie Update", complete with graphs of the baby's projected growth and detailed explanations of milk feeding.

I think parental blogging is a rather nice addition to the blogging world as opposed to say, diaries of one's sexual exploits.

28 January 2005

Title of this blog

To my loyal readers,

I am trying to come up with a new title for my blog. Here are some ideas:
  • One path of a quantum mechanical engineer
  • Qmechanic's picture
  • Life, quantum mechanics, and all that
  • Learning to love the uncertainty

and the original title: "Some thoughts from a quantum mechanical engineer."

Please let me know what you think and/or give me your favorite idea.

- qmechanic

Additional note added 5 February 2005:
Amoebe thought my ideas were lame, so I have came up with the accurate but unexciting title above.

What is a quantum computer?

Let me first explain how a "classical" computer works. The main components of a classical computer are the CPU (central processing unit), memory (in a modern computer, the RAM and hard drive), and the software. Of course, you usually have user input and output devices (e.g. keyboard, monitor), but they are just for communication with the computer and not central to the computing process itself. The software contains lines of "code" which are written instructions for the CPU to execute. For example, one instruction might be for the CPU to add the numbers 5 and 6. Another instruction could be to save the number 15 in memory. How is the memory implemented? Well, the information is saved in bits. Each bit can be in the state 0 or 1. Physically, a bit is usually implemented by placing a certain electrical charge on a capacitor (two small metal plates very close to each other). The voltage on the capacitor will then depend on how much charge is on it. If the voltage is between say 0 and 0.5 volts then we identify that state as 0 and if the voltage is greater than 0.5 volts, then that state is 1. We can change the state of the bit by moving charge on and off the capacitor.

In the last ten years, scientists have become interested in studying quantum computers. There are several reasons. First, we know that there are limits to how much classical computer power we can pack into a given volume. The rise of the computing age has been spurred by the fact that semiconductor companies can squeeze more and more circuits into smaller and smaller chips with each passing year. Computers that used to fill rooms (40 - 50 years ago) now fit into 5 pound packages. However, we know from fundamental physics principles that this trend cannot continue. After all, you can't make a circuit out of one atom! So one motivation is that to continue increasing our computing power, we will have to look into alternative approaches from silicon-based classical computers. One of these is quantum computation.

Second, it appears that quantum computers can calculate some things "faster" than classical computers. What do I mean by faster? An algorithm is a set of instructions that when executed perform a useful task (like putting a bunch of words in alphabetical order or multiplying two numbers). Computer scientists measure the speed of the algorithm by comparing how many instructions have to be executed (i.e. the number of steps) and the size of the input data. For example, if the algorithm is to multiply two numbers, the size of the input data would be the total number of digits in the two numbers. In 1994, Peter Shor discovered that if you have a N-digit number that is the product of two prime factors, a quantum computer can find the factors in approximately N squared steps. In comparison, the best known algorithm for classical computers needs exp(N^(1/3)) steps. So the quantum algorithm is exponentially faster than the classical algorithm. It happens that modern encryption of data depends on the fact that it takes a classical computer exponentially increasing time to find the two prime factors. If a quantum computer could be built, it could conceivably break all the encryption codes at banks, the CIA, etc.!

Now that I've explained why quantum computers are interesting, I will try to explain how they work. A quantum computer has all the same elements as a classical computer: CPU, memory, software. The distinction is in the implementation of these elements. Recall that a classical computer saves information in bits, which can be in the state 0 or 1. A quantum computer, however, stores information in quantum bits ("qubits") that can be in both 0 and 1 at the same time. To be more precise, the most general state of a qubit is
|psi> = |state 0> + |state 1> * exp(i*phi)
Here exp(i*phi) is a complex number whose absolute value is one and phi is a continuous number between 0 and 2*pi. Notice that I've put the words "state 0" inside "|>". This notation emphasizes that these states are no longer classical objects (like voltages on capacitors), but they are quantum states. This is a difficult concept to explain without a course in quantum mechanics, so I will merely try to give you a flavor of the idea. If we tried to put a classical bit in both states 0 and 1 at the same time, it wouldn't work. For instance, if we added 0.3 volts (the capacitor in state 0) to 0.7 volte (the capacitor in state 1), we would get 1 volt which the CPU would read at state 1. However, for a qubit, we can perform an operation on the quantum state |psi> and this operation would be performed independently on state 0 and state 1 at the same time. It's as if we are performing a computation on one classical bit that is in state 0 and on a separate classical bit that is in state 1. So we already have double the computing power! If we have N qubits, then we can perform computations on 2^N different states at the same time.

