Global search for solutions of quantum control problems through path integral Monte Carlo techniques

• Applicant: Privatdozent Dr. Jürgen Stockburger
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 524764293

One of the main requirements for a scalable quantum computer lies in elementary qubit operations with a fidelity well above a high threshold. Above-threshold improvements in fidelity lead to greatly reduced complexity of error correction, thus removing obstacles in the way of scalable quantum computation. For realistic models of hardware imperfections (noise, decoherence) the optimal control methods currently employed for gate design can get trapped in local minima of the control landscape. The current proposal is for a numerical "pre-processing" of quantum control problems which yields near-optimal control trajectories sampled from all the deepest minima of the control landscape. In combination with existing iterative methods, this strategy holds the promise of finding true global cost minima. The approach combines two known techniques, a) path-integral mapping of control problems and b) replica-exchange Monte Carlo techniques, which provide the resulting path integral simulations with coupled layers of importance sampling with variable selectivity, resulting in a sampling chain which is highly mobile yet capable of probing deep minima. Both techniques have been used successfully in a different context (a - optimal control in biomechanics and robotics, b - protein folding and many other fields). The project will combine both techniques to yield an algorithmic approach to global optimization of quantum control capable of finding global and near-global optimal control solutions in complex, rugged control landscapes. The path integrals employed here have no sign problem, since the path measure is essentially a probability measure. The combined technique will be developed primarily for the control of quantum propagation. However, its relevance will likely reach beyond quantum computation and quantum sensing, being applicable to any optimal control problem with a complex control landscape featuring local minima which "trap" other methods.

• DFG Programme: Research Grants