###### New efficient algorithms for quantum chemistry

The simulation of molecules is a widely anticipated application of quantum computers. However, recent studies have cast a shadow on this hope by revealing that the complexity in gate count of such simulations increases with the number of spin orbitals N as N8, which becomes prohibitive even for molecules of modest size N∼100. This study was partly based on a scaling analysis of the Trotter step required for an ensemble of random artificial molecules.

EQuS research performed by Andrew Doherty and collaborators at Microsoft, ETH Zurich and Sherbrooke has analyzed the errors in quantum simulations of quantum chemistry, finding that this scaling can be improved for real molecules, and introduced improvements to the implementation of the algorithm. The key advance is a reduction by well over a factor of 10 in the number of gates required for useful simulations.

*The Trotter Step Size Required for Accurate Quantum Simulation of Quantum Chemistry.*, D. Poulin, M. B. Hastings, D. Wecker, N. Wiebe, A. C. Doherty, and M. Troyer, Quantum Information and Computation, 15, 0361 (2015).

###### Breakthrough in numerical methods for studying exotic quantum matter

Calculations performed by EQuS researcher Ian McCulloch together with Stefan Debenbrock and Professor Ulrich Shollwöck in Munich were instrumental in resolving the nature of the ground-state phase of the Heisenberg spin model on the Kagome lattice, which had been a source of much conjecture over many decades. The evidence strongly points to this model describing a topological spin liquid with Z2 symmetry. This work represents a breakthrough in detecting topological states of matter in models that are representative of real materials. This calculation represents the current state of the art, and should be regarded as a prototype for future work. Beyond simply characterizing the nature of topological phases, the next step is the simulation of dynamical properties and excitation spectra that will move the field beyond simple characterization of ground-states to probing transport properties and modeling engineered devices.

*Nature of the Spin-Liquid Ground State of the S=1/2 Heisenberg Model on the Kagome Lattice, *Stefan Depenbrock, Ian P. McCulloch, and Ulrich Schollwöck, Phys. Rev. Lett., 109, 067201 – Published 7 August 2012

###### Symmetry-protected topological order as a resource for processing quantum information

Strongly correlated many body states stabilised in topologically ordered matter offer the possibility of naturally fault tolerant computing, but are both challenging to engineer and coherently control and cannot be easily adapted to different physical platforms. A team of EQuS researchers at the University of Sydney have proposed an architecture for quantum computation that achieves some of the robustness properties of topological models, but with a drastically simpler construction. Our breakthrough came by relating the quantum computational power of a zero-temperature quantum phase to a phenomenon known as symmetry-protected topological order. This order characterises the way in which hidden long-range entanglement is contained in a system (which gives the phase its quantum computational power), the relation between this entanglement and the presence of gapless edge modes (which form the logical quantum information), and the way in which the entanglement and the edge modes transform under a particular symmetry (which enables the quantum logic gates).

*Symmetry-protected phases for measurement-based quantum computation*, Dominic V. Else, Ilai Schwarz, Stephen D. Bartlett, and Andrew C. Doherty, Phys. Rev. Lett., 108, 240505 (2012)

###### Understanding quantum coherent effects in photosynthesis

Recent evidence suggests that quantum coherence enhances excitation energy transfer through individual photosynthetic light-harvesting protein complexes (LHCs). Its role in living systems remains unclear however, where transfer to chemical reaction centres spans larger, multi-LHC networks. A multi-scale analysis reveals the dependence of energy transfer dynamics in a hierarchical network structure. Surprisingly, thermal decoherence rate declines at larger length scales for physiological parameters and coherence length is instead limited by localization due to static disorder. Physiological parameters support coherence lengths up to ~ 5 nm, which is consistent with observations of solvated LHCs and invites experimental tests for intercomplex coherences in multi-LHC networks. Results further suggest that a semiconductor quantum dot network engineered with hierarchically clustered structure and small static disorder may support coherent energy transfer over larger length scales, at ambient temperatures.

*Multiscale photosynthetic and biomimetic excitation energy transfer*, A. K. Ringsmuth, G. J. Milburn & T. M. Stace, Nature Physics, 8, 562–567 (2012), doi:10.1038/nphys2332