As this year comes to a close, people around the world will be counting down the last few seconds of 2012. But, how come we never count up the first few seconds of the new year? What is it about the last few seconds of the year that makes them so special? Maybe it has to do with surviving a Mayan apocalypse, but that was just this year. I guess it always comes down to letting go of the good and of the difficult moments in our past. The champagne helps. Still, I would like to take a moment to pay tribute to the first few seconds of 2013 (the future) with a simple problem and a twist…
The question is simple enough: What is the longest sequence of consecutive numbers, such that each element of the sequence is a power of a prime number?
You will arrive at the answer soon after asking yourself the question: How often is a number divisible by both 2 and 3? The answer is every 6 numbers (since the number in question has to be divisible by ). So, the best one can do is to count the numbers from one to five. That is, if you count 1 as the power of a prime number, then the first five numbers have the incredible property of being the only such sequence of numbers (right?). [Note: Recalling that 1 is not a prime number (see Redemption: Part I, for a hint), we will allow ourselves to use 0 as a valid power to which we may raise a prime number, thus getting , which completes the argument.]
Now, here comes the twist…
Challenge: Is there a sequence of 10 consecutive numbers such that none of them is a power of a prime number?
To get the ball rolling, here are the first such sequences with one, two and three elements, respectively: [6], [14,15], [20,21,22].
Super Challenge: Can you find a sequence of 2013 consecutive numbers, such that none of them is a power of a prime number?
Impossible Challenge: Can you solve the first challenge, giving the sequence containing the smallest numbers satisfying the conditions of the problem?
Good luck and enjoy the rest of 2012! Who knows, maybe some genius will solve the above challenges before 2013 rolls around…
I heard of Jeff Kimble long before I met him in person. Legend had it that he was extremely rigorous with research and very tough on nonsense. So when I decided to approach him in October of 1996, at the annual OSA meeting in Rochester for a possible postdoc position, I was as nervous as I was excited. As a graduate student, I had learned theory of quantum optics from Marlan Scully, and learned advanced experimental techniques from Jan Hall. The experiences working with Jan laid a critical foundation for my scientific work. Likewise, Jeff had spent a sabbatical with Jan in 1985 that enabled their work on squeezing, as well as Jeff’s subsequent research in cavity QED, which provided me some comfort with this tall stranger. But, here was a guy who dealt with the annihilation operator as deftly in the lab as on paper; so I was hesitant. Then I listened to Jeff’s lecture on flying qubits and single-photon quantum logic gates – his speech for the Max Born Award. Armed with courage after surviving my own very first invited talk at OSA, I decided to give it a try.
I still remember most of our discussions from that first meeting, but none is as clear as my recollection of the pain from Jeff’s handshake. His grip was more than just firm; it actually squeezed the bones of my hand. So naturally, I took the handshake as a sign that he really wanted me to join his group. When an offer of a Caltech fellowship arrived three months later, I accepted it without hesitation. In 1997, I had no way of knowing that Jeff’s way of doing science would leave a profound mark on my career and that his deep friendship would continue to enrich my life and that of my family for many years.
I’m lazy. The only reason I ever do anything is that sometimes in a weak moment I agree to do something, and after that I don’t have the nerve to back out. And that’s how I happened to give the introductory lectures leading off the 12th Canadian Summer School on Quantum Information last June.
The video of the lectures recently became available on YouTube in two one-hour segments, which is my reason for posting about them now:
Here are the slides I used. The school is pitched at beginning graduate students who have a solid background in quantum mechanics but may not be very familiar with quantum information concepts.
Andrew Childs, who knows my character flaws well, invited me to lecture at the school nearly a year in advance. Undaunted by my silence, he kept resending the invitation at regular intervals to improve his chances of catching me on a weak day. Sure enough, feeling a twinge of guilt over blowing off David Poulin when he made the same request the year before, and with a haunting sense that I had refused to do something Andrew had asked me to do on an earlier occasion (though I can’t recall what), one day in September I said yes, feeling the inevitable stab of regret just seconds after pushing the Send button. I consoled myself with the thought that this could be a Valuable Service to the Community.
Actually, it was fun to think about what to include in my lectures. The job was easier because I knew that the other lecturers who would follow me, all of them excellent, would be able to dig more deeply into some of the topics I would introduce. I decided that my first responsibility should be to convey what makes the topic important and exciting, without getting too bogged down in technicalities which were likely to be addressed later in the school. That meant emphasizing the essence of what makes quantum information different from ordinary “classical” information, and expounding on the theme that classical systems cannot in general simulate quantum systems efficiently.
The conditions under which I delivered the lectures were not quite ideal. Preparing PowerPoint slides is incredibly time consuming, and I believe in the principle that such a task can fill however much time is allotted for it. Therefore, as a matter of policy, I try to delay starting on the slides until the last moment, which has sometimes gotten me into hot water. In this case it meant working on the slides during the flight from LA to Toronto, in the car from Toronto to Waterloo, and then for a few more hours in my hotel room until I went to bed about midnight, with my alarm set for 6 am so I could finish my preparations in the morning.
It seemed like a good plan. But around 2 am I was awakened by an incredibly loud pounding, which sounded like a heavy mallet hammering on the ceiling below me. As I discovered when I complained to the front desk, this was literally true — they were repairing the air-conditioning ducts in the restaurant underneath my room. I was told that the hotel could not do anything about the noise, because the restaurant is under different ownership. I went back to bed, but lost patience around 3:30 am and demanded a different room, on the other side of the hotel. I was settled in my (perfectly quiet) new room by 4 am, but I was too keyed up to sleep, and read a book on my iPad until it was 6 am and time to get up.
