US Gross Product is 1/3 Quantum, and Chapulines

According to an article in Science, quantum = $$$.

Is Quantum Mechanics Tried, True, Wildly Successful, and Wrong?

[…] Sure, it’s the most powerful and accurate scientific theory ever devised. Yes, its bizarre predictions about the behavior of atoms and all other particles have been confirmed many times over with multi-decimal-place exactitude. True, technologies derived from quantum mechanics may account for 30% of the gross national product of the United States. So what’s not to like? [emphasis mine]

Why would this be? Well, electronics are an essential part of the US economy, and transistors are fundamentally quantum mechanical. This figure doesn’t include any quantum computing private companies.

On that subject, I just witnessed the founder of D:Wave (the first quantum computation private company) eat a taco de chapulines. Yes, that means grasshopper taco.

Tunneling is fun. -Alan

Quantum Stochastic Walks

We just posted a paper in the arXiv.

Quantum stochastic walks: A generalization of classical random walks and quantum walks

We introduce the quantum stochastic walk (QSW), which determines the evolution of generalized quantum mechanical walk on a graph that obeys a quantum stochastic equation of motion. Using an axiomatic approach, we specify the rules for all possible quantum, classical and quantum-stochastic transitions of a vertex as defined from its connectivity. We show how the family of possible QSW encompasses both the classical random walk (CRW) and the quantum walks (QW) as special cases, but also includes more general probability distributions. As an example, we study the QSW on the line, its QW to CRW transition and transitions to genearlized QSWs that go beyond the CRW and QW. QSWs provide a new framework to the study of quantum walks with environmental effects as well as quantum algorithms.

I promise a simple explanation of Classical Random Walks soon!

Imagine a molecule. Now Imagine a quantum computer solving it.

A quantum circuit, a molecular spectra, a molecule: will they ever have a threesome?
A quantum circuit, a molecular spectra, a molecule: will they ever have a threesome?

So, we have the periodic table. We know that atoms combine into molecules depending on their energy spectrum, its energy levels. We know quantum physics, the theory that reigns in the atomic regime.We know math. We know quite a lot, actually.

So, we want to create new chemicals. Having new materials would give us new technologies, having new molecules would provide us with new medicines, saving millions of lives.

How come it is so hard to use what we know to get what we want?

The problem is that atoms have many electrons, and you have to calculate the equations for each electron. But, electrons interact with other, the solution of the equations of one depend on the solutions of the equations of the other. The solutions are interconnected, coupled. This is know as the many body problem. This makes solving the equations very hard.

Although we know what to do to calculate the energy of a complicated molecule, we can’t actually do it. It takes too long, even for a computer. Computers get faster every year, but they don’t get fast fast enough for the problem. Making the molecule just a bit more complicated demands us to have a computer much much much more powerful than for one a bit simpler. In other words, the problem of solving the energy of a molecule doesn’t “scale” well.

Enter quantum computers.

Unlike a conventional computer, Aspuru-Guzik and his colleagues say, a quantum computer could complete the steps necessary to simulate a chemical reaction in a time that doesn’t increase exponentially with the reaction’s complexity.

What is a quantum computer? How is it different from other computers? What tricks can it do to solve chemical reactions faster than a normal computer?

This blog is about those questions and more. Stay tuned.