Time-Dependent Hamiltonian Simulation Using Discrete-Clock Constructions

Compared with time-independent Hamiltonians, the dynamics of generic quantum Hamiltonians H(t) are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty prevents a direct adaptation of many time-independent simulation algorithms for time-dependent simulation. However, there exists a framework within the theory of dynamical systems that eliminates time ordering by adding a "clock"degree of freedom. In this work, we provide a computational framework, based on this reduction, for encoding time-dependent dynamics as time-independent systems. As a result, we make two advances in digital Hamiltonian simulation. First, we create a time-dependent simulation algorithm based on performing qubitization on the augmented clock system and, in doing so, provide the first qubitization-based approach to time-dependent Hamiltonians that goes beyond Trotterization of the ordered exponential. Second, we define a natural genera...