Talks

We present a tensor-network-based classical algorithm (equipped with guarantees) for simulating $n$-qubit quantum circuits with arbitrary single-qubit noise. Our algorithm represents the state of a noisy quantum system by a particular ensemble of matrix product states from which we stochastically sample a pure quantum state. Each single qubit noise process acting on a pure state is then represented by the ensemble of states that achieve the minimal average entanglement (the entanglement of formation) between the noisy qubit and the rest of the system. This approach provides a connection between the entanglement of formation and the accuracy of the simulation algorithm. For a given maximum bond dimension $\chi$ and circuit, our algorithm comes with an upper bound on the simulation error (in total variation distance), runs in $poly(n,\chi)$-time and improves upon related prior work (1) in scope: by extending from the three commonly considered noise models to general single qubit noise (2) in performance: by employing a state-dependent locally-entanglement-optimal unraveling and (3) in conceptual contribution: by showing that the fixed unraveling used in prior work becomes equivalent to our choice of unraveling in the special case of depolarizing and dephasing noise acting on a maximally entangled state. This is joint work with Simon Cichy, Paul K. Faehrmann, Lennart Bittel and Jens Eisert.

Beginning with the intimate relationship between recursive algorithms and dynamical systems, I shall describe some common dynamics that serve as templates for `stateless' learning. This will be followed by reinforcement learning for dynamic systems, using Markov decision processes as a test case.

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

In the ultimatum minigame, proposers can offer either half the total prize or just $1$. Responders can accept or reject. At the subgame perfect equilibrium, proposers offer $1$ and responders accept. We apply the best experienced payoff (BEP) dynamic to the large population version of this game. The BEP dynamic is generated when players try their strategies a certain number of times and choose the strategy that generates the highest average payoff. We establish conditions under which the subgame perfect equilibrium is stable or unstable. If it is unstable, another stable state can arise where a significant fraction of proposers make high offers.

Infectious diseases or epidemics spread through human society via social interactions among infected and healthy individuals. In this talk, we explore the coupled evolution of the epidemic and protection adoption behavior of humans.

In the first part of the talk, we focus on the class of susceptible-infected-susceptible (SIS) epidemic model where individuals choose whether to adopt protection or not based on the trade-off between the cost of adopting protection and the risk of infection; the latter depends on the current prevalence of the epidemic and the fraction of individuals who adopt protection in the entire population. We define the coupled epidemic-behavioral dynamics by modeling the evolution of individual protection adoption behavior according to the replicator dynamics. We fully characterize the equilibria and their stability properties. We further analyze the coupled dynamics under timescale separation when individual behavior evolves faster than the epidemic, and characterize the equilibria of the resulting discontinuous hybrid dynamical system. Numerical results illustrate how the coupled dynamics exhibits oscillatory behavior and convergence to sliding mode solutions under suitable parameter regimes.

In the second part of the talk, we discuss a dynamic population game model to capture individual behavior against susceptible-asymptomatic-infected-recovered (SAIR) epidemic model. Each node chooses whether to activate (i.e., interact with others), how many other individuals to interact with, and which zone to move to in a time-scale which is comparable with the epidemic evolution. We define and analyze the notion of equilibrium in this game, and investigate the transient behavior of the epidemic spread in a range of numerical case studies, providing insights on the effects of the agents' degree of future awareness, strategic migration decisions, as well as different levels of lockdown and other interventions.

In a series of four lectures, I give an introduction to evolutionary game theory and the literature on the evolution of cooperation. This series covers
(i) Evolutionary game theory in infinite and finite populations (Replicator dynamics, Moran process);
(ii) Evolution of cooperation and direct reciprocity
(iii) Social norms and the evolution of indirect reciprocity
(iv) Some current research directions (e.g., direct reciprocity in complex environments).

I will explain a recently proposed holographic scenario for pure dS3 Einstein quantum gravity. The dual description is a double-scaled matrix model, which is capable of capturing bulk cosmological correlators integrated over the metric at future infinity in order to define gauge-invariant observables. Moreover the matrix model has precisely the right number of degrees of freedom to account for the de Sitter entropy associated with the cosmological horizon seen by an observer. A key step in the logic is a reformulation of the gravity theory in terms of a novel topological quantum field theory. Based on work with Lorenz Eberhardt, Beatrix Mühlmann, building on previous work with Victor Rodriguez.

The measurement of the electron magnetic moment (g-2)_e has reached the spectacular precision of sub-parts-per-trillion, and is currently the highest-precision measurement of a property of a fundamental particle. The next iteration of the measurement is expected to improve the precision by almost an order of magnitude, at which point the leading systematic uncertainty will be the “cavity shift”: the modification of the electron energy levels due to the conducting walls of the cavity in which the electron is trapped. This quantity cannot be directly measured at the required precision, and must be calculated. I will review the setup of the (g-2)_e experiment and present a new calculation of the cavity shift using the full machinery of quantum mechanics and quantum electrodynamics, which improves upon previous classical calculations with a consistent renormalization scheme while allowing for individual quality factors for each cavity mode.