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Convex optimization, linear and semidefinite programming in particular, has been a standard tool in quantum information theory, giving certificates of local and quantum correlations, contextuality, and more. Increasingly, similar methods are making headways in quantum many-body physics, giving lower bounds -- and thus certificates -- on the ground state energy. The disadvantage of such methods is that they do not scale well to large system sizes, whether those systems are multiparty Bell scenarios or lattice models of numerous sites. Machine
learning is entering the field as the latest buzzword. While it provides a more scalable alternative to convex programming and enables forming new conjectures, the outcome of learning methods remains uncertified. In this talk, I introduce the most important paradigms in machine learning for quantum information theory, give an overview of some earlier work in the field, argue for the importance of certifiable predictions of learning algorithms, and present some of our preliminary results.

Three fundamental factors determine the quality of a statistical learning algorithm: expressiveness, generalization and optimization.  The classic strategy for handling these factors is relatively well understood.  In contrast, the radically different approach of deep learning, which in the last few years has revolutionized the world of artificial intelligence, is shrouded by mystery.  This talk will describe a series of works aimed at unraveling some of the mysteries revolving expressiveness, arguably the most prominent factor behind the success of deep learning.  I will begin by showing that state of the art deep learning architectures, such as convolutional networks, can be represented as tensor networks -- a computational model commonly employed in quantum physics.  This connection will inspire the use of quantum entanglement for defining measures of data correlations modeled by deep networks.  Next, I will turn to a quantum max-flow / min-cut theorem characterizing the entanglement captured by tensor networks.  This theorem will give rise to new results that shed light on expressiveness in deep learning, and in addition, provide new tools for deep network design.

Works covered in the talk were in collaboration with Yoav Levine, Or Sharir, David Yakira and Amnon Shashua.

Short-depth algorithms are crucial for reducing computational error on near-term quantum computers, for which decoherence and gate infidelity remain important issues. Here we present a machine-learning inspired approach for discovering such algorithms. We apply our method to a ubiquitous primitive: computing the overlap Tr(rho*sigma) between two quantum states rho and sigma. The standard algorithm for this task, known as the Swap Test, is used in many applications such as quantum support vector machines, and, when specialized to rho=sigma, quantifies the Renyi entanglement. Here, we find algorithms that have shorter depths than the Swap Test, including one that has constant depth (independent of problem size). Furthermore, we apply our approach to the hardware-specific connectivity and gate alphabets used by Rigetti's and IBM's quantum computers and demonstrate that the shorter algorithms that we derive significantly reduce the error - compared to the Swap Test - on these computers.