Although a quantum computer is commonly modelled as a closed physical system, in practice the computer inevitably interacts with its environment and other systems. The aim of this thesis is to ascertain the advantages offered by controlled open-system phenomena and the limitations placed by unwanted system-environment interactions on quantum computation. This thesis is divided into two parts. The first part aims to ascertain whether a changing Hilbert-space inner product (IP), which is a controlled open-system phenomenon, enhances the power of quantum computers. The uniqueness of the IP associated to a quantum system has come under scrutiny following the advent of PT-symmetric quantum mechanics. A changing IP is valuable for quantum information processing applications; however, perfunctory use of this change can lead to counterfactual conclusions. In the first part of this thesis, we develop an operational framework for a changing IP, which is fully consistent with quantum mechanics. Next, to determine the utility of this change for computation, we construct a model of computation that uses IP changing operations along with unitary gates. We prove that the new model is equivalent to the quantum circuit model in terms of computational power. We also simulate the changing IP of a single qubit on Aspen-11 qubit and qutrit processors, and certify the quality of simulations. This experiment lays the foundation for simulating non-Hermitian dynamics on quantum computers. The second part of this thesis focuses on the effect of photon losses on certifiability of boson computers. Although improving the programmability of a boson computer is necessary for the demonstration of quantum advantage, it comes with the added challenge of increased photon losses. We develop a validation protocol that certifies the output of a lossy boson computer against an adversary with limited interferometer programmability. We also analyze the resource cost for validation with respect to two models of photon losses and show that validation becomes infeasible if each interferometer mode of the computer loses photons with a fixed probability. This work highlights the importance of accurately characterizing and suppressing photon losses in near-term boson computers.