Simulating Chemistry on Quantum Computers: From atoms to algorithms – a holistic review: Quantum Engineering CDT (Advanced Quantum Information Theory Essay)

The aim of this essay is to provide a holistic overview of the field of quantum chemistry simulation. Given the diverse nature of the subject it is often hard to find literature which gives a full perspective of the field’s many facets. Therefore this paper attempts to give a technical overview of the many areas needed to understand the full challenge presented by quantum chemical situations.
To achieve this Section 2 begins by asking the question of why we want to simulate quantum chemistry, and is it feasible to do so? Section 3 gives a brief overview of the two simulation techniques available: analogue and digital quantum simulation. Having discussed the abstract concept of quantum simulation, Section 4 begins the technical material by discussing the two main chemical systems we typically desire to simulate and gives their characteristic Hamiltonians. With chemical Hamiltonians in hand Section 5 explains the different qubit mappings we can apply to simulate the systems on our quantum computer. Section 6 concludes the technical material by considering the more practical implications of the aforementioned simulation methods with respect to scaling and resource estimation. Lastly, Section 7 finishes by making some final concluding remarks and gives an outlook for the future quantum chemistry simulation research efforts.