Solutions to the time-independent Schrödinger equation for molecular systems allow chemical properties to be studied without the direct need for the material. However, the dimension of this problem grows exponentially with the size of the quantum system under consideration making conventional treatment intractable. Quantum computers can efficiently represent and evolve quantum states. Their use offers a possible way to perform simulations on molecules previously impossible to model. However, given the constraints of current quantum computers even studying small systems is limited by the number of qubits, circuit depth and runtime of a chosen quantum algorithm. The work in this thesis is to explore and provide new tools to make chemical simulation more practical on near-term devices. First, the unitary partitioning measurement reduction strategy is explored. This reduces the runtime of the variational quantum eigensolver algorithm (VQE). We then apply this reduction technique to the contextual subspace method, which approximates a problem by introducing artificial symmetries based on the solution of noncontextual version of the problem that reduces the number of qubits required for simulation. We provide a modification to the original algorithm that makes an exponentially scaling part of the technique quadratic. Finally, we develop the projection-based embedding (PBE) technique to allow chemical systems to be studied using state-of-the-art classical methods in conjuncture with quantum computing protocols in a multiscale hierarchy. This allows molecular problems much larger than conventionally studied on quantum hardware to be approached.