A new paper claims that a common digital security system could be tweaked to withstand attacks even from a powerful quantum computer.
A new paper claims that a common digital security system could be tweaked to withstand attacks even from a powerful quantum computer.
.. If researchers could build a quantum computer that could outperform classical supercomputers, the thinking goes, cryptographers could use a particular algorithm called Shor’s algorithm to render the RSA cryptosystem unsalvageable. The deadline to avert this may arrive sooner than we think: Google recently claimed that its quantum computers will be able to perform a calculation that’s beyond the reach of any classical computer by the end of the year.
.. The authors of the paper estimate that attacking a terabyte-size key using Shor’s algorithm would require around 2100 operations on a quantum computer, an enormous number comparable to the total number of bacterial cells on Earth.
.. The authors report that generating a terabyte-size RSA key and carrying out the encryption-decryption process takes about five days.
Quantum Questions Inspire New Math
In order to fully understand the quantum world, we may have to develop a new realm of mathematics.
Mathematics might be more of an environmental science than we realize. Even though it is a search for eternal truths, many mathematical concepts trace their origins to everyday experience. Astrology and architecture inspired Egyptians and Babylonians to develop geometry. The study of mechanics during the scientific revolution of the 17th century brought us calculus.
.. The bizarre world of quantum theory — where things can seem to be in two places at the same time and are subject to the laws of probability — not only represents a more fundamental description of nature than what preceded it, it also provides a rich context for modern mathematics. Could the logical structure of quantum theory, once fully understood and absorbed, inspire a new realm of mathematics that might be called “quantum mathematics”?
.. Ideas that originate in particle physics have an uncanny tendency to appear in the most diverse mathematical fields. This is especially true for string theory.
.. in the quantum world everything that can happen does happen.
.. Mirror symmetry illustrates a powerful property of quantum theory called duality: Two classical models can become equivalent when considered as quantum systems, as if a magic wand is waved and all the differences suddenly disappear. Dualities point to deep but often mysterious symmetries of the underlying quantum theory. In general, they are poorly understood and an indication that our understanding of quantum theory is incomplete at best.
.. A succinct way to summarize that theory is that mass tells space how to curve, and space tells mass how to move.
.. It is comforting to see how mathematics has been able to absorb so much of the intuitive, often imprecise reasoning of quantum physics and string theory, and to transform many of these ideas into rigorous statements and proofs.
Einstein and Quantum Theory
Albert Einstein famously rejected parts of the theory of quantum mechanics. His skepticism is understandable. The theory, after all, said that a single subatomic particle could occupy multiple places at the same time. A particle could move from one location to another without traversing the space between. And multiple particles that had previously interacted and then separated by vast distances, could somehow “know” what each other was up to. It didn’t seem to align with what scientists thought they knew.
.. Even though Einstein was never fully satisfied by it, quantum mechanics is now generally accepted as the fundamental way of the world.
.. One of the hard-to-get-your-head-around concepts at the heart of quantum mechanics is called superposition. Simplistically, superposition is the idea that something can be in multiple states at the same time. A single electron can have both up and down spin, a single photon can travel both this path and that one, and, conceptually, a luckless cat in a box can be both dead and alive. Until you check, that is. Once the electron’s spin is measured, or the photon is tracked, or the box lid is lifted, the system goes classical and assumes either one state or the other.
The lifting of the lid causes decoherence—another oddity of the quantum world. For a system to exist in a state of superposition it must not interact with its environment at all, including observers or scientific instruments. The loss of any information from the system to the environment—the lid being lifted and the condition of the cat becoming known—causes the system to decohere.
.. Particles that interact with one another enter into a strange relationship with one another. This relationship, known as entanglement, is preserved as long as the two particles remain sheltered from the rest of the environment, lest their entanglement decohere.
The Case Against Reality
A professor of cognitive science argues that the world is nothing like the one we experience through our senses.
.. researchers scratching their chins raw trying to understand how a three-pound lump of gray matter obeying nothing more than the ordinary laws of physics can give rise to first-person conscious experience. This is the aptly named “hard problem.”
.. On the other side are quantum physicists, marveling at the strange fact that quantum systems don’t seem to be definite objects localized in space until we come along to observe them. Experiment after experiment has shown—defying common sense—that if we assume that the particles that make up ordinary objects have an objective, observer-independent existence, we get the wrong answers... As the physicist John Wheeler put it, “Useful as it is under ordinary circumstances to say that the world exists ‘out there’ independent of us, that view can no longer be upheld.”.. According to evolution by natural selection, an organism that sees reality as it is will never be more fit than an organism of equal complexity that sees none of reality but is just tuned to fitness... Suppose there’s a blue rectangular icon on the lower right corner of your computer’s desktop — does that mean that the file itself is blue and rectangular and lives in the lower right corner of your computer? Of course not. But those are the only things that can be asserted about anything on the desktop — it has color, position, and shape. Those are the only categories available to you, and yet none of them are true about the file itself or anything in the computer. They couldn’t possibly be true. That’s an interesting thing. You could not form a true description of the innards of the computer if your entire view of reality was confined to the desktop. And yet the desktop is useful. That blue rectangular icon guides my behavior, and it hides a complex reality that I don’t need to know... Evolution has shaped us with perceptions that allow us to survive. They guide adaptive behaviors. But part of that involves hiding from us the stuff we don’t need to know. And that’s pretty much all of reality, whatever reality might be. If you had to spend all that time figuring it out, the tiger would eat you... As a teenager, I was very interested in the question “Are we machines?” My reading of the science suggested that we are. But my dad was a minister, and at church they were saying we’re not. So I decided I needed to figure it out for myself... It suggests that I can take separate observers, put them together and create new observers, and keep doing this ad infinitum. It’s conscious agents all the way down... The neuroscientists are saying, “We don’t need to invoke those kind of quantum processes, we don’t need quantum wave functions collapsing inside neurons, we can just use classical physics to describe processes in the brain.” I’m emphasizing the larger lesson of quantum mechanics: Neurons, brains, space … these are just symbols we use, they’re not real. It’s not that there’s a classical brain that does some quantum magic. It’s that there’s no brain! Quantum mechanics says that classical objects—including brains—don’t exist... As a conscious realist, I am postulating conscious experiences as ontological primitives, the most basic ingredients of the world. I’m claiming that experiences are the real coin of the realm. The experiences of everyday life—my real feeling of a headache, my real taste of chocolate—that really is the ultimate nature of reality.