Cao, Y, Romero, J, Olson, JP, Degroote, M, Johnson, PD, Kieferová, M, Kivlichan, ID, Menke, T, Peropadre, B, Sawaya, NPD, Sim, S, Veis, L & Aspuru-Guzik, A 2019, 'Quantum Chemistry in the Age of Quantum Computing', Chemical Reviews, vol. 119, no. 19.View/Download from: Publisher's site
Practical challenges in simulating quantum systems on classical computers
have been widely recognized in the quantum physics and quantum chemistry
communities over the past century. Although many approximation methods have
been introduced, the complexity of quantum mechanics remains hard to appease.
The advent of quantum computation brings new pathways to navigate this
challenging complexity landscape. By manipulating quantum states of matter and
taking advantage of their unique features such as superposition and
entanglement, quantum computers promise to efficiently deliver accurate results
for many important problems in quantum chemistry such as the electronic
structure of molecules. In the past two decades significant advances have been
made in developing algorithms and physical hardware for quantum computing,
heralding a revolution in simulation of quantum systems. This article is an
overview of the algorithms and results that are relevant for quantum chemistry.
The intended audience is both quantum chemists who seek to learn more about
quantum computing, and quantum computing researchers who would like to explore
applications in quantum chemistry.
Kieferova, M, Scherer, A & Berry, DW 2019, 'Simulating the dynamics of time-dependent Hamiltonians with a truncated Dyson series', PHYSICAL REVIEW A, vol. 99, no. 4.View/Download from: Publisher's site
Heat-bath algorithmic cooling provides algorithmic ways to improve the purity of quantum states. These techniques are complex iterative processes that change from each iteration to the next and this poses a significant challenge to implementing these algorithms. Here, we introduce a new technique that on a fundamental level, shows that it is possible to do algorithmic cooling and even reach the cooling limit without any knowledge of the state and using only a single fixed operation, and on a practical level, presents a more feasible and robust alternative for implementing heat-bath algorithmic cooling. We also show that our new technique converges to the asymptotic state of heat-bath algorithmic cooling and that the cooling algorithm can be efficiently implemented; however, the saturation could require exponentially many iterations and remains impractical. This brings heat-bath algorithmic cooling to the realm of feasibility and makes it a viable option for realistic application in quantum technologies.
Berry, DW, Kieferova, M, Scherer, A, Sanders, YR, Low, GH, Wiebe, N, Gidney, C & Babbush, R 2018, 'Improved techniques for preparing eigenstates of fermionic Hamiltonians', NPJ QUANTUM INFORMATION, vol. 4.View/Download from: Publisher's site
Kieferova, M & Nagaj, D 2012, 'Quantum Walks on Necklaces and Mixing'.
We analyze continuous-time quantum walks on necklace graphs - cyclical graphs
consisting of many copies of a smaller graph (pearl). Using a Bloch-type ansatz
for the eigenfunctions, we block-diagonalize the Hamiltonian, reducing the
effective size of the problem to the size of a single pearl. We then present a
general approach for showing that the mixing time scales (with growing size of
the necklace) similarly to that of a simple walk on a cycle. Finally, we
present results for mixing on several necklace graphs.
We study the glued-trees problem from A. M. Childs, R. Cleve, E. Deotto, E. Farhi, S. Gutmann, and D. Spielman, in Proceedings of the 35th Annual ACM Symposium on Theory of Computing (ACM, San Diego, CA, 2003), p. 59. in the adiabatic model of quantum computing and provide an annealing schedule to solve an oracular problem exponentially faster than classically possible. The Hamiltonians involved in the quantum annealing do not suffer from the so-called sign problem. Unlike the typical scenario, our schedule is efficient even though the minimum energy gap of the Hamiltonians is exponentially small in the problem size. We discuss generalizations based on initial-state randomization to avoid some slowdowns in adiabatic quantum computing due to small gaps.