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We propose an imaginary time equivalent of the well-established Pauli gadgetprimitive for Trotter-decomposed real time evolution, using mid-circuitmeasurements on a single ancilla qubit. Imaginary time evolution (ITE) iswidely used for obtaining the ground state of a system on classical hardware,computing thermal averages, and as a component of quantum algorithms thatperform non-unitary evolution. Near-term implementations on quantum hardwarerely on heuristics, compromising their accuracy. As a result, there is growinginterest in the development of more natively quantum algorithms. Since it isnot possible to implement a non-unitary gate deterministically, we resort tothe implementation of probabilistic imaginary time evolution (PITE) algorithms,which rely on a unitary quantum circuit to simulate a block encoding of the ITEoperator - that is, they rely on successful ancillary measurements to evolvethe system non-unitarily. Compared with previous PITE proposals, the suggestedblock encoding in this paper results in shorter circuits and is simpler toimplement, requiring only a slight modification of the Pauli gadget primitive.This scheme was tested on the transverse Ising model and the fermionic Hubbardmodel and is demonstrated to converge to the ground state of the system.

Non-unitary Trotter circuits for imaginary time evolution