Particles produced in high energy collisions that are charged under one of the fundamental forces will radiate proportionally to their charge, such as photon radiation from electrons in quantum electrodynamics. At sufficiently high energies, this radiation pattern is enhanced collinear to the initiating particle, resulting in a complex, many-body quantum system. Classical Markov Chain Monte Carlo simulation approaches work well to capture many of the salient features of the shower of radiation, but cannot capture all quantum effects. I will show how quantum algorithms are well-suited for describing the quantum properties of final state radiation. In particular, I will describe a polynomial time quantum final state shower that accurately models the effects of intermediate spin states similar to those present in high energy electroweak showers. The algorithm is explicitly demonstrated for a simplified quantum field theory on a quantum computer. One of the greatest challenges for current quantum computers is their significant noise. I will present new techniques for mitigating both readout noise and gate error noise. Readout errors are equivalent to detector effects in high energy physics (HEP) and I will show how building a bridge between fields can improve quantum computing in general, not only for HEP. For gate error mitigation, I have proposed a new technique that can achieve a better precision than existing methods with a significantly reduced quantum complexity. Finally, I will discuss future directions at the interface between quantum computing and high energy physics. See 1901.08148, 1904.03196, 1910.00129, and 2003.04941 for details.