Diagrammatic Quantum Circuit Compression for Hamiltonian Simulation

One of the promising applications for early quantum computers is the simulation of of dynamical quantum systems. Due to the limited coherence time of such devices, the depth-compression of quantum circuits is crucial to facilitate useful results. It has been shown that certain quantum models can even be compressed to constant depth, meaning it is only linearly dependent on the number of qubits, but independent of the simulation time and the number of Trotter steps. This has been done by extracting the circuit structure derived from the model characteristics via Hamiltonian simulation. Based on these results, we present a diagrammatic approach to circuit compression utilizing a powerful technique for reasoning about quantum circuits called ZX-calculus. We demonstrate our approach by deriving constant-depth circuit compressions for quantum models known to be constant-depth, as well as novel models previously unstudied. Our method could serve as a first step toward the development of more advanced circuit compression methods, that could be employed to enable Hamiltonian simulation of a larger variety of quantum models, and beyond.