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Analog quantum optimization methods, such as quantum annealing, are promisingand at least partially noise tolerant ways to solve hard optimization andsampling problems with quantum hardware. However, they have thus far failed todemonstrate broadly applicable quantum speedups, and an important contributingfactor to this is slowdowns from embedding, the process of mapping logicalvariables to long chains of physical qubits, enabling arbitrary connectivity onthe short-ranged 2d hardware grid. Beyond the spatial overhead in qubit count,embedding can lead to severe time overhead, arising from processes whereindividual chains ``freeze" into ferromagnetic states at different times duringevolution, and once frozen the tunneling rate of this single logical variabledecays exponentially in chain length. We show that this effect can besubstantially mitigated by local AC variation of the qubit parameters as in theRFQA protocol (Kapit and Oganesyan, Quant. Sci. Tech. \textbf{6}, 025013(2021)), through a mechanism we call Symphonic Tunneling. We provide generalarguments and substantial numerical evidence to show that AC-driven multi-qubittunneling is dramatically faster than its DC counterpart, and since ST is not a1d-specific mechanism, this enhancement should extend to clusters of coupledchains as well. And unlike a uniform transverse field, in higher dimensionsthis method cannot be efficiently simulated classically. We explore schemes tosynchronize the AC tones within chains to further improve performance.Implemented at scale, these methods could significantly improve the prospectsfor achieving quantum scaling advantages in near-term hardware.

Embedding quantum optimization problems using AC driven quantum ferromagnets