Scientific Series

I will present a method for the implementation of a universal set of fault-tolerant logical gates using homological product codes. In particular, I will show how one can fault-tolerantly map between different encoded representations of a given logical state, enabling the application of different classes of transversal gates belonging to the underlying quantum codes. This allows for the circumvention of no-go results pertaining to universal sets of transversal gates and provides a general scheme for fault-tolerant computation while keeping the stabilizer generators of the code sparse.

Recently there have been several proposals of low-energy precision experiments that can search for new particles, new forces, and the Dark Matter of the Universe in a way that is complementary to collider searches. In this talk, I will present some examples involving atomic clocks, nuclear magnetic resonance, and astrophysical black holes accessible to LIGO.

Entanglement spectrum (ES) contains more information than the entanglement entropy, a single number. For highly excited states, this can be quantified by the ES statistics, i.e. the distribution of the ratio of adjacent gaps in the ES. I will first present examples in both random unitary circuits and Hamiltonian systems, where the ES signals whether a time-evolved state (even if maximally entangled) can be efficiently disentangled without precise knowledge of the time evolution operator. This allows us to define a notion of entanglement complexity that is not revealed by the entanglement entropy.

In the second part, I will discuss how quantum states are scrambled via braiding in systems of non-Abelian anyons through the lens of ES statistics. We define a distance between the entanglement level spacing distribution of a state evolved under random braids and that of a Haar-random state, using the Kullback-Leibler divergence $D_{\mathrm{KL}}$. We study $D_{\mathrm{KL}}$ numerically for random braids of Majorana fermions (supplemented with random local four-body interactions) and Fibonacci anyons. Our results reveal a hierarchy of scrambling among various models --- even for the same amount of entanglement entropy --- at intermediate times, whereas all models exhibit the same late-time behavior. In particular, we find that braiding of Fibonacci anyons scrambles more efficiently than the universal H+T+CNOT set. Our results promote $D_{\mathrm{KL}}$ as a quantifiable metric for scrambling and quantum chaos, which applies to generic quantum systems.

Most current dark matter detection strategies, including both direct and indirect efforts, are based on the assumption that the galactic dark matter number density is quite high, allowing for the detection of rare scattering events. Such a paradigm arises naturally if the dark matter self-interactions are weak. However, strong interactions within the dark sector can give rise to large composite objects, whose detection requires a different experimental paradigm. We call these object Dark Blobs. In such theories, the energy transfer due to a single collision with a Standard Model particle tends to be small, below the energy threshold of many nuclear recoil experiments. Fortunately, due to their exponentially large composite nature, the interactions between these objects and a terrestrial detector can be coherently enhanced. Therefore, while the effect on a single probe is small, the large collective effect can be quite dramatic and, importantly, above experimental thresholds. In this talk, I will briefly motivate the early Universe formation of certain types of Dark Blobs and then focus on multiple detection avenues for these objects.

This talk will explore the applications of the computing power of numerical relativity to gravitational theories beyond general relativity. Specifically, I will consider dynamical Chern-Simons gravity, which has roots in string theory and loop quantum gravity. I will discuss our  formalism and efforts to simulate binary black holes in this theory to generate waveforms LIGO and LISA. Additionally, I will discuss the generation of numerical black hole solutions in this theory, and applications to probing black hole shadows with the Event Horizon Telescope. 

Stars orbiting in the halo of our galaxy, the Milky Way, are a window into the distribution of dark matter. In particular, tidally disrupted star clusters, which produce thin stellar streams, are optimal tracers of matter. Based on a Fisher-information calculation, we expect that the current data on the known Milky Way streams should constrain the radial profile and the shape of the inner halo to a precision of a few percent. In addition, stellar streams retain a detailed record of the matter field on small scales. Typically, streams are very thin -- approximately 100 times longer than they are wide, so even small gravitational perturbations introduce observable variations in the density of stars along the stream. Recently, significant gaps were detected in the GD-1 stellar stream, as well as stream stars displaced from the main stream. The observed structure is naturally reproduced in simulations where a stream like GD-1 encounters a massive perturber. None of the known Milky Way satellites has recently crossed paths with GD-1. If confirmed, the encounter scenario indicates the presence of an unknown, massive (~10^7 Msun) and compact (~<10 pc) object in the Milky Way -- the first evidence of dark substructure in a galactic halo.

