## Dominic Berry - ARC Future Fellow

### Macquarie University

My research is in the areas of quantum information and quantum optics. In quantum information, I developed the most efficient known algorithms for simulation of physical systems, which has been used as the basis for important new quantum algorithms. In the area of quantum optics, I invented the most accurate known methods to measure optical phase by using adaptive techniques, and am actively collaborating with experimental groups for demonstration of these methods.

My CV is available here.

- 20/2/2014: My quantum algorithm for solving differential equations is now published in Journal of Physics A. This is my 50'th published paper.

- 27/1/2014: My work with Alexander Hayes showing that feedback can give improvements for interferometric measurements with low visibility (as with NV centres) is now published in Physical Review A.

- 1/1/2014: My work with Richard Cleve and Sev Gharibian on simulation of continuous-time query algorithms has now been published in QIC.

- 20/12/2013: I have posted a video on quantum algorithms on Youtube. It covers the basics of quantum algorithms, and discusses Deutsch's algorithm and Grover's algorithm.

- 9/12/2013: We now have an even better method of simulating Hamiltonian evolution. In a new paper in collaboration with Andrew Childs, Robin Kothari and others, we have obtained a simulation with improved speed and much simpler than the previous algorithm. This new work subsumes the previous work.

- 14/11/2013: We have developed adaptive phase measurements via swarm optimisation that give accurate results with low visibility interference. These measurements are suitable to use for NV-centre magnetometry.

- 25/09/2013: Our paper on a new technique for decomposing single-qubit channels has just appeared in Physical Review Letters.

- 10/09/2013: Our paper on the Heisenberg limit for a fluctuating phase has just appeared in Physical Review Letters.

- 26/08/2013: We have developed a new technique for simulating Hamiltonian evolution that is polynomial in the logarithm of the allowable error. What this means is that, in effect, doubling the number of significant digits needed only increases the calculation time by a constant factor. This is an exponential improvement over previous techniques.

- 6/06/2013: We have discovered a new form of the Heisenberg limit that applies for a stochastic phase. This stochastic Heisenberg limit holds for any signal with a correlation spectrum that asymptotically follow a power law. In the limit where the high frequency variation is suppressed, the usual Heisenberg limit is recovered. For Wiener noise we obtain the same scaling as can be achieved using adaptive measurements.

- 14/05/2013: We have developed a technique for decomposing single qubit channels in terms of a universal gate set. This can be regarded as a Solovay-Kitaev decomposition strategy for channels.

- 16/02/2013: My citation count on Google Scholar has just reached 1000.

- 10/01/2013: I have been selected as an outstanding referee by the American Physical Society.

- 8/01/2013: We have released an erratum on an earlier paper published in 2006. This erratum means that the results are better than in the original paper. We found that adaptive measurements can provide greater accuracy than was predicted originally.

- 20/11/2012: We have released a paper on the simulation of continuous time query algorithms. Continuous time query algorithms are a promising approach for developing quantum algorithms, but they cannot be performed directly. Our work shows that such algorithms can be efficiently simulated on a quantum computer.

- 13/11/2012: Our extended paper on the universality of the Heisenberg limit has now been published in Physical Review A.

- 21/9/2012: We have a new publication in Science! It reports a demonstration of phase measurement enhanced with squeezing for a rapidly fluctuating phase. This was performed by collaborators at the University of Tokyo, and is based on a theoretical proposal by me and Howard Wiseman more than ten years ago.

- 18/9/2012: We have released an extended paper on the universality of the Heisenberg limit. This includes some analytic results giving the expansion with higher-order terms for the Holevo variance. It is available at arXiv:1209.3547.

- 13/9/2012: Hossein Dinani has now joined our group as a PhD student. There is still one PhD scholarship available.

- 13/4/2012: Our latest work showing that the Heisenberg limit is universal has now been published in Physical Review A Rapid Communications.

- 3/01/2012: Alexander Hayes has now joined the group as a new postdoctoral fellow.

- 1/01/2012: My work with Andrew Childs on Hamiltonian simulation and implementation of black-box unitaries has now been published in Quantum Information and Computation. This work gives the most efficient known algorithm for simulation of physical systems.

- 4/11/2011: Some recent publications have brought the Heisenberg limit into question. In new work we have shown that the Heisenberg limit is in fact universal, provided you are averaging over all phase shifts. The preprint is available at arXiv:1111.0788.