Dissipative learning of a quantum classifier

He Wang, Chuanbo Liu, Jin Wang

Patrick Odagiu, Vasilis Belis, Lennart Schulze +6 more

Soumik Adhikary, Siddharth Dangwal, Debanjan Bhowmik

Ufuk Korkmaz, Melih Can Topal, Ekin Erdem Aygül +1 more

Quantum machine learning (QML) aims to embed the power of quantum computation with learning theory. Quan-tum noise and finding the best recipe for encoding classical information into a quantum register could be seen as challenges to overcome for computational performance. Classification of quantum information is a subtask for QML. In this study, we adopt a dissipative route for quantum data classification and examine the developed theory on a gradient descent-based learning task. In particular, we follow repeated interactions based on open quantum dynamics where the binary decision is encoded on a steady state. Based on the analytical results, we develop a cost function for training an open quantum neuron. We demonstrate that the dissipation-driven protocol is suitable for a supervised learning scheme.

Jeffrey Marshall, Lorenzo Campos Venuti, Paolo Zanardi A

We investigate a general class of dissipative quantum circuit capable of computing arbitrary conjunctive normal form (CNF) Boolean formulas. In particular, the clauses in a CNF formula define a local generator of Markovian quantum dynamics which acts on a network of qubits. Fixed points of this dynamical system encode the evaluation of the CNF formula. The structure of the corresponding quantum map partitions the Hilbert space into sectors, according to decoherence-free subspaces (DFSs) associated with the dissipative dynamics. These sectors then provide a natural and consistent way to classify quantum data (i.e., quantum states). Indeed, the attractive fixed points of the network allow one to learn the sector(s) for which some particular quantum state is associated. We show how this structure can be used to dissipatively prepare quantum states (e.g., entangled states) and outline how it may be used to generalize certain classical computational learning tasks.

John H. Miller, Martha Villagrán