Iteratively-Layered Variational Quantum Eigensolver with Shallow Ansatz Circuits

Adaptive variational quantum eigensolvers (VQEs) are a class of quantum algorithms, suitable for finding the ground state of molecular Hamiltonians. Current VQE algorithms are not noise robust enough for implementations on noisy intermediate-scale quantum (NISQ) hardware. Here, we present the Iteratively Layered VQE (IL-VQE) Algorithm. Using non-commutation relations, our algorithm compresses the sparsely and iteratively appended gates in the quantum circuits of adaptive VQEs into packed layers. We numerically demonstrate that IL-VQE constructs shallower, more noise-tolerant circuits than previous methods. We further show that IL-VQE reduces the calls to the NISQ hardware. Ultimately, this work brings the experimental realisation of useful VQE algorithms one step closer.