Scientific Series

In this talk, I will describe how ideas from geometry and combinatorics can help us understand the mathematical and physical properties of cosmological integrals. From efficiently deriving canonical differential equations to a systematic method for finding a minimal basis for the physical subspace. Time permitting, I will also comment on how geometry and combinatorics control the zeros of cosmological integrands.

I will introduce how to incorporate loop contributions into positivity bounds in a massless scalar theory with shift symmetry. The allowed region of Wilson coefficients is called the EFT-hedron. With loop contributions, the n=4 null constraint, which plays an important role in determining the allowed region for g3–g4 (the Wilson coefficients of dimension-10 and dimension-12 operators, respectively), is modified. This modification of the null constraint reveals new features of the EFT-hedron. We obtained a much stronger bound for g2 (the Wilson coefficient of dimension-8 operators) without using the full unitarity condition. Furthermore, we found a negative g4, which is not possible under the tree-level bound. It would be interesting to generalize our method to more complicated theory and test our results.

Continuous variable (CV) systems play an important role in quantum foundations and quantum information processing, especially because of their quantum optical realization. Gaussian states of CV systems, on the one hand have non-trivial quantum properties, and on the other hand, can be realized in the laboratory.  There are non-Gaussian states which can be obtained from Gaussian states via physically realizable operations and these too can be useful in enhancing  non-classicality and improving the performance of quantum information processing protocols.  In the talk, I will  introduce CV systems and their Gaussian and non-Gaussian states. The violation of Bell-type inequalities using CV systems will be discussed. Quantum key distribution protocols and quantum teleportation schemes using Gaussian and non-Gaussian states will also be taken up. 

In this talk I will discuss the energy probability density function of an evaporating near-extremal charged black hole. At sufficiently low energies, such black holes experience large quantum metric fluctuations in the $AdS_{2}$ throat which are governed by a Schwarzian action. These fluctuations modify Hawking evaporation rates, and therefore also affect how the black hole state evolves over time. In previous work on Schwarzian-corrected Hawking radiation, the black hole was taken to be in the microcanonical or canonical ensemble [arXiv:2411.03447]. However, we find that an initially fixed-energy or fixed-temperature state does not remain so in the regime where Schwarzian corrections are important. We consider three decay channels: the emission of massless scalars, photons, and entangled pairs of photons in angular momentum singlet states. In each of the three cases, we find that in the very low energy, quantum dominated regime, the probability distribution of the black hole energy level occupation tends toward a particular attractor function that effectively depends on only one combination of time and energy. This function is independent of the initial state and gives new predictions for the energy fluxes and Hawking emission spectra of near-extremal charged black holes.

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.

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.

I discuss work in progress on the no-boundary state of the universe in quantum cosmology, emphasizing the key role played by the inclusion of an observer in obtaining a reasonable no-boundary state. For concreteness we focus on a 2d toy model, namely dS JT gravity. This model has avatars of important issues with the wavefunction of the universe in inflationary models. The issues are that the wavefunction predicts a small universe (whereas our universe is rather large), and that it is not normalizable. I show that the non-normalizability is resolved by promoting dS JT gravity to sine dilaton gravity, a type of UV completion of dS JT gravity of which I discuss the cosmological interpretation. I then argue that the issue of predicting a small universe (in this toy model) is resolved by including an observer in the theory. With the observer, the leading contribution is a bra-ket wormhole. The observer's no boundary state is a (maximally mixed) identity matrix, and thus prefers neither small nor large universes.

In this talk, I will discuss the complexity of a fermionic analogue of Quantum k-SAT. In this Fermionic k-SAT problem, one is given the task to decide whether there is a fermionic state in the null-space of a collection of fermionic, parity-conserving, projectors on n fermionic modes, where each fermionic projector involves at most k fermionic modes. We prove that this problem can be solved efficiently classically for k = 2. In addition, we show that deciding whether there exists a satisfying assignment with a given fixed particle number parity can also be done efficiently classically for Fermionic 2-SAT: this problem is a quantum-fermionic extension of asking whether a classical 2-SAT problem has a solution with a given Hamming weight parity. We also prove that deciding whether there exists a satisfying assignment for particle-number-conserving Fermionic 2-SAT for some given particle number is NP-complete. Complementary to this, we show that Fermionic 9-SAT is QMA_1-hard.