  We propose an imaginary time equivalent of the well-established Pauli gadget
primitive for Trotter-decomposed real time evolution, using mid-circuit
measurements on a single ancilla qubit. Imaginary time evolution (ITE) is
widely used for obtaining the ground state of a system on classical hardware,
computing thermal averages, and as a component of quantum algorithms that
perform non-unitary evolution. Near-term implementations on quantum hardware
rely on heuristics, compromising their accuracy. As a result, there is growing
interest in the development of more natively quantum algorithms. Since it is
not possible to implement a non-unitary gate deterministically, we resort to
the implementation of probabilistic imaginary time evolution (PITE) algorithms,
which rely on a unitary quantum circuit to simulate a block encoding of the ITE
operator - that is, they rely on successful ancillary measurements to evolve
the system non-unitarily. Compared with previous PITE proposals, the suggested
block encoding in this paper results in shorter circuits and is simpler to
implement, requiring only a slight modification of the Pauli gadget primitive.
This scheme was tested on the transverse Ising model and the fermionic Hubbard
model and is demonstrated to converge to the ground state of the system.
