Quantum state tomography is an essential task in quantum information technology. It aims to reconstruct a quantum state from repeated measurements of copies of the state. While reconstructing the full density matrix requires exponentially many samples in many-body systems, predicting a collection of (possibly exponentially many) properties of the quantum system can be efficiently achieved with only a polynomial number of samples under the name of shadow tomography. Huang, Kueng, Preskill further propose a more experiment-friendly shadow tomography scheme, called the classical shadow tomography, which reduces the data acquisition and classical post-processing complexity while retaining the superior polynomial sample complexity.
Mass is a basic property of matter in physics. The origin of mass for matter particles is one of the most fundamental questions about our universe. The standard mechanism for fermions to acquire a mass is the Yukawa-Higgs mechanism, which is based on the spontaneous symmetry breaking via the condensation of a scalar Higgs field (that couples to the fermion field as a bilinear mass via the Yukawa coupling). The Yukawa-Higgs mechanism is responsible for the mass generation of fundamental fermions (leptons and quarks) in the Standard Model, a significant theoretical discovery acknowledged by the Nobel Prize in Physics 2013.
The known universe consists of four fundamental forces: electromagnetic force, weak force, strong force, and gravity. The first three forces can be described theoretically. Gravity, however—which makes up the vast space of the universe—lacks a quantum theory. For three decades, scientists have tried to understand quantum gravity by using a model called the holographic universe.
The Noether theorem is a profound theorem in physics, relating continuous symmetries to conservation laws. The German mathematician Emmy Noether first proved it. Some famous examples include space-time translation symmetry and momentum-energy conservation, rotation symmetry and angular momentum conservation, internal U(1) symmetry and charge conservation. In quantum many-body systems, the discussion of symmetry can be more involved. For example, new symmetry that does not exist in the system can even emerge at low energy. Such a phenomenon generally occurs when the symmetry breaking terms are all irrelevant under the renormalization group (RG) flow in the field theory description. Do emergent symmetries also lead to emergent conservation laws?
The emergent phenomenon is a central theme of condensed matter physics. Not only matter and forces can be emergent, spacetime and gravity could also be emergent. These exciting ideas are being actively explored in the frontier of physics research. But wait a moment, aren’t all these physics theories themselves also emergent phenomena? This is an interesting idea. Physics theories are indeed collective neural activations in human’s brain. It is unclear how the ideas of physics emerge in the neural network of a physicist, or more generally, in the physics community. Understanding the universal principles of emergent intelligence in complex networks should be one important goal of science.
