Abstract for Talk 1:

Response theory has a successful history of connecting experimental observations with theoretical predictions. Of particular interest is the optical response of matter, from which spectroscopy experiments can be modelled. However, the calculation of response properties for quantum systems is often prohibitively expensive, especially for nonlinear spectroscopy, as it requires access to either the time evolution of the system or to excited states. In this work, we introduce a generalized quantum phase estimation framework designed for multi-variate phase estimation. This allows the treatment of general correlation functions enabling the recovery of response properties of arbitrary orders. The generalized quantum phase estimation circuit has an intuitive construction that is linked with a physical process of interest, and can directly sample frequencies from the distribution that would be obtained experimentally. In addition, we provide a single-ancilla modification of the new framework for early fault-tolerant quantum computers. Overall, our framework enables the efficient simulation of spectroscopy experiments beyond the linear regime, such as Raman spectroscopy. This opens up an exciting new field of applications for quantum computers with potential technological impact."

Abstract for Talk 2:

The art of simulating quantum dynamics in recent years has become synonymous with Hamiltonian simulation. That is to say, we often assume implicitly that the quantum dynamical system of interest is specified by a sparse Hamiltonian matrix whose matrix elements are efficiently computable and use an oracle to input the Hamiltonian to a simulation algorithm. Hamiltonians, however, are not always available for simulating physical systems. This fact is particularly noticeable for simulations of quantum field theories wherein the Lagrangians are often easy to derive are often used rather than the Hamiltonian to simulate quantum dynamics using the path integral formalism.  We address these problems in this paper by showing that quantum dynamics can be simulated efficiently using the path integral formalism using the Lagrangian in place of the Hamiltonian.  The nature of the oracle used here is fundamentally different than that used in Hamiltonian simulation because the Lagrangian is a scalar and the Hamiltonian is a matrix.  This means that our approach to simulation is fundamentally different than existing approaches and further allows quantum simulation to be performed for quantum field theories where the Hamiltonian is not explicitly known but the Lagrangian is simple to compute.  We further investigate new simulation methods based on path integrals for Hamiltonians and show that in certain cases, such as near-adiabatic quantum dynamics, these simulation methods may have substantial advantages compared to conventional strategies.