



01881nas a2200193   4500008004100000245007300041210006900114260001400183490000600197520129800203100002001501700002201521700002101543700001601564700001801580700002401598700002801622856003701650       2023                        eng d00aExperimental Observation of Thermalization with Noncommuting Charges0 aExperimental Observation of Thermalization with Noncommuting Cha  c4/28/20230 v43 a<p>Quantum simulators have recently enabled experimental observations of quantum many-body systems&#39; internal thermalization. Often, the global energy and particle number are conserved, and the system is prepared with a well-defined particle number - in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6-21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, whose predictions can now be tested.</p>1 aKranzl, Florian1 aLasek, Aleksander1 aJoshi, Manoj, K.1 aKalev, Amir1 aBlatt, Rainer1 aRoos, Christian, F.1 aHalpern, Nicole, Yunger  uhttps://arxiv.org/abs/2202.0465202171nas a2200289   4500008004100000245007500041210006900116260001400185520131000199100002201509700002001531700002001551700002401571700002401595700002001619700001901639700002001658700002901678700001801707700002001725700001801745700002301763700001701786700001701803700002401820856003701844       2023                        eng d00aVerifiable measurement-based quantum random sampling with trapped ions0 aVerifiable measurementbased quantum random sampling with trapped  c7/26/20233 a<p>Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. Moreover, by exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states--in single instances and on average--and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.</p>1 aRingbauer, Martin1 aHinsche, Marcel1 aFeldker, Thomas1 aFaehrmann, Paul, K.1 aBermejo-Vega, Juani1 aEdmunds, Claire1 aPostler, Lukas1 aStricker, Roman1 aMarciniak, Christian, D.1 aMeth, Michael1 aPogorelov, Ivan1 aBlatt, Rainer1 aSchindler, Philipp1 aEisert, Jens1 aMonz, Thomas1 aHangleiter, Dominik  uhttps://arxiv.org/abs/2307.14424