Circuit partitioning is a powerful technique in the Noisy Intermediate Scale Quantum era. This method allows the evaluation of many-qubit algorithms with fewer qubits by writing the expectation...Show moreCircuit partitioning is a powerful technique in the Noisy Intermediate Scale Quantum era. This method allows the evaluation of many-qubit algorithms with fewer qubits by writing the expectation value of an observable as a weighted sum of products of inner products which are obtained by evaluating smaller circuits. However the number of terms in this sum generally scales exponentially with the depth of the circuit. The recently introduced Subset Partition Model only evaluates a subset of these terms. Here we explore the application of the Subset Partition Model for Variational Quantum Eigensolvers. Based on our investigation, we conjecture that this model may not be generally applicable to this Variational Quantum Algorithm due to the breaking of the Variational Principle. In addition, optimizing Partitioned Quantum Circuits is challenging due to the Barren Plateau problem that arises for even small circuit sizes. To address this problem, this thesis proposes a novel optimization algorithm that takes advantage of the additional structure on the cost function induced by circuit partitioning. By utilizing this new algorithm, we demonstrate that we can alleviate the barren plateau problem in the optimization of Partitioned Quantum Circuits.Show less
Quantum computers can possibly help in the near future to simulate mole-cules and do electronic structure calculations. To work on the near term quantum devices the variational quantum eigensolver ...Show moreQuantum computers can possibly help in the near future to simulate mole-cules and do electronic structure calculations. To work on the near term quantum devices the variational quantum eigensolver (VQE) is an auspicious candidate and particularly the application of the unitary coupled-cluster singles and doubles ansatz. Despite the high accuracy the scaling in the number of terms is unfavourable making the circuit depth too large. In this thesis we look at a possible truncation scheme based on classical quantum chemistry methods to decrease the number of terms while preserving accurate ground state energies. This truncation is shown with numerical results for H$_4$ and N$_2$ giving a significantly reduced number of terms.Show less
