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Variational Quantum Algorithms (VQA) have been identified as a promisingcandidate for the demonstration of near-term quantum advantage in solvingoptimization tasks in chemical simulation, quantum information, and machinelearning. The standard model of training requires a significant amount ofquantum resources, which led us to use classical shadows to devise analternative that consumes exponentially fewer quantum resources. However, theapproach only works when the observables are local and the ansatz is theshallow Alternating Layered Ansatz (ALA), thus severely limiting its potentialin solving problems such as quantum state preparation, where the ideal statemight not be approximable with an ALA. In this work, we present a protocolbased on shallow shadows that achieves similar levels of savings for almost anyshallow ansatz studied in the literature, when combined with observables of lowFrobenius norm. We show that two important applications in quantum informationfor which VQAs can be a powerful option, namely variational quantum statepreparation and variational quantum circuit synthesis, are compatible with ourprotocol. We also experimentally demonstrate orders of magnitude improvement incomparison to the standard VQA model.

Ansatz-Agnostic Exponential Resource Saving in Variational Quantum Algorithms Using Shallow Shadows