The bad news is that we can only read the result from one of these 2^N states. This is a consequence of a fundamental postulate in quantum mechanics. Therefore, we have to design very clever quantum algorithms that somehow focus all the information into one state, the state that we read out. So far besides the prime factoring algorithm, scientists have only found a handful of useful quantum algorithms which are faster than their classical counterparts.

How do we actually build these quantum computers? The key is to find a way to implement the qubit. There are many ideas so far, but the simplest is to use an ion (an electrically charged atom). If you remember your high school chemistry, you may recall pictures of an electron orbiting a nucleus. That electron can occupy different quantum states, which can be used to implement a qubit. Then you can shine a laser on the ion to move the electron from one state to another (analagous to the CPU). The problem is that if you put an electron in an excited state (as opposed to its ground state which is the most energetically favorable), then the electron will be "unhappy" and want to return to its ground state. The technical term for this behavior is "decoherence." We lose quantum information because our quantum bits interact with the environment, which causes them to relax to their most energetically favorable state. The decoherence problem has limited quantum computers to 10 qubits or less so far.

Thus quantum computers are an interesting piece of science but not yet a practical technology.

24 January 2005

Larry Summers' comments on women in science

Larry Summers, the president of Harvard, recently made some comments about women in science at an academic conference. Allegedly, he said that women are discouraged from pursuing science because 1) they don't want to work 80 hour weeks and because 2) women are innately less inclined towards science and/or less able to do science. (Here I am using science as a generic term for math, physics, chemistry, biology, neuroscience, psychology, economics, etc.) There was supposedly a third reason, but it was not reported.

Since I am a woman scientist, I've decided to write my comments here. America is a nation of free speech and Larry Summers should have the right to voice his (unpopular) opinion especially in an academic venue that is closed from the public. If Summers had made the same speech in front of an audience that included adolescent girls, the critics would have a right to protest since these statements would have been damaging to a young girl's self-esteem. But that was not the case.

I don't completely agree with Summers' statements themselves (assuming they were accurately reported.) He seems to imply that genetics is more important a factor than social/environmental influences. In Asian culture, no one believes in talent, only in the value of hard work. Thus despite their minority status in America, Asians are very successful. I don't have any hard facts in front of me, but I think this is a fair statement. Everyone knows that talent has to be nourished for a person to realize his/her full potential. Behind every star pitcher is a legion of family, friends, and coaches. As for the 80 hour/week barrier, I agree that is a problem, but I don't know how significant it is compared to the genetic and social/environmental factors I just discussed.

It is unfortunate that no one has an actual transcript of the Summers speech. Harvard supposedly has a tape, but refuses to release it. Without knowing what Summers actually said, it's difficult to judge whether he was merely being academic or really being offensive.

14 January 2005

Inspiration from young theorists

Nature (the scientific publication) has profiled four promising young theoretical physicists in honor of Einstein who published some of his most groundbreaking papers one hundred years ago. The physicists include a particle phenomenologist working on extra-large dimensions, a quantum information theorist working on error correction, a loop gravity physicist studying cosmology, and a condensed matter theorist studying exotic materials and quantum phase transitions.

09 January 2005

Another beautiful bit of writing

The great novelists of the Victorian age really know to write! For instance, take Charles Dickens' preface for David Copperfield:

"I remarked in the original Preface to this Book, that I did not find it easy to get sufficiently far away from it, in the first sensations of having finished it, to refer to it with the composure which this formal heading would seem to require. My interest in it was so recent and strong, and my mind was so divided between pleasure and regret-pleasure in the achievement of a long design, regret in the separation from many companions-that I was in danger of wearying the reader with personal confidences and private emotions.

Besides which, all that I could have said of the Story to any purpose, I had endeavoured to say in it.

It would concern the reader little, perhaps, to know how sorrowfully the pen is laid down at the close of a two-years' imaginative task; or how an Author feels as if he were dismissing some portion of himself into the shadowy world, when a crowd of the creatures of his brain are going from him for ever. Yet, I had nothing else to tell; unless, indeed, I were to confess (which might be of less moment still), that no one can ever believe this Narrative, in the reading, more than I believed it in the writing.