I worked in my room as late as I could, then grabbed a taxi, showing the driver a map with the location of the summer school marked on it. Soon after he dropped me off, I discovered I was on the wrong side of the University of Waterloo campus, about a 20 minute walk from where I was supposed to be. It was about 8:15, and the school was to begin at 8:30, so I started jogging, though not, as it turned out, in the right direction. After twice asking passersby for help, I got to the lecture hall just in time, my heart pounding and my shirt soaked with sweat. Not in the best of moods, I barked at Andrew that I needed coffee, which he dutifully fetched for me.
Though my head was pounding and my legs felt rubbery, adrenalin kicked in as I started lecturing. I felt like I was performing in a lower gear than usual, but I wasn’t sure whether the audience could tell.
And as often happens when I reluctantly agree to do something, when it was all over I was glad I had done it.
Joe Polchinski was a Caltech undergrad, class of 1975 (before my time here). I first met Joe in 1982 when he arrived as a postdoc at Harvard, where I was then on the faculty, and it did not take long for me to recognize his genius. I was teaching a course that fall on advanced quantum field theory, and Joe sat in, at least for a while. One of my lectures was about renormalizability, and I talked about how the renormalization group can organize and simplify the horrible combinatoric task of taming the overlapping divergences in Feynman diagrams to all orders of perturbation theory. I had learned this idea from Curt Callan‘s wonderful 1975 Les Houches Summer School Lectures. Continue reading →
This is fantastic news! I assume the Prize recognizes Stephen’s great discovery that black holes radiate, one of the most transformative developments in theoretical physics during my lifetime. That’s just one of Stephen’s many important contributions. And of course his supreme skill as a popularizer and the unparalleled courage he displays in response to his disability have made him the most famous living scientist in the world. Congratulations, Stephen!
Stephen has a long-standing relationship with Caltech. He spent a sabbatical year here during 1974-75, when he wrote his famous paper formulating the black hole information paradox, and he has made more or less annual extended visits to Caltech since the 1990s. Stephen and I had many memorable discussions about black holes over the years, culminating when he conceded a bet, for which I received far more attention than I deserved. I’ve been proud to be Stephen’s friend for the past 30 years, and we’ve shared a lot of laughter.
Jeff Kimble played college basketball. I conjecture that he is more than two meters tall, though being a theorist I have never measured him. Jeff certainly stands tall in the Pantheon of outstanding physicists, and we at Quantum Frontiers were thrilled to hear that Jeff has received the 2013 Herbert Walther Award, which is very well deserved.
About four years ago, Jeff gave a public lecture at Caltech about “The Quantum Internet,” and I had the honor of introducing him. The video of Jeff’s lecture and my introduction are embedded at the end of this post. You’ll have to watch the video to hear all the Buddy Holly references in my introduction (Jeff and Buddy come from the same county in Texas). Jeff’s lecture was memorable, too, featuring a dance performance by his research group.
One of my most annoying quirks is that I like to use poems to introduce people, so I wrote one to fit the topic of the lecture. Among many other achievements, Jeff’s group has done pioneering experiments distributing quantum entanglement among multiple nodes in a quantum network, which is probably all you need to know to understand the poem.
Fluorescence image of four laser-cooled atomic ensembles, each used as a quantum node in an entanglement distribution experiment by the Kimble group.
Listening to one of my poems tends to make the audience uncomfortable (which I’ve been told is a sign that it’s good poetry). But Jeff did not seem to mind the poem too much, so I will seize the opportunity to post it here to commemorate the occasion.
Congratulations, Jeff!
The Quantum Internet
Professor HJ Kimble Is much larger than a thimble And a veritable symbol Of the physicist today.
Could it be prodigious height Explains his knack for squeezing light Or is Jeff’s mind extremely bright? I guess that’s hard to say…
Jeff wants to build a quantum net It seems quite hard, but still I bet Someday we’ll get there, just not yet. There’ll be a slight delay.
At least they’ve made a quantum node, That’s a start along the road. They showed a photon could be stowed And then released. Okay?
Jeff’s students stay up very late And try to share a quantum state Between two nodes. But when you wait Entanglement decays.
Once entanglement is strong And they can make it last quite long One node could be inside Hong Kong The other in Bombay.
And once the quantum net’s begun We’re going to have a lot of fun Exploiting work that Jeff has done Hear what he has to say!
Prof. Kimble knew Prof. Walther personally and has profound respect for him and his accomplishments. He is greatly honored by this award.
H. Jeff Kimble, William L. Valentine Professor of Physics at Caltech, is the recipient of the 2013 Herbert Walther award. This award is jointly made by the Deutsche Physikalische Gesellschaft (DPG, the German Physical Society) and the Optical Society of America (OSA), and is presented by each society in alternate years.
Quantum correlations are monogamous. Bob can be highly entangled with Alice or with Carrie, but not both.
Back in the early 1990s, I was very interested in the quantum physics of black holes and devoted much of my research effort to thinking about how black holes process quantum information. That effort may have prepared me to appreciate Peter Shor’s spectacular breakthrough — the discovery of a quantum algorithm for factoring intergers efficiently. I told the story here of how I secretly struggled to understand Shor’s algorithm while attending a workshop on black holes in 1994.
Since the mid-1990s, quantum information has been the main focus of my research. I hope that some of the work I’ve done can help to hasten the onset of a new era in which quantum computers are used routinely to perform super-classical tasks. But I have always had another motivation for working on quantum information science — a conviction that insights gained by thinking about quantum computation can illuminate deep issues in other areas of physics, especially quantum condensed matter and quantum gravity. In recent years quantum information concepts have begun penetrating into other fields, and I expect that trend to continue. Continue reading →
Quantum Frontiers 