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We develop circuit implementations for digital-level quantum Hamiltoniandynamics simulation algorithms suitable for implementation on a reconfigurablequantum computer, such as trapped ions. Our focus is on the co-design of aproblem, its solution, and quantum hardware capable of executing the solutionat the minimal cost expressed in terms of the quantum computing resources usedwhile demonstrating the solution of an instance of a scientifically interestingproblem that is intractable classically. The choice for Hamiltonian dynamicssimulation is due to the combination of its usefulness in the study ofequilibrium in closed quantum mechanical systems, a low cost in theimplementation by quantum algorithms, and the difficulty of classicalsimulation. By targeting a specific type of quantum computer and tailoring theproblem instance and solution to suit physical constraints imposed by thehardware, we are able to reduce the resource counts by a factor of $10$ in aphysical-level implementation and a factor of $30$ to $60$ in a fault-tolerantimplementation over state of the art.

Low cost quantum circuits for classically intractable instances of the Hamiltonian dynamics simulation problem