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
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
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, 'Quantum Chemistry in the Age of Quantum Computing'.
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.
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.