11/3/2022 0 Comments Eloquent hair braiding![]() But shouldn’t a scientist find inspiration in every fiber of nature? The sunlight spilling through a window illuminates no less than the hair spilling over a shoulder. Could you decode a Greek hairdo? Might it represent the first 18 digits in pi? How long an algorithm could you run on Rapunzel’s hair?Ĭall me one bobby pin short of a bun. The addition brings to mind particles created (and annihilated) during a topological quantum computation.Īncient Greek statues wear elaborate hairstyles, replete with braids and twists. You add strands to the clump while braiding. What computation might it represent? What about the French braid? You begin French-braiding by selecting a clump of hair. I gave up on his lecture notes as the analogy sprouted legs. I hadn’t realized that I was fidgeting till I found John’s analysis. Like the corkscrews formed as I twirled my hair around a finger. The braidings would look identical to a beetle hiding atop what had begun as the middle hunk of hair.Ī quantum corkscrew (“twisted worldribbon,” in technical jargon) But I could have passed the right hand first, then the left. When I braid my hair, I pass my left hand over the back of my neck. But an eight-year-old could grasp the half the relation. It might sound like a sneeze in a musty library. “Yang-Baxter relation” might sound, to nonspecialists, like a mouthful of tweed. I looked at the hair draped over my left shoulder. That Sunday morning, I looked at John’s swap diagrams. You’d see the same circling if you stood atop pea 2 during the 3-2-1 braiding. You’d see peas 1 and 3 circle around you counterclockwise. The relation states also that 1-2-3 is topologically equivalent to 3-2-1: Imagine standing atop pea 2 during the 1-2-3 braiding. You’ve shown that each braid turns 1-2-3 into 3-2-1. That sequence, or braid, appears below.Ĭongratulations! You’ve begun proving the Yang-Baxter relation. You could, instead, morph 1-2-3 into 3-2-1 via a different sequence of swaps. The peas end up ordered oppositely the way they began-end up ordered as 3, 2, 1. You swapped 1 with 2, then 1 with 3, and then 2 with 3. Let’s recap: You began with peas 1, 2, and 3. Letting time run amounts to following the diagram from bottom to top. ![]() Each strip would show one instant in time. Imagine slicing the figure into horizontal strips. The diagram below shows how the peas move. ![]() The swap represents a computation, in Alexei’s scheme. You could push peas 1 and 2 until they swapped places. We can encode information in radio signals, in letters printed on a page, in the pursing of one’s lips as one passes a howling dog’s owner, and in quantum particles. Imagine three particles on a tabletop.Ĭonsider pushing the particles around like peas on a dinner plate. 1 His computational scheme works like this. ![]() Alexei Kitaev largely dreamed up the harness. Alexei, a Caltech professor, is teaching Ph 219 this spring. Scientists are harnessing this physics to build quantum computers. Topologists study spheres, doughnuts, knots, and braids. The Yang-Baxter relation belongs to a branch of math called “topology.” Topology resembles geometry in its focus on shapes. The phrase concerned a mathematical statement called “the Yang-Baxter relation.” A sunbeam had winked on in my mind: The Yang-Baxter relation described my hair. I underlined a phrase, braided my hair so my neck could cool, and flipped a page. So did the howling of a dog that’s deepened my appreciation for Billy Collins’s poem “Another reason why I don’t keep a gun in the house.” My desk space warmed up, and I unbuttoned my jacket. Pasadena sunlight spilled through my window. I previewed lecture material one sun-kissed Sunday. I’m TAing (the teaching assistant for) Ph 219. Morning sunlight illuminated John Preskill’s lecture notes about Caltech’s quantum-computation course, Ph 219. ![]()
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