My research is in the areas of quantum information and quantum optics. In quantum information, I developed many of 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 collaborating with experimental groups for demonstration of these methods.
My CV is available here.
PhD and Masters projects
Are you interested in doing a PhD or Masters project in quantum algorithms? Projects are available in quantum algorithms for quantum chemistry, as well as quantum field theory. For more details please contact me at .
- 16/01/2017: We now have an algorithm to solve linear differential equations on a quantum computer with complexity logarithmic in the error. Our method is to encode a Taylor series for the differential equation into a linear system.
- 11/01/2017: Shibdas Roy and I have worked out estimators for phase measurement of a varying phase where the system parameters are not precisely known. We have also examined whether sub-optimal estimators can be considered as equivalent to loss or added noise. This work is available on the arXiv.
- 5/12/2016: We have shown how to perform measurements using squeezed states and feedback to achieve accuracy scaling as the Heisenberg limit for a varying phase. These measurements work for a general signal with power-law correlation spectrum. This work is also released on the arXiv.
- 1/12/2016: Leonardo Novo and I have shown how to use corrections to obtain more efficient simulation of Hamiltonians via a Taylor series. This is released on the arXiv.
- 1/11/2016: Our work showing how to more efficiently simulate Hamiltonian evolution using a corrected quantum walk is now published at QIC.
- 16/09/2016: We have shown how to use adaptive measurements to achieve accurate phase estimation with two-mode squeezed vacuum. It was previously unclear how to achieve this task, because of pathological properties of these states. This work is released on the arXiv.
- 27/07/2016: We have devised a state recycling technique to produce larger optical number states from single photons. This technique has an exponential improvement in efficiency from the single-shot scheme. This work is published in Physical Review A.
- 13/06/2016: We have shown that it is possible to achieve Hamiltonian simulation that is at the theoretical lower bound, up to double-logarithmic factors. The method is to apply corrections to a quantum walk with a superposition of numbers of steps. This work is on the arXiv.
- 7/06/2016: We have a new paper out in Physical Review A. This is the work showing that entangled states can be used for spectroscopy using information from both the phase shift and the absorption.
- 24/03/2016: Our work on more efficient simulation of quantum chemistry using the linear combinations of unitaries approach has just been published in New Journal of Physics.
- 15/03/2016: Normal spectroscopy just estimates a transition frequency based on absorption of light. We have now shown that in some parameter regimes better measurement accuracy may be obtained by using joint information from the absorption and the phase shift via entangled states. This work is also on the arXiv.
- 2/03/2016: We have been developing ways of processing single-photon sources to obtain Fock states with higher photon numbers. The efficiency is exponentially better than previous techniques, because the rate is polynomial in the desired photon number, rather than exponential. This work is released on the arXiv.
- 17/11/2015: Our paper on NV centre magnetometry has just been published in Nature Nanotechnology. There is also a News and Views article about this work.
- 30/10/2015: We have just been awarded a Discovery Project on Quantum Algorithms for Computational Physics. We will shortly be offering postdoctoral positions for research in this area.
- 18/08/2015: We have a new paper out in Physical Review X, showing how to bound the accuracy for measurement of a varying phase. It uses the new technique of the multiparameter quantum Ziv-Zakai bound, which enables much more powerful results than the Cramér-Rao bound.
- 17/08/2015: Our experimental collaborators have now demonstrated our scheme for magnetometry with NV centres using adaptive measurements found by swarm optimization. This work is released on the arXiv.
- 10/08/2015: Macquarie University is having an open day on 12 September.
- 4/06/2015: We have two new papers on the arXiv showing how to simulate quantum chemistry using our more advanced algorithms for Hamiltonian simulation. The first paper uses second quantisation, together with on-the-fly integrals to obtain scaling as N5, where N is the number of orbitals. The best proven bound was previously N8 (although better scaling was found numerically). The second paper uses the Configuration Interaction matrix to obtain even better scaling as N3.
- 3/03/2015: Our paper showing how to simulate Hamiltonians using a Taylor series has just appeared in Physical Review Letters.
- 9/01/2015: We have a new paper on the arXiv showing how to perform the most efficient quantum simulations yet. I will be presenting it at QIP on Monday (12/01/2015).
- 16/12/2014: We have a new paper on the arXiv with a simplified algorithm for Hamiltonian simulation. This gives polylog scaling in the error, but is based on implementing a Taylor series, rather than a Lie-Trotter formula.
- 25/11/2014: Our paper on the processing of photodetectors has now been published in Physical Review A.
- 7/11/2014: Our paper on the experimental demonstration of Bell tests with postselection violating Tsirelson's bound has now been published in Scientific Reports.
- 30/09/2014: We have a new paper on the arXiv proving a Heisenberg limit for a varying phase. Unlike previous work this lower bound holds for all possible states, and in addition we show that it is achievable.
- 28/08/2014: Hossein's paper on loss-resistant states for phase measurement is now published in Physical Review A.
- 4/08/2014: We have another paper on the arXiv on linear optical processing of inefficient detectors. We find that it is not possible to improve on the maximum efficiency of detectors even allowing for adaptive measurements.
- 20/06/2014: Today we have two papers on the arXiv. The second paper is an experimental demonstration of Bell tests with postselection violating Tsirelson's bound, which I originally proposed in 2007. In this new work we not only demonstrate that, we use it to demonstrate violation of information causality.
- 20/06/2014: We have a new paper on the arXiv on generating loss-resistant states from downconversion. We not only show how to generate loss-resistant states, we show how to combine them to provide an unambiguous phase measurement. This work is by my PhD student Hossein Dinani and myself.
- 20/02/2014: My quantum algorithm for solving differential equations is now published in Journal of Physics A. This is my 50'th published paper.
- 27/01/2014: 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.
- 1/01/2014: 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.
- 21/09/2012: 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.