Non-Unitary Trotter Circuits for Imaginary Time Evolution

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 (GS) 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 ITE (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, our suggested block encoding 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 fermionic Hubbard model and is demonstrated to converge to the GS of the system [1].