  There has been recent progress in understanding chaotic features in many-body
quantum systems. Motivated by the scrambling of information in black holes, it
has been suggested that the time dependence of out-of-time-ordered (OTO)
correlation functions such as $\langle O_2(t) O_1(0) O_2(t) O_1(0) \rangle $ is
a faithful measure of quantum chaos. Experimentally, these correlators are
challenging to access since they apparently require access to both forward and
backward time evolution with the system Hamiltonian. Here, we propose a
protocol to measure such OTO correlators using an ancilla which controls the
direction of time. Specifically, by coupling the state of ancilla to the system
Hamiltonian of interest, we can emulate the forward and backward time
propagation, where the ancilla plays the role of a 'quantum clock'. Within this
scheme, the continuous evolution of the entire system (the system of interest
and the ancilla) is governed by a time-independent Hamiltonian. Our protocol is
immune to errors that could occur when the direction of time evolution is
externally controlled by a classical switch.
