Abstract: Transpilation of quantum circuits involves transforming a given quantum circuit into an equivalent one that can be directly executed on quantum hardware. A common assumption in circuit transpilation is that either the global quantum operation or the underlying quantum state must be preserved. However, this assumption can be relaxed in cases where the goal is to preserve only the expectation value with respect to a given Hamiltonian. This opens up new possibilities for quantum compilation, especially in solving fermionic systems, where the quantum state may not immediately be explicitly represented in a form of a qubit-based quantum circuit.

In my talk, I will introduce a new framework for quantum compilation, specifically in the context of quantum circuits as solutions to problems that naturally reside in fermionic space. This framework enables efficient and reliable compilation of circuits, offering fine-grained control not only over translating circuits onto available quantum hardware but also over interpreting the results of quantum measurements. The presentation will include several examples highlighting scenarios where this framework proves especially effective and convenient.