Quantum Algorithms for Dynamics and Dynamical Observables

Response functions are a fundamental aspect of physics; they represent the link between experimental observations and the underlying quantum many-body state. In particular, dynamicalresponse functions are part of the toolbox that physicists use to unravel the nature of correlated matter. In this talk, I will discuss some aspects of obtaining response functions on quantum computers.<br/><br/>First, I will introduce a new method for measuring response functions by using a linear response framework and making the experiment an inextricable part of the quantum simulation. This method can be frequency- and momentum-selective, avoids limitations on operators that can be directly measured, and is ancilla-free. As prototypical examples of response functions, we demonstrate that both bosonic and fermionic Green’s functions can be obtained, and apply these ideas to the study of a charge- density-wave material. The linear response method provides a robust framework for using quantum computers to study systems in physics and chemistry. It also provides new paradigms for computing response functions on classical computers. I will illustrate the use of this idea for equilibrium and non-equilibrium Green’s functions.<br/><br/>Second, I will discuss some of our recent work that uses a little-known property of Green’s functions – and in particular Green’s functions – to eliminate a large portion of the noise resulting from NISQ quantum computers. Green’s functions are positive definite functions, a fact that high constrains the relationship between the values of the Green’s function at each point in time. We make use of this by insisting that the measured (discretized) Green’s function forms a positive semi-definite matrix, and project the noisy data onto the nearest positive function.