Date: 11 JULY 2022 from 11:30 to 12:30
Variational Quantum Algorithms (VQAs) incorporate hybrid quantum-classical computation aimed at harnessing the power of Noisy Intermediate-Scale Quantum (NISQ) computers, by using a classical optimizer to train a Parametrized Quantum Circuit (PQC) to solve tractable quantum problems.
The Variational Quantum Eigensolver (VQE) is one such algorithm designed to determine the ground-state of many-body Hamiltonians. Here we apply the VQE to study the ground state properties of 𝑁-component fermions. To this end, we devise an SU(𝑁) fermion-to-qubit encoding based on an extension of the Jordan–Wigner (JW) mapping. We specifically obtain the ground-state of various Hubbard models by using a spin-conserving PQC. The persistent current, having applications in the emergent field of atomtronics, is then investigated and numerically obtained by varying the magnetic flux and adiabatically assisting the VQE. Our approach lays out the basis for a current-based quantum simulator of many-body systems that can be implemented on NISQ computers.
Another VQA is designed for the preparation of quantum Gibbs states, which have many applications in quantum simulation, quantum optimisation, and quantum machine learning. The main issue in variationally preparing a Gibbs state is the difficulty in measuring the von Nuemann Entropy. We alleviate this issue entirely, by carefully constructing a PQC that is able to determine the von Neumann entropy via simple post-processing of computational basis measurements, carried out on ancillary qubits. We certify the preparation of Gibbs states, across a broad range of temperatures, by comparing various figures of merit with the exact Gibbs states of the Ising Model, such as fidelity, trace distance, and relative entropy.
One final VQA determines the Closest Separable State (CSS) of an entangled state with respect to the Hilbert–Schmidt Distance (HSD). While the HSD is not considered a general entanglement measure, it can in some cases quantify the amount of entanglement of specific states, or else provide a useful construction of an entanglement witness. The VQA can also possibly lead to the characterisation of multipartite quantum states, if the algorithm is adapted and improved to obtain the Closest 𝑘-Separable State (CkSS).