Imaginary Time Propagation on a Physical Quantum Chip*

In standard computation one possibility for computing ground state properties of a given system is to operate a Wick rotation on the real time evolution operator. The resulting propagator is not unitary, and implements a dissipation mechanism. Evolution in imaginary time is a well-known technique for finding the ground state of quantum many-body systems, and the heart of a number of numerical methods, including Quantum Monte Carlo techniques, that have been used with great success in quantum chemistry, condensed matter and nuclear physics. Although the great use, the computation time increases exponentially due to the exponential growth of the model space with the increasing number of particles. There is therefore a desire to develop quantum versions of prominent quantum many-body methods, and in particular quantum algorithms that can be efficiently applied to emerging prototypes  of  quantum  computing  platforms.

A possible way to introduce dissipation through an Imaginary time method  will be presented. This is done by expanding the Hilbert space of the system under investigation introducing ancillary qubits. The projection is obtained by applying a series of unitary transformations having the effect to move the components of the initial state along excited states of the Hamiltonian H to the ancillary space. Such components should then be removed by a measurement of the ancillary qubits.

Some tests for atomic and nuclear spin  systems through different quantum platforms, IBM QPUs and LLNL quantum testbed simulator, will be illustrated.