Simulating nonnative cubic interactions on noisy quantum machines

Abstract

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates instead of a restricted set of standard gates. We demonstrate the general methodology by solving a cubic interaction problem, which appears in nonlinear optics, gauge theories, as well as plasma and fluid dynamics. To encode the nonnative Hamiltonian evolution, we decompose the Hilbert space into a direct sum of invariant subspaces in which the nonlinear problem is mapped to a finite-dimensional Hamiltonian simulation problem. In a three-states example, the resultant unitary evolution is realized by a product of ~20 standard gates, using which ~10 simulation steps can be carried out on state-of-the-art quantum hardware before results are corrupted by decoherence. In comparison, the simulation depth is improved by more than an order of magnitude when the unitary evolution is realized as a single cubic gate, which is compiled directly using optimal control. Alternatively, parametric gates may also be compiled by interpolating control pulses. Modular gates thus obtained provide high-fidelity building blocks for quantum Hamiltonian simulations.

4 figures. pages 1-6 are main text and bibliography, and pages 7-8 are supplemental material

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• Observability of fidelity decay at the Lyapunov rate in few-qubit quantum simulations
• Simulating nonlinear optical processes on a superconducting quantum device
• Direct pulse-level compilation of arbitrary quantum logic gates on superconducting qutrits
• Efficient control pulses for continuous quantum gate families through coordinated re-optimization
• Pulse family optimization for parametrized quantum gates using spectral clustering
• Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement
• A time-marching quantum algorithm for simulation of the nonlinear Lorenz dynamics
• Quantum Instability
• Quantum Calculation for Two-Stream Instability and Advection Test of Vlasov-Maxwell Equations: Numerical Evaluation of Hamiltonian Simulation
• Algebraic discrete quantum harmonic oscillator with dynamic resolution scaling
• Simulating plasma wave propagation on a superconducting quantum chip
• Using optimal control to guide neural-network interpolation of continuously-parameterized gates