So true are these avowals at the present day, that I can now only take the reader into one confidence more. Of all my books, I like this the best. It will be easily believed that I am a fond parent to every child of my fancy, and that no one can ever love that family as dearly as I love them. But, like many fond parents, I have in my heart of hearts a favourite child. And his name is DAVID COPPERFIELD. 1869"

How do I learn to write like that? What happened to the English language? My guess is that as literacy became increasingly wide-spread, it became necessary to decrease the floweriness of prose to reach a wider audience -- not everyone can afford a university education. Too bad we can't bring back this style.

08 January 2005

Book review/analysis: Middlemarch

I just finished reading George Eliot's Middlemarch (1871-1872). It's considered one of the best novels of the Victorian era and was originally published in serial form. I should mention that George Eliot was actually the pseudonym of an upper-middle class woman named Mary Ann Evans.

The novel is set in English countryside near a town called Middlemarch during the 1830s. Eliot centers the plot around three couples. The first couple is Rosamond Vincy, a manufacturing factory owner's daughter, and Tertius Lydgate, a young ambitious doctor. The second couple is Mary Garth, a land surveyor's daughter, and Fred Vincy, brother of Rosamond. The third couple is Dorothea Brooke, niece of a well-to-do landed gentleman, and Mr. Causabon, a clergyman and historical scholar. Their unhappy marriage is further nettled by the appearance of Causabon's cousin, Will Ladislaw.

The main thesis of Middlemarch might be summarized as "what happens when idealism and the real world clash." Idealism is represented by the characters of Dorothea and Lydgate. Dorothea, at the age of twenty, has already decided that she wants to spend her life doing good, specifically helping a great man do his great work. She has (almost comical) fantasies about reading to and ministering to the blind John Milton. Lydgate has the ambition of making breakthrough medical discoveries and has come to Middlemarch because he believes it will be easier to do his research away from the city. I won't give away the plot but both characters marry the wrong people for the wrong reasons. Instead of marriage being supportive of their goals, they find it to be a yoke. Being such selfless and honorable people, they give up their idealism and submit to the whims of their spouses. Neither Mary nor Fred are idealistic, but their relationship does succeed because Mary acts as the sensible, practical half to guide Fred, who becomes good to win Mary's hand in marriage. Fred's true love for Mary might be considered a form of idealism. So what is Eliot's message? She is advocating idealism tempered by practicality. Under the best circumstances, idealism will enable a person to become greater than him/herself. In the worst cases, idealism is completely crushed by harsh reality. Probably most idealists fall into the middle. They make mistakes and compromise, but eventually they do accomplish some good in the world. Eliot is telling these people to be brave and endure their trials because in the end, their efforts will pay off (see the second quote below).

A secondary theme in Middlemarch is class differences and social expectations. Many examples are sprinkeld throughout the novel. Rosamond's main aim is to secure an upper class husband with high connections so she can rise above the Middlemarch crowd. Thus Dr. Lydgate's noble connections (his uncle is a baronet) immediately attract her attention. Mrs. Vincy objects to her son Fred courting Mary because Mary's family has a lower social status than the Vincys. The irony is that Fred actually ends up happier than his sister Rosamond. Dorothea wants to do saintly good but is severely restricted by her gender and lack of education. It is no coincidence that Eliot chooses to set the novel during the 1830s when reform was a weighty topic in British politics.

Now I'll move on to stylistic comments. Eliot adopts the omniscient narrator method like all the novelists of the Victorian period. I imagine that some people find this style annoyingly didactic, but I rather enjoy the thoughtful commentary. It's nice to see what's going through each character's head. This method is particularly powerful during Rosamond and Dr. Lydgate's marital squabbles as Eliot jumps back and forth between their contrasting perspectives. Having read quite a few modern 20th century novels, it's refreshing not to having to guess the author's intentions. One minor complaint I have is that occasionally Eliot's narrations are overbearing. It is probably emphasized at least a dozen times that Mr. Causabon does not really love his wife and that Rosamond Vincy is a selfish brat. At one point, Eliot even goes into a long segway about why she's spending so much time discussing "low characters." She tells the reader (presumably upper-class folk) to treat it as a parable! Moreover, I occasionally had trouble following the wordy 19th century language.