Work of Bezrukavnikov on local geometric Langlands correspondence and works of Gorsky, Neguţ, Rasmussen and Oblomkov, Rozansky on knot homology and matrix factorizations suggest that there should be a categorical version of a certain natural homomorphism from the affine Hecke algebra to the finite Hecke algebra in type A, sending basis lattice elements on the affine side to Jucys-Murphy elements on the finite side. I will try to explain some of the structures involved and will talk about recent progress towards a construction of such a categorification in the setting of Hecke categories.

I will sketch why self-dual versions of the moduli of G-Higgs bundles are expected to arise physically from the study of 4d theories of class S. I will then describe an extension of the Langlands duality results of Hausel-Thaddeus (G=SL(n)) and Donagi-Pantev (arbitrary reductive G) that yields self-dual moduli spaces as a corollary.

The Alday-Gaiotto-Tachikawa correspondence connects gauge theory on a fourfold with conformal field theory. We are interested in a certain algebro-geometric incarnation of this framework, where the fourfold is an algebraic surface and instantons/differential geometry are replaced with sheaves/algebraic geometry. In this talk, we will present a certain approach to AGT that yields partial results for quite general surfaces, and ask questions about what still needs to be done to state and prove the full correspondence in the language of algebraic geometry.

I will discuss certain irrelevant operator deformations of holographic conformal field theories that define a one parameter family of quantum field theories which are thought to be dual to quantum gravity in finite regions. 
Some examples include the "$T\bar{T}$ deformation of two dimensional holographic CFTs, its generalisations and higher dimensional cousins.
I will emphasise the key role played by emergent radial diffeomorphism invariance in this scenario. In particular, I will present an additional criterion for a theory, in the appropriate regime, to possess a dual description in terms of general relativity coupled to matter in one higher dimension. I will also discuss entanglement properties of such theories, and in a particular example, I will show how the holographic entanglement entropy conjectures still hold in the finite radius setting. This is based on the following work: arXiv:1707.08118 [hep-th], arXiv:1712.07955 [hep-th], arXiv:1806.07444 [hep-th] and arXiv:1808.07760 [hep-th]."

Performing a quantum adiabatic optimization (AO) algorithm with the time-dependent Hamiltonian H(t) requires one to have some idea of the spectral gap γ(t) of H(t) at all times t. With only a promise on the size of the minimal gap γmin, a typical statement of the adiabatic theorem promises a runtime of either O(γmin-2) or worse. In this talk, I provide an explicit algorithm that, with access to an oracle that returns the spectral gap γ(t) to within some multiplicative constant, reliably performs QAO in time Õ(γmin-1) with at most O(log(γmin-1)) oracle queries. I then construct such an oracle using only computational basis measurements for the toy problem of a complete graph driving Hamiltonian on V vertices and arbitrary cost function. I explain why one cannot simply perform adiabatic Grover search and prove that one can still perform QAO in time Õ(V2/3)  without any a priori knowledge of γ(t). This work was done in collaboration with Brad Lackey, Aike Liu, and Kianna Wan.

In this talk I will review the results of recent work in collaboration with  Cecilia De Fazio, Benjamin Doyon and István M. Szécsényi. We studied the entanglement of excited states consisting of a finite number of particle excitations. More precisely, we studied the difference between the entanglement entropy of such states and that of the ground state in a simple bi-partition of a quantum system, where both the size of the system and of the bi-partition are infinite, but their ratio is finite. We originally studied this problem in massive 1+1 dimensional QFTs where analytic computations were possible. We have found the results to apply more widely, including to higher dimensional free theories. In all cases we find that the increment of entanglement is a simple function of the ratio between region's and system's size only. Such function, turns out to be exactly the entanglement of a qubit state where the coefficients of the state are simply associated with the probabilities of particles being localised in one or the other part of the bi-partition. In this talk I will describe the results in some detail and discuss their domain of applicability. I will also highlight the main QFT techniques that we have used in order to obtain them analytically and  present some numerical data.