## Dominic Berry - Senior Lecturer

### Macquarie University

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.

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 .

News- 18/06/2019: We have shown how to perform simulations of time-dependent Hamiltonians with complexity scaling as the integral of the norm of the Hamiltonian, rather than the maximum value. This is useful for Hamiltonians arising from collisions where the size of the Hamiltonian can vary dramatically over time. This work is available on the arXiv.

- 9/05/2019: We have proposed a new technique for quantum encryption using Boson sampling. This work is available on the arXiv.

- 5/04/2019: Our paper showing how to simulate time-dependent quantum systems with exponential precision is now published in Physical Review A.

- 4/04/2019: Our new algorithm for solving SYK models with many orders of magnitude improvement is now published in Physical Review A as a Rapid Communication.

- 12/03/2019: Our work showing how to more accurately perform sensing with with NV centres at room temperature is now published in Physical Review B.

- 27/02/2019: We have analysed the Trotter approach to quantum simulation, providing several improvements and showing that simulations may be performed with a surprisingly small number of quantum gates.

- 6/02/2019: We have shown how to take advantage of the low rank nature of Hamiltonians to provide a significant speed improvement for simulating FeMoco.

- 17/01/2019: Our work on removing arithmetic from state preparation is now published in Physical Review Letters. It is an Editors' Suggestion!

- 2/11/2018: Our work on performing phase measurements at the exact Heisenberg limit is now published in Nature Communications.

- 24/10/2018: Our work showing how to reduce the complexity of quantum chemistry algorithms by about a factor of a million is now published in Physical Review X.

- 27/07/2018: We have shown how to do quantum chemistry simulations with complexity scaling as
*N*^{1/3}, where*N*is the number of orbitals. In comparison, the first work had scaling*N*^{10}.

- 10/07/2018: We have developed a way to perform black-box state preparation without arithmetic. Prior work required calculation of an arcsine, whereas we just require an inequality test, reducing the number of gates needed by orders of magnitude.

- 7/06/2018: We have proposed a much more efficient way to simulate the Sachdev-Ye-Kitaev model on a quantum computer. The complexity is reduced to
*N*^{3.5}, as compared to*N*^{10}in prior work.

- 5/06/2018: We developed new ways to perform quantum sensing with NV centres at room temperature, where single-shot detection is not available. The accuracy is improved by using all the information from the photon detections, instead of using a threshold.

- 11/05/2018: In work with researchers at Google, we have reduced the complexity for quantum algorithms for quantum chemistry by about a factor of a million.

- 3/05/2018: We have now shown how to perform Hamiltonian simulation of time-dependent systems with exponential precision.

- 2/05/2018: Our work on preparing antisymmetrised states for quantum chemistry is now published in npj Quantum Information.

- 23/04/2018: Our work showing how to perform optimal measurement of a varying phase with coherent states is now published in Physical Review A.

- 18/12/2017: We have demonstrated how to perform phase estimation at the exact Heisenberg limit with no overhead for 3 photon passes (2 entangled photons, with one passing through a phase shift twice). This work is available on the arXiv.

- 7/12/2017: Our work on exponentially precise simulation of quantum chemistry using the configuration interaction representation has now been published in Quantum Science and Technology.

- 29/11/2017: We have shown how to antisymmetrise states for quantum chemistry simulation using a circuit depth that is logarithmic in the number of electrons. This is an exponential improvement over previously known schemes, which scaled as the cube of the number of electrons. This work is on the arXiv.

- 23/10/2017: We have new results on measurement of varying phase with coherent states, giving a standard quantum limit. Using smoothing (all data) gives the ultimate limit to accuracy, and can give an unbounded improvement over filtering (only data up to the current time). This work is on the arXiv.

- 15/06/2017: Our latest work on how to perform adaptive measurements of varying phase using squeezed states has just been published in Physical Review A.

- 1/06/2017: My work with Leonardo Novo on how to simulate Hamiltonians using a Taylor series with corrections has just appeared in Quantum Information and Computation.

- 30/05/2017: Cristian Bonato and I have shown how to estimate a varying frequency with an NV centre. This work is published in Physical Review A.

- 12/05/2017: Our work on how to perform adaptive phase measurements using two-mode squeezed vacuum is now published in Physical Review A.

- 11/05/2017: The work with Shibdas Roy on robust estimators for a varying phase is now published in Physical Review A.

- 6/04/2017: Hossein Dinani has won a CONICYT fellowship, which he has just taken up at Pontificia Universidad Catolica de Chile.

- 4/03/2017: The complete version of our work on simulating Hamiltonian evolution with complexity polylogarithmic in the error has now been published in Forum of Mathematics. This is the complete version of the paper which was published in STOC in 2015.

- 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
*N*^{5}, where*N*is the number of orbitals. The best proven bound was previously*N*^{8}(although better scaling was found numerically). The second paper uses the Configuration Interaction matrix to obtain even better scaling as*N*^{3}.

- 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.