The story itself is so intricate and finely woven together that it feels like a tapestry of provincial life. This unique feature separates this novel from the works of other Victorian writers I've read (Dickens, Hardy). Somehow Eliot manages to tie together the lives of a French-educated doctor, a manufacturing owner's family, a vicar, a rich banker, a surveyor's family, and landed gentry. By the end of the book, you feel like you know the whole town! No wonder Eliot subitled her novel "a study of provincial life."

I especially enjoyed Eliot's witty and eloquent descriptions. My favorite passages were at the beginning and end of the book. Here's an example (which appeared on a College English Literature AP Exam):
Miss Brooke had that kind of beauty which seems to be thrown into relief by poor dress. Her hand and wrist were so finely formed that she could wear sleeves not less bare of style than those in which the Blessed Virgin appeared to Italian painters...
A few years ago, I included this beautiful passage in our family Christmas newsletter following the September 11th tragedy:
For the growing good of the world is partly dependent on unhistoric acts; and that things are not so ill with you and me as they might have been, is half owing to the number who lived faithfully a hidden life, and rest in unvisited tombs.
Supposedly one of our friends cried after reading it.

In summary, I highly recommend Middlemarch! I have but two reservations for the interested reader: 1) the book is over 900 pages long and 2) you must like idealistic epics told by a didactic narrator.

My motivation for reading the book came from watching the BBC dramatization (1994). After finishing the book, I found that the dramatization covered 95% of the book and only left out one major plot detail. The BBC production is vivid and moving; the acting is so convincing that you feel like you have lived in Middlemarch.

I would recommend reading the book (to get the finer details) and then watching the miniseries as a treat. If you find Eliot's narration overly verbose/moralistic or are short on time, the miniseries stands extremely well on its own.

06 January 2005

Politzer's Nobel Prize lecture and physics as a career

I've been away on vacation, but it's time to start blogging again.

This evening I found two intriguing links in the recent entries of Sean Carroll's blog.

First, there is a link to the text of H. David Politzer's Nobel Prize lecture (posted by Politzer himself on his webpage and not on the Nobel Prize site).

The lecture is essentially the story behind how Politzer made his discovery (jointly with David Gross and Frank Wilczek) and the later work that established the veracity of the result. Politzer makes an interesting comment about theoretical physics being a "parasitic profession" and emphasizes the fiscal limitations on further exploration of physics beyond the standard model; he claims that we would need $10^22 to study grand unification. The lecture itself is concise and well-written; my only complaint is the frequent appearance of jargon that I myself confess to not understanding.

Second, Sean Carroll links to an essay called "Don't Become a Scientist!" written by Jonathan Katz at Washington University. He writes of how there is a scarcity of jobs, no grants, poor pay, etc -- creating a situation so dismal that young people should not pursue a career in scientific academia. This is an issue that I believe most young scientists like myself are aware of, but so painful that we try to move it to the back of our minds. (Feigned) ignorance, after all, is bliss. Clearly many people don't listen to the advice of people like Katz, otherwise we wouldn't have this problem.

The more disturbing side of the issue (mentioned by Katz in the essay) I find is that the effort-payoff ratio may be so great that talented people are turned away. One of my undergraduate professors claimed that the talent pool he encounters in faculty job searches is much thinner than in the past. As an example, he pointed to Russia, the birthplace of many famous theoretical physicists (most notably Landau). He claimed that there are hardly any more talented theoretical physicists coming out of Russia because with the dissolution of the Soviet Union, bright young people have many other possibilities. I think there is general agreement among scientists that interest in physics has dropped off considerably in the last few decades due to the decrease in funding and the rise of life sciences (biology, neuroscience, etc.). In a recent American Physical Society newsletter, a physicist rightly pointed out that it is grossly misleading to tell women and minorities that they should do physics because there won't be enough people to fill job slots in the future. Yet this is a common argument advanced by many women science interest groups. Rather it should be the aim of all physicists to inspire the bright students to join the field. Somehow we need to both convince them that physics is worth doing and fix the system to improve the average physicist's quality of life. The former has a clear solution in K-12 science outreach programs and inspiring classroom teaching. I won't comment on the latter as I know very little of the burearcracy behind academia and grants.