Trying to disentangle my incoherent thoughts

Here a few notes and comments on some of todays talks on the Conference on Quantum Information and Quantum Control in Toronto.

Andrew White (University of Queensland)
Quantum Chemistry on a Quantum Computer: First Steps and Prospects

He showed some nices pictures of potential energy surfaces. In passing I mention that John Polanyi, a long-time faculty member in Chemistry at U. Toronto who shared a Nobel Prize in 1986 for illuminating the significance of such surfaces for reaction kinetics.

Essentially the work described seems to be diagonalising a 2x2 matrix on a quantum computer (by the phase estimation algorithm). It was not clear from the talk how the matrix elements in this matrix were evaluated since they involve performing various real space integrals (i.e., matrix elements) of the real space Hamiltonian. Practical quantum chemists would say that evaluating such integrals is an essential part of a real calculation. Even disregarding this issue calculations with more realistic basis sets will require many more qubits. Hence, I wonder if a better direction for such simulations of quantum systems is to focus on simulating systems with small Hilbert spaces interacting with an environment. The simplest such model Hamiltonian would be the spin-boson model. Simulating the quantum dynamics of this on classical computer is a real challenge but in a quantum computer simulation one could have the significant advantage that an artiificial source of decoherence would have few cost overheads...

Shohini Ghose (Wilfrid Laurier University)
Entanglement and nonlocality in multiqubit pure states

This is based on a recent PRL.

Consider pairs of qubits in a pure state. Then the states are entangled if and only if they violate Bell-type inequalities. [If the state is mixed then Werner showed there exist states which are entangled but not violate Bell].

For 3 qubits one can uses the 3 particle tangle (introduced by Coffman, Kundu, and Wootters) to quantify entanglement and there is an inequality due to Svetlichny which is the 3-qubit generalisation of Bell-CSCH inequalities.

A few really striking aspects of the results presented
(they are "counter-intuitive" because they are different to what occurs in the 2 qubit case) :

• There exist tripartite entangled states that do not violate the Svetlichny inequality.
• The tangle is not a smooth function of the state coefficients.

Talking to Shohini afterwards she drew my attention to a paper by Cai et al. which introduces a measure for true 2N-particle entanglement. I am particularly interested in this because I want to quantify the amount of entanglement in the resonating valence bond state of benzene.

Chris Monroe (University of Maryland)
Quantum Networks with Ions, Phonons, and Photons

Chris showed how to simulate a 3 spin Ising model in a transverse field. The spin-spin interaction is mediated by phonons (i.e., relative motion of the ions). Given the state of ion trap technology extending this to as many as 10 spins. This should make possible some of the simulations that Gerard Milburn and I considered several years ago with a student John Paul Barjaktarevic and described here. These have the significant advantage that one does not have to worry about Trotter decomposition.

well its midnight in Toronto and 2pm in brisbane.... time to go back to bed and try and get over the jet lag....