Scientific Series

The remarkable experimental advances made it possible to create highly tunable quantum systems of ultracold atoms and trapped ions. These platforms proved to be uniquely suited for probing non-equilibrium behavior of interacting quantum systems. From statistical mechanics, we expect that a non-equilibrium system will thermalize, settling to a state of thermodynamic equilibrium. Surprisingly, there are classes of systems which do not follow this expectation. I will give examples of systems which avoid thermalization, thanks to disorder-induced localization and quantum scarring. While thermalization leads to “scrambling” of quantum information, its absence may protect local quantum coherence. This enables non-equilibrium states of matter not envisioned within the framework of statistical mechanics. I will highlight the recent theoretical insights into the remarkable physical properties of such states, based on the underlying patterns of quantum entanglement. I will finally describe a possible theoretical route towards developing a classification of dynamical universality classes in many-body systems.

I will discuss the recent Hamiltonian derivation of dual BMS charges at null infinity using the first order formalism.  More generally, I will discuss how this idea can be used to classify asymptotic charges in gravity.

We present a quantum architecture based on a linear chain of trapped 171Yb+ ions with individual laser beam addressing and readout. The collective modes of motion in the chain are used to efficiently produce entangling gates between any qubit pair. In combination with a classical software stack, this becomes in effect an arbitrarily programmable and fully connected quantum computer. The system compares favorably to commercially available alternatives [2].
We use this versatile setup to perform a quantum walk algorithm that realizes a simulation of the free Dirac equation where the quantum coin determines the particle mass [3]. We are also pursuing digital simulations towards models relevant in high-energy physics among other applications. Recent results from these efforts, and concepts for expanding and scaling up the architecture will be discussed.
[1] S. Debnath et al., Nature 563:63 (2016); P. Murali et al., IEEE Micro, 40:3 (2020); [3] C. Huerta Alderete et al., Nat. Communs. 11:3720 (2020).

Extreme-mass-ratio inspirals (EMRIs) are the only gravitational-wave sources for the future LISA detector that combine the issue of strong-field complexity with that of long-lived signals. The result is a profoundly difficult inverse problem, with many theoretical and computational challenges presented both by the forward modeling of the predicted EMRI waveform, and by the recovery of an inverse solution for the presence and properties of actual EMRI signals in LISA data. I outline recent progress and ongoing work on both fronts. Specifically, I describe: i) the next generation of accurate, efficient and extensive models for (the response of LISA to) an EMRI signal; and ii) a heuristic study of degeneracy in the space of LISA-observable EMRIs, with a view to informing analysis strategies for EMRI search and characterization.

Discriminating between unknown objects in a given set is a fundamental task in experimental science. Suppose you are given a quantum system which is in one of two given states with equal probability. Determining the actual state of the system amounts to doing a measurement on it which would allow you to discriminate between the two possible states. It is known that unless the two states are mutually orthogonal, perfect discrimination is possible only if you are given arbitrarily many identical copies of the state.

In this talk we consider the task of discriminating between quantum channels, instead of quantum states. In particular, we discriminate between a pair of unitary channels acting on a quantum system whose underlying Hilbert space is infinite-dimensional. We prove that in contrast to state discrimination, one only needs a finite number of uses of these channels in order to discriminate perfectly between them. Furthermore, no entanglement is needed in the discrimination task. The measure of discrimination is given in terms of the energy-constrained diamond norm, and a key ingredient of the proofs of these results is a generalization of the Toeplitz-Hausdorff Theorem of convex analysis . Moreover, we employ our results to study a novel type of quantum speed limits which apply to pairs of quantum evolutions. This work was done jointly with Simon Becker (Cambridge), Ludovico Lami (Ulm) and Cambyse Rouze (Munich).

There are several important conceptual and computational questions concerning path integrals in QM and QFT, which have recently been approached from new perspectives motivated by "resurgent asymptotics", a novel mathematical formalism that seeks to unify perturbative and non-perturbative physics. I will discuss the basic ideas behind the connections between resurgent asymptotics and physics, ranging from differential equations to phase transitions and QFT. I will also discuss the reconstruction problem: how to optimally reconstruct non-perturbative information from a finite amount of perturbative information.

I discuss a new approach to the Higgs naturalness problem, where the value of the Higgs mass is tied to cosmic stability and the possibility of a large observable Universe. The Higgs mixes with the dilaton of a CFT sector whose true ground state has a large negative vacuum energy. If the Higgs VEV is non-zero and below O(TeV), the CFT also admits a second metastable vacuum, where the expansion history of the Universe is conventional. As a result, only Hubble patches with unnaturally small values of the Higgs mass support inflation and post-inflationary expansion, while all other patches rapidly crunch. I will also comment on alternative realizations of the mechanism that do not require a CFT sector and have a simple perturbative description.

The outskirts of accreting dark matter haloes exhibit a sudden drop in density delimiting the virialized region. After briefly describing the physics shaping this feature and how it is measured, I will discuss its applications. I will examine its connection to structure formation and how it can constrain the screening mechanisms of beyond-GR models of gravity.

We discuss the dynamics of (Rényi) mutual information, logarithmic negativity, and (Rényi) reflected entropy after exciting the ground state by a local operator in (1+1)d conformal field theories. In particular, we contrast "integrable" and "chaotic" conformal field theories, by looking at the quasi-particle picture and its possible breakdown. In comparing the calculations in the two classes of theories, we are able to identify the dynamical mechanism for the breakdown of the quasi-particle picture in 2D conformal field theories. Intriguingly, we also find preliminary evidence that our general lessons apply to quantum systems considerably distinct from conformal field theories, such as integrable and chaotic spin chains, suggesting a  universality of entanglement dynamics in non-equilibrium systems.

Understanding gravity in the framework of quantum mechanics is one of the great challenges in modern physics. Along this line, a prime question is to find whether gravity is a quantum entity subject to the rules of quantum mechanics. It is fair to say that there are no feasible ideas yet to test the quantum coherent behaviour of gravity directly in a laboratory experiment. Here, I will introduce an idea for such a test based on the principle that two objects cannot be entangled without a quantum mediator. I will show that despite the weakness of gravity, the phase evolution induced by the gravitational interaction of two micron size test masses in adjacent matter-wave interferometers can detectably entangle them even when they are placed far apart enough to keep Casimir-Polder forces at bay. I will provide a prescription for witnessing this entanglement, which certifies gravity as a quantum coherent mediator, through simple correlation measurements between two spins: one embedded in each test mass. Fundamentally, the above entanglement is shown to certify the presence of non-zero off-diagonal terms in the coherent state basis of the gravitational field modes.

Every toric variety is a GIT quotient of an affine space by an algebraic torus. In this talk, I will discuss a way to understand and compute the symplectic mirrors of toric varieties from this universal perspective using the concept of window subcategories. The talk is based on results from a work of myself and a joint work in progress with Peng Zhou.

Unitary t-designs are the bread and butter of quantum information theory and beyond. An important issue in practice is that of efficiently constructing good approximations of such unitary t-designs. Building on results by Aubrun (Comm. Math. Phys. 2009), we prove that sampling dtpoly(t,logd,1/ϵ) unitaries from an exact t-design provides with positive probability an ϵ-approximate t-design, if the error is measured in one-to-one norm. As an application, we give a randomized construction of a quantum encryption scheme that has roughly the same key size and security as the quantum one-time pad, but possesses the additional property of being non-malleable against adversaries without quantum side information. Joint work with Cécilia Lancien.