Nathan Lysne, University of Arizona
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Abstract:
As uncorrected quantum processors grow in sophistication, many are being used for analog quantum simulation (AQS) of novel physics beyond the capabilities of classical devices. However, without the guarantee of bounded errors achieved by digitizing the computation, we do not know when and how much to trust an AQS result in the presence of inevitable imperfections. Here we present the results of using our experiment as a testbed for studying the impact of errors on AQS. We have developed a small but highly-accurate processor over a 16-dimensional Hilbert space comprising the combined electron-nuclear spin of a single Cs-133 atom in the electronic ground state. Advances in EigenValue-Only (EVO) optimal control enable us to perform many (>100) arbitrary unitary transformations in this space while maintaining accuracy on the device. We use this capability to simulate model systems known to exhibit features of interest, such as chaos and hypersensitivity (quantum kicked top) and quantum phase transitions (the transverse Ising and Lipkin-Meshkov-Glick models). Experimental simulations show high fidelity of the quantum state and dynamical features in the presence of native imperfections. We discuss these results in the context of a new framework for quantifying the average sensitivity of simulator outcomes to errors. These theoretical and experimental results support the idea that AQS of 'macroscopic' observables (e.g., total magnetization) can be robust in the presence of errors, while observables tied to a specific quantum state (e.g., the fidelity) are not.
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