



02434nas a2200205   4500008004100000245006200041210006200103260001500165300001100180490000800191520186900199100001502068700001902083700001902102700001602121700001702137700001702154700002002171856003702191       2018                        eng d00aRecovering quantum gates from few average gate fidelities0 aRecovering quantum gates from few average gate fidelities  c2018/03/01  a1705020 v1213 a<p><span style="font-family: &quot;Lucida Grande&quot;, helvetica, arial, verdana, sans-serif; font-size: 14.4px;">Characterising quantum processes is a key task in and constitutes a challenge for the development of quantum technologies, especially at the noisy intermediate scale of today&#39;s devices. One method for characterising processes is randomised benchmarking, which is robust against state preparation and measurement (SPAM) errors, and can be used to benchmark Clifford gates. A complementing approach asks for full tomographic knowledge. Compressed sensing techniques achieve full tomography of quantum channels essentially at optimal resource efficiency. So far, guarantees for compressed sensing protocols rely on unstructured random measurements and can not be applied to the data acquired from randomised benchmarking experiments. It has been an open question whether or not the favourable features of both worlds can be combined. In this work, we give a positive answer to this question. For the important case of characterising multi-qubit unitary gates, we provide a rigorously guaranteed and practical reconstruction method that works with an essentially optimal number of average gate fidelities measured respect to random Clifford unitaries. Moreover, for general unital quantum channels we provide an explicit expansion into a unitary 2-design, allowing for a practical and guaranteed reconstruction also in that case. As a side result, we obtain a new statistical interpretation of the unitarity -- a figure of merit that characterises the coherence of a process. In our proofs we exploit recent representation theoretic insights on the Clifford group, develop a version of Collins&#39; calculus with Weingarten functions for integration over the Clifford group, and combine this with proof techniques from compressed sensing.</span></p>1 aRoth, Ingo1 aKueng, Richard1 aKimmel, Shelby1 aLiu, Yi-Kai1 aGross, David1 aEisert, Jens1 aKliesch, Martin  uhttps://arxiv.org/abs/1803.00572