**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.