Wolfram Science

Jamie Williams: Entanglement Dynamics in Quantum Cellular Automata

Natural Sciences lecture series

Jamie Williams of Wolfram Research discusses quantum computing with NKS

Jamie described a quantum system where atoms are loaded in a lattice-like array, providing an alternative quantum circuit model. Lattice-like structures occur naturally, but can also be engineered. It is desirable to be able to address individual atoms in the lattice, and this can be accomplished by applying global control fields with laser light.

Recent literature has shown that any quantum TM can be efficiently simulated by a 1D partitioned QCA. Another result showed that open 1D lattice composed of alternating array of two types of qubits with Ising-type interactions can be used for quantum computation.

Quantum CA work by considering atoms in cells, where each atom can have one of two spin states, or in fact a superposition of both states. What often happens though is that the states of the cells become entangled, such that the system is not factorizable in general. As Jamie described, normal ECA-type rules don't work for simulating quantum systems, and so his solution is to utilize a block-partitioned QCA, first updating the odd sites in a lattice, and then the even sites. These two steps combine to form one full update step.

QCA are not very amenable to the NKS approach, since the computational resources needed scales exponentially with the size of the system. On a standard computer, up to only about 20 sites can be included. One potential solution for this is Vidal's time-dependent DMRG sumulation of 1D, which could allow over 100 sites, but has the disadvantage of using a truncated representation.

Eric Mjolsness, "Toward a Searchable Space of Dynamical System Models"

Posted by Kathryn Cramer.

Mjolsness set out criteria for simple formal systems: expressive power, discrete labeled graph structure, & self-applicability. he showed a wide variety of examples from a number of disciplines and on multiple scales. He argued that the stochastic process operators can form the semantics of a language, and that operator algebra then leads to novel algorithms. This results in a searchable space of simple dynamical system models.

Abstract. Also, here is Eric Mjolsness's web site, which he  suggests you visit for more information, is here.

Stephen Wolfram's Keynote Address: "The core of NKS is exploring the computational universe."

Posted by Kathryn Cramer.

Stephen Wolfram gave a wide-ranging Keynote Address that touched on many (or perhaps even all) of the subjects of the papers to be presented at the conference.

The central organizing metaphor of the talk was the field of NKS as an exploration of the computational universe: The core of NKS is exploring the computational universe.

My favorite line from the talk, from the portion in which he discussed NKS and aesthetics is: We are seeing the beauty of nature but not just from our world, but from all possible worlds.

As I was listening to his talk I explored the relationship between the various items on the program today. Here is my first draft version of this. As I listen to the talks I will modify and improve upon this.

Larger versions of the graphic are available here: 1024 x 642 and 3869 x 2424.

The talk will be available later. We will post the URL when we have it.