Summary

In this chapter, we have studied Hamiltonians and observables in detail. In particular, we have learned how to derive mathematical expressions for their expectation values and how to estimate these quantities using quantum computers.

Then, we studied the VQE algorithm and how it can be used to find ground states of general Hamiltonians. We also described a modification of VQE called VQD that can also be used to compute excited states and not just states of minimum energy.

Then, we moved to practical matters and learned how to use Qiskit to run VQE and VQD. We illustrated this with a very interesting problem: that of finding the ground state of a simple molecule. We then introduced methods to simulate the behavior of quantum algorithms when there is noise and how to reduce the adverse effect of readout errors with some mitigation techniques. We also studied how to run VQE problems on actual quantum computers with IBM runtime.

After that, we also learned how to implement and run...