Quantum computers have seen rapid development over the last two decades. Despite this, they are not yet scalable or fault-tolerant (i.e. we cannot address arbitrarily many error-corrected qubits). Therefore, improvements that include consideration of the underlying physics are paramount. To do this, we must reduce existing errors and understand how algorithms perform without error correction. In this dissertation, we provide contributions toward these goals. We organize these efforts into three groups. Firstly, we focus on quantum control. We introduce a novel scheme for performing entangling gates on superconducting qubits. We create fast, high-fidelity entangling operations and single-qubit gates to implement arbitrary quantum operations. Then, we implement entangling gates on real transmon qubits. Finally, we develop new techniques for entangling gates on spin qubits. In total, we improve low-level device performance with high-fidelity entangling operations. Secondly, we focus on quantum simulation algorithms. First, we apply error mitigation techniques to a quantum simulation algorithm while simultaneously performing device characterization. Then we take advantage of known symmetries of the input Hamiltonian to improve the same algorithm. Then, we demonstrate that this reduces resources compared to other approaches in the presence of noise. Then we compare this technique with state-of-the-art approaches. Then, we improve this algorithm with approaches from quantum control. Finally, we develop a novel algorithm to simulate spin chains on a quantum processor with improved resources compared to other techniques. In total, we improve quantum simulation algorithms, with the aim of better utilizing current devices. Thirdly, we consider the ADAPT-VQE algorithm, which is used to construct quantum circuits for preparing trial states in quantum simulation. In total, we improve gate counts for the algorithm, improve a separate algorithm by utilizing the gradient criterion, and leverage the repeating structure of an input Hamiltonian to improve performance. Finally, we provide a deeper understanding of ADAPT-VQE and demonstrate its robustness to scaling issues of competing algorithms. In total, we improve the algorithm and its applicability. Thus, we improve quantum simulation algorithms that can be run in the near term. / Doctor of Philosophy / The computers that we interact with every day rely on the processing of bits, represented as 1's or 0's. The rules that govern how they operate mostly rely on classical physics (i.e. discovered before quantum physics), which does not include any quantum effects. If we instead allow for quantum rules and quantum bits ("qubits"'), new types of algorithms are possible. That is to say, quantum computers can do some things more efficiently than classical computers. As such, there is a massive effort to build these devices. Because these devices are so delicate and in their early stages, this requires an understanding of the algorithm and the physical device performing it. Therefore, improving the overall performance requires taking high and low-level aspects of this design into consideration. In this dissertation, we provide three groups of contributions to achieving this goal. In the first group, we improve the device performance by considering how operations are performed on qubits, primarily in terms of producing quantum operations that have no classical analog. In the second group, we improve the simulation of quantum systems on quantum devices with a focus on how existing imperfections in the device impact the results. In the third group, we make improvements to an algorithm used to simulate quantum systems like molecules, while also developing a deeper understanding of how the algorithm functions. In each of these parts, we develop novel techniques to improve device and algorithm performance, contributing to the applicability and utility of current and future quantum devices.