Quantum Tunneling: From Theory to Error-Mitigated Quantum Simulation

Ever since the discussions about a possible quantum computer arised, quantum simulations have been at the forefront of possible utilities and the task of quantum simulations is one that promises quantum advantage. In recent years, simulations of large molecules through VQE or dynamics of many-body spin Hamiltonians may be possible, and even able to achieve useful results with the use of error mitigation techniques. Simulating smaller models is also important, and currently, in the NISQ (Noisy intermediate-scale quantum) era, it is easier and less prone to errors. This current study encompasses the theoretical background and the hardware aware circuit implementation of a quantum tunneling simulation. Specifically, this study presents the theoretical background needed for such implementation and highlights the main steps of development. Building on classic approaches of quantum tunneling simulations, this study improves the result of such simulations by employing error mitigation techniques (ZNE and REM) and uses them in conjunction with multiprogramming of the quantum chip for solving the hardware under-utilization problem that arises in such contexts. Moreover, we highlight the need for hardware-aware circuit implementations and discuss these considerations in detail to give an end-to-end workflow overview of quantum simulations.