Scientific Series

Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the real-time dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantum-mechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first digital quantum simulation of a lattice gauge theory, by realising 1+1-dimensional quantum electrodynamics (Schwinger model) on a few-qubit trapped-ion quantum computer. We are interested in the real-time evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electron-positron pairs. Our work represents a first step towards quantum simulating high-energy theories with atomic physics experiments, the long-term vision being the extension to real-time quantum simulations of non-Abelian lattice gauge theories. 

The theory of relativity associates a proper time with each moving object via its spacetime trajectory. In quantum theory on the other hand, such trajectories are forbidden. I will discuss an operation approach to exploring this conflict, considering the average time measured by a quantum clock in the weak-field, low-velocity limit. Considering the role of the clock’s state of motion, one finds that all ``good'' quantum clocks experience the time dilation prescribed by general relativity for the most classical states of motion. For nonclassical states of motion, on the other hand, one finds that quantum interference effects give rise to a discrepancy between the proper time and the time measured by the clock. I will also describe how ignorance of the clock's state of motion leads to a larger uncertainty in the time as measured by the clock, a consequence of entanglement between the clock time and its center-of-mass degrees of freedom.

The study of strongly  interacting quantum matter has been at the forefront of condensed matter research in the last several decades. An independent development is the discovery of topological band insulators.  In this talk I will  describe phenomena that occur at the confluence of topology and strong interactions. I will first discuss  how insights from the study of the relatively simple topological insulators are revolutionizing our theoretical understanding of more complex quantum many body systems.  Next I will describe some experimental situations in which both band topology and strong correlations are present, the resulting novel phenomena, and the theoretical challenges they present.

The near horizon region of any black hole looks like flat space and displays an approximate Poincare symmetry. We study the way these symmetries are realized for near extremal black holes.

We construct SL(2) generators that move matter fields relative to the boundaries. The construction is exact to all orders in the gravitational coupling. We also display an approximate realization of these generators in terms of simple operators defined at the boundary. These can also be realized in the boundary quantum mechanical theory. We also discuss the realization of these in the SYK model.

Let G be a split semi-simple algebraic group over Q. We introduce a natural cluster structure on moduli spaces of G-local systems over surfaces with marked points. As a consequence, the moduli spaces of G-local systems admit natural Poisson structures, and can be further quantized. We will study the principal series representations of such quantum spaces. It will recover many classical topics, such as the q-deformed Toda systems, quantum groups, as well as the modular functor conjecture for such representations, which should lead to new quantum invariants of threefolds. This talk will mainly be based on joint work with A.B. Goncharov.

We derive Schwarzian correlation functions using the BF formulation of Jackiw-Teitelboim gravity, where bilocal operators are interpreted as boundary-anchored Wilson lines in the bulk. Crossing Wilson lines are associated with OTO-correlators and give rise to 6j-symbols. We discuss the semi-classical bulk black hole physics contained within the correlation functions.

Extensions including bulk defects related to the other coadjoint orbits are discussed.

How violently do two quantum operators disagree? Different subfields of physics feature different notions of incompatibility: i) In quantum information theory, uncertainty relations are cast in terms of entropies. These entropic uncertainty relations constrain measurement outcomes. ii) Condensed matter and high-energy physics feature interacting quantum many-body systems, such as spin chains. A local perturbation, such as a Pauli operator on one side of a chain, preads through many-body entanglement. The perturbation comes to overlap, and to disagree, with probes localized on the opposite side of the system. This disagreement signals that quantum information about the perturbation has scrambled, or become hidden in highly nonlocal correlations. I will unite these two notions of quantum operator disagreement, presenting an entropic uncertainty relation for quantum-information scrambling. The entropies are of distributions over weak and strong measurements' possible outcomes. The uncertainty bound strengthens when a spin chain scrambles in numerical simulations. Hence the subfields - quantum information, condensed matter, and high-energy physics - can agree about when quantum operations disagree. Our relation can be tested experimentally with superconducting qubits, trapped ions, and quantum dots. 

NYH, Bartolotta, and Pollack, accepted by Comms. Phys. (in press) arXiv:1806.04147.

Computing vacuum expectation values is paramount in studying Quantum Field Theories (QFTs) since they provide relevant information for comparing the underlying theory with experimental results. However, unless the ground state of the system is explicitly known, such computations are very difficult and Monte Carlo simulations generally run months to years on state-of-the-art high performance computers. Additionally, there are various physically interesting situations, in which most numerical methods currently in use are not applicable at all (e.g., the early universe or setting requiring Lorentzian backgrounds). Thus, new algorithms are required to address such problems in QFT. In recent joint work with K. Jansen (NIC, DESY Zeuthen), I have shown that zeta-functions of Fourier integral operators can be applied to regularize vacuum expectation values with Euclidean and Lorentzian backgrounds and that these zeta-regularized vacuum expectation values are in fact physically meaningful. In order to prove physicality, we introduced a discretization scheme which is accessible on a quantum computer. Using this discretization scheme, we can efficiently approximate ground states on a quantum device and henceforth compute vacuum expectation values. Furthermore, the Fourier integral operator $\zeta$-function approach is applicable to Lattice formulations in Lorentzian background. 

Optimally encoding classical information in a quantum system is one of the oldest and most fundamental challenges of quantum information theory. Holevo’s bound places a hard upper limit on such encodings, while the Holevo-Schumacher-Westmoreland (HSW) theorem addresses the question of how many classical messages can be “packed” into a given quantum system. In this article, we use Sen’s recent quantum joint typicality results to prove a one-shot multiparty quantum packing lemma generalizing the HSW theorem. The lemma is designed to be easily applicable in many network communication scenarios. As an illustration, we use it to straightforwardly obtain quantum generalizations of well-known classical coding schemes for the relay channel: multihop, coherent multihop, decode-forward, and partial decode-forward. We provide both finite blocklength and asymptotic results, the latter matching existing formulas. Given the key role of the classical packing lemma in network information theory, our packing lemma should help open the field to direct quantum generalization.

Over the years, many rich ideas have been exchanged between particle theory and condensed matter theory, such as particle/hole theory, superconductivity and dynamical symmetry breaking, universality and critical phenomena. Here I discuss the interesting case of how the two fields converged independently along different paths on the physics of symmetry-protected topological order: condensed matter physicists motivated by the quantum Hall effect and superconductivity, the particle physicists driven by the desire to understand anomalies and chirality, and to compute QCD and supersymmetry on a lattice -- where the Quantum Hall effect, the Quantum Spin Hall effect and Majorana surface modes have all played a role in practical computations since the 1990s.  

We study the possibility of a deconfined quantum phase transition in a realistic model of a two dimensional Shastry-Sutherland quantum magnet, using both numerical and field theoretic techniques. We argue that the quantum phase transition between a two fold degenerate plaquette valence bond  solid (pVBS) order and N\'eel ordered phase may be described by a deconfined quantum critical point (DQCP) with emergent O(4) symmetry. Further, using the infinite density matrix renormalization group (iDMRG) numerical technique, we verify the emergence of an intermediate pVBS order, between the dimer and Neel ordered phases. By analyzing the correlation length spectrum, we provide evidence for deconfinement and emergent O(4) symmetry at the phases transistion between the pVBS and N\'eel orders. Such a phase transition has been reported in the recent pressure tuned experiments in the Shastry-Sutherland lattice material  SrCu2(BO3)2. The non-symmorphic lattice structure of the Shastry-Sutherland compound leads to extinction points in the scattering, where we predict sharp signatures of a DQCP in both the phonon and magnon spectra associated with the spinon continuua. Our results can guide future experimental studies of DQCP in quantum magnets.

A common criticism directed against many-world theories is that, being deterministic, they cannot make sense of probability. I argue that, on the contrary, deterministic theories with