Physics

Demonstrating quantum supremacy, a complexity-guaranteed quantum advantage against over the best classical algorithms by using less universal quantum devices, is an important near-term milestone for quantum information processing. Here we develop a threshold theorem for quantum supremacy with noisy quantum circuits in the pre-threshold region, where quantum error correction does not work directly. By using the postselection argument, we show that the output sampled from the noisy quantum circuits cannot be simulated efficiently by classical computers based on a stable complexity theoretical conjecture, i.e., non-collapse of the polynomial hierarchy. By applying this to fault-tolerant quantum computation with the surface codes, we obtain the threshold value 2.84% for quantum supremacy, which is much higher than the standard threshold 0.75% for universal fault-tolerant quantum computation with the same circuit-level noise model. Moreover, contrast to the standard noise threshold, the origin of quantum supremacy in noisy quantum circuits is quite clear; the threshold is determined purely by the threshold of magic state distillation, which is essential to gain a quantum advantage.

Conformal Field Theory (CFT) describes the long-distance
dynamics of numerous quantum and statistical many-body systems. The
long-distance limit of a many-body system is often so complicated that
it is hard to do precise calculations. However, powerful new
techniques for understanding CFTs have emerged in the last few years,
based on the idea of the Conformal Bootstrap. I will explain how the
Bootstrap lets us calculate critical exponents in the 3d Ising Model
to world-record precision, how it explains striking relations between
magnets and boiling water, and how it can be applied to questions
across theoretical physics.

A research line that has been very active recently in quantum information is that of recoverability theorems. These, roughly speaking, quantify how well can quantum information be restored after some general CPTP map, through particular 'recovery maps'. In this talk, I will outline what this line of work can teach us about quantum thermodynamics.

On one hand, dynamical semigroups describing thermalization, namely Davies maps, have the curious property of being their own recovery map, as a consequence of a condition named quantum detailed balance. For these maps, we derive a tight bound relating the entropy production at time t with the state of the system at time 2t, which puts a strong constraint on how systems reach thermal equilibrium. 
On the other hand, we also show how the Petz recovery map appears in the derivation of quantum fluctuation theorems, as the reversed work-extraction process. From this fact alone, we show how a number of useful expressions follow. These include a generalization of the majorization conditions that includes fluctuating work, Crooks and Jarzynski's theorems, and an integral fluctuation theorem that can be thought of as the second law as an equality.