Term Grouping Techniques for VQE and Quantum Dynamics Circuits

Digital quantum simulations are among the most promising near-term applications of quantum computation. Variational Quantum Eigensolver and time evolution of quantum dynamics are two examples of such algorithms. However, the amount of required quantum resources typically do not scale favorably as the desired accuracy of the calculations increases. Both VQE and quantum dynamics circuits are represented by tensor products of Pauli matrices that are obtained from the second quantization form using transformation methods such as Jordan-Wigner or Bravyi-Kitaev. We demonstrate various grouping techniques that optimize the order of these tensor products, with the goal of optimizing the total quantum resource cost. For VQE circuits, we minimize the number of required measurement operations. For quantum dynamics circuits, we minimize the circuit depth and maximize its fidelity.