A major part of quantum information processing concerns the robust and efficient verification of algorithms implemented on quantum hardware. This can be achieved via quantum state tomography. State tomography is concerned with establishing algorithms providing an effective description of an unknown quantum state given access to multiple copies of a system prepared in that state. As the size of quantum devices continues to increase, the community faces a new challenge known as the curse of dimensionality: the number of parameters needed to fully describe an $n$-qubit quantum system scales as $2^{\Omega(n)}$, making full state estimation prohibitively resource-intensive. However, this seemingly pessimistic outlook improves significantly when focusing on states of physically relevant many-body systems, where one can exploit their inherent local structure. At Quriosity, we develop sample-optimal algorithms for learning and testing ground and Gibbs states of complex quantum systems, drawing on tools from entropic methods and quantum optimal transport.
Associated PIs: Cambyse Rouzé, Marco Fanizza
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