Publications
135 results found
Callison A, Chancellor N, Mintert F, et al., 2019, Finding spin glass ground states using quantum walks, New Journal of Physics, Vol: 21, Pages: 1-20, ISSN: 1367-2630
Quantum computation using continuous-time evolution under a natural hardware Hamiltonian is a promising near- and mid-term direction toward powerful quantum computing hardware. We investigate the performance of continuous-time quantum walks as a tool for finding spin glass ground states, a problem that serves as a useful model for realistic optimization problems. By performing detailed numerics, we uncover significant ways in which solving spin glass problems differs from applying quantum walks to the search problem. Importantly, unlike for the search problem, parameters such as the hopping rate of the quantum walk do not need to be set precisely for the spin glass ground state problem. Heuristic values of the hopping rate determined from the energy scales in the problem Hamiltonian are sufficient for obtaining a better quantum advantage than for search. We uncover two general mechanisms that provide the quantum advantage: matching the driver Hamiltonian to the encoding in the problem Hamiltonian, and an energy redistribution principle that ensures a quantum walk will find a lower energy state in a short timescale. This makes it practical to use quantum walks for solving hard problems, and opens the door for a range of applications on suitable quantum hardware.
Tranter A, Love P, Mintert F, et al., 2019, Ordering of Trotterization: impact on errors in quantum simulation of electronic structure, Entropy: international and interdisciplinary journal of entropy and information studies, Vol: 21, ISSN: 1099-4300
Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most for systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamil
Zhao H, Knolle J, Mintert F, 2019, Engineered nearest-neighbor interactions with doubly modulated optical lattices, Publisher: AMER PHYSICAL SOC
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Walker BT, Hesten HJ, Nyman RA, et al., 2019, Collective excitation profiles and the dynamics of photonic condensates, Physical Review A: Atomic, Molecular and Optical Physics, Vol: 100, Pages: 1-7, ISSN: 1050-2947
Photonic condensates are complex systems exhibiting phase transitions due to the interaction with their molecular environment. Given the macroscopic number of molecules that form a reservoir of excitations, numerical simulations are expensive, even for systems with few cavity modes. We present a systematic construction of molecular excitation profiles with a clear hierarchical ordering, such that only modes in the lowest order in the hierarchy directly affect the cavity photon dynamics. In addition to a substantial gain in computational efficiency for simulations of photon dynamics, the explicit spatial shape of the mode profiles offers a clear physical insight into the competition among the cavity modes for access to molecular excitations.
Walker BT, Hesten HJ, Dhar HS, et al., 2019, Non-critical slowing down of photonic condensation, Physical Review Letters, Vol: 123, ISSN: 0031-9007
We investigate the response of a photonic gas interacting with a reservoir ofpumped dye-molecules to quenches in the pump power. In addition to the expecteddramatic critical slowing down of the equilibration time around phasetransitions we find extremely slow equilibration even far away from phasetransitions. This non-critical slowing down can be accounted for quantitativelyby fierce competition among cavity modes for access to the molecularenvironment, and we provide a quantitative explanation for this non-criticalslowing down.
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