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A fundamental result in solid-state physics asserts that a crystalline material cannot be insulating unless the number of electrons per unit cell is an integer. Statements of this nature are immensely powerful because they are sensitive only to the general structure of the system and not to the microscopic details of the interactions. Such "kinematic constraints" have been extensively generalized in contemporary times, commonly under the term "quantum anomaly”. In this colloquium, I will first review some basic aspects of anomaly constraints in many-body quantum physics. Subsequently, I will demonstrate, through several recent examples, the significant role of quantum anomaly in constraining, understanding, and even unveiling novel quantum phases of matter.

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The essential requirement for fault-tolerant quantum computation (FTQC) is the total protocol design to achieve a fair balance of all the critical factors relevant to its practical realization, such as the space overhead, the threshold, and the modularity. A major obstacle in realizing FTQC with conventional protocols, such as those based on the surface code and the concatenated Steane code, has been the space overhead, i.e., the required number of physical qubits per logical qubit. Protocols based on high-rate quantum low-density parity-check (LDPC) codes gather considerable attention as a way to reduce the space overhead, but problematically, the existing fault-tolerant protocols for such quantum LDPC codes sacrifice the other factors. Here we construct a new fault-tolerant protocol to meet these requirements simultaneously based on more recent progress on the techniques for concatenated codes rather than quantum LDPC codes, achieving a constant space overhead, a high threshold, and flexibility in modular architecture designs. In particular, under a physical error rate of 0.1%, our protocol reduces the space overhead to achieve the logical CNOT error rates 10^{−10} and 10^{−24} by more than 90% and 97%, respectively, compared to the protocol for the surface code. Furthermore, our protocol achieves the threshold of 2.4% under a conventional circuit-level error model, substantially outperforming that of the surface code. The use of concatenated codes also naturally introduces abstraction layers essential for the modularity of FTQC architectures. These results indicate that the code-concatenation approach opens a way to significantly save qubits in realizing FTQC while fulfilling the other essential requirements for the practical protocol design.

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Particle production can occur in a curved spacetime like, for example, in the case of thermal emission of particles from black holes, otherwise known as Hawking radiation. The Unruh effect is a quantum field theory result that is closely connected to Hawking radiation. It states that accelerated observers associate a thermal bath of particles to the vacuum state of inertial observers. The Unruh effect has been given special attention because contrary to black hole evaporation, it is a prediction made in a flat (Minkowski) spacetime and therefore can be, in principle, tested in the laboratory. Recently, we have investigated the connection between the Unruh effect and classical radiation for a uniformly accelerated particle. This link seems counter-intuitive since the former is a purely quantum effect while the latter is a classic one. Nonetheless, we find that using a full quantum field treatment of the radiation exchanged by an accelerated charge with the surrounding Unruh thermal bath, the resultant power reduces at tree-level to the usual Larmor formula. The results are also consistent with the observation made by Unruh and Wald which states that the emission of a photon in the inertial frame corresponds to the emission or absorption of a photon in the accelerated frame. The fact that the derivation makes the link between the Unruh effect and the Larmor radiation from a uniformly accelerated charged particle clearer will perhaps help in resolving some of the controversies that have surrounded the Unruh effect since its discovery.

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What is a measurement? This, it turns out, is the most difficult question in physics today. In this talk, I will explain why the measurement problem is important and why all attempts to solve it so far have failed. I will then discuss the obvious solution to the problem that was, unfortunately, discarded half a century ago without ever being seriously considered: Superdeterminism. After addressing some common objections to this idea, I will summarize the existing approaches to develop a theory for it.

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