Quantum Physics

the no-cloning theorem is an essential result in quantum information on top of which many quantum cryptography protocols are built. In this talk we examine the cloning question in the context of classical mechanics/Hamiltonian mechanics. We find the answer is quite subtle: whether a mechanical system can be cloned depends on the topological structure of its phase space. In particular, for a system to be clonable, its phase space must be contractible. This means certain systems (e.g. particle moving on a line) is clonable, while others (e.g. the simple pendulum) cannot be cloned. We explain the idea of the proof, which uses tools from algebraic topology (homotopy groups and Whitehead’s theorem). Finally we discuss the physical interpretations of this result: how do we reconcile this theorem with the experience that generally speaking, classical information is clonable? Can we use this no-cloning theorem to build secure communication protocols in classical systems instead of quantum ones?

Understanding quantum noise is an essential step towards building practical quantum information processing systems. Pauli noise is a useful model widely applied in quantum benchmarking, quantum error mitigation, and quantum error correction. Despite previous research, the problem of how to learn a Pauli noise model self-consistently, completely, and efficiently has remained open. In this talk, I will introduce a framework of gate-set Pauli noise learning that aims at addressing this problem. The framework treats initialization, measurement, and a set of quantum gates to suffer from unknown Pauli noise channels, which are allowed to have customized locality constraints. The goal is to learn all the Pauli noise channels using only those noisy operations. I will first introduce a theory on the “learnability” of Pauli noise model, i.e., what information is fundamentally identifiable within the model and what is not. This is established using tools from algebraic graph theory and ideas from gate set tomography; I will then discuss a sample-efficient procedure to learn all learnable information of a Paul noise model to any desired precision; Finally, I will demonstrate how to apply our theoretic framework for concrete practical gate set and noise assumptions, and discuss the potential impact on quantum error mitigation and other applications.