Modified Quantum Imaginary Time Evolution Algorithm and Potential Applications in Fusion Energy Science*

There is increasing interest in quantum algorithms that are based on the imaginary-time evolution (ITE), a successful

classical numerical approach to obtain ground states. However, most of the proposed quantum algorithms that are based

on ITE require heavy post-processing computational steps on a classical computer, such as solving linear equations. In

this talk we introduce an alternative implementation of ITE on gate-based quantum computers -- modified quantum imaginary

time evolution (MQITE) algorithm [1]. MQITE allows the propagated state to be efficiently expressed

in terms of a limited number of orthogonal basis states at every step of the evolution. The small number of basis states

means the  quantum circuit depth can be bounded to only $mathcal{O}(poly(n))$, given $n$ qubits. The algorithm is not

restricted to local Hamiltonian, which renders it useful for studying highly nonlocal systems, such as the occupation-representation

nuclear shell model. MQITE as an algorithm to simulate non-unitary time evolution, such as plasma dynamics, is discussed as well. 

The algorithm is illustrated through numerical implementation on IBM quantum simulator.

[1] P. Jouzdani, C. W. Johnson, E. R. Mucciolo, and I. Stetcu, Phys. Rev. A 106, 062435 (2022)