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As a milestone for general-purpose computing machines, we demonstrate thatquantum processors can be programmed to efficiently simulate dynamics that arenot native to the hardware. Moreover, on noisy devices without errorcorrection, we show that simulation results are significantly improved when thequantum program is compiled using modular gates instead of a restricted set ofstandard gates. We demonstrate the general methodology by solving a cubicinteraction problem, which appears in nonlinear optics, gauge theories, as wellas plasma and fluid dynamics. To encode the nonnative Hamiltonian evolution, wedecompose the Hilbert space into a direct sum of invariant subspaces in whichthe nonlinear problem is mapped to a finite-dimensional Hamiltonian simulationproblem. In a three-states example, the resultant unitary evolution is realizedby a product of ~20 standard gates, using which ~10 simulation steps can becarried out on state-of-the-art quantum hardware before results are corruptedby decoherence. In comparison, the simulation depth is improved by more than anorder of magnitude when the unitary evolution is realized as a single cubicgate, which is compiled directly using optimal control. Alternatively,parametric gates may also be compiled by interpolating control pulses. Modulargates thus obtained provide high-fidelity building blocks for quantumHamiltonian simulations.

Simulating nonnative cubic interactions on noisy quantum machines