Plenary Talks - abstract
DOMINIC BERRY
ADVANCES IN QUANTUM ALGORITHMS FOR HAMILTONIAN
SIMULATION
Hamiltonian simulation is a major potential application of quantum computers, because it
enables predictions to be made for physical quantum systems, as well as providing a
foundation for other quantum algorithms. Standard methods for Hamiltonian simulation
involve product formulae, where the Hamiltonian evolution is a product of evolutions for a
series of short times. We have developed a range of advanced algorithms with greatly
improved performance. One method is to compress product formulae, which gives an
exponential improvement in some parameters. A crucial part of this is an oblivious form of
amplitude amplification, which allows the steps of this procedure to be performed
deterministically. This also enables us to perform evolution based on a truncated Taylor
series. Another approach is to use a quantum walk; using oblivious amplitude amplification
we are able to perform a superposition of different numbers of steps of the walk, providing
greatly improved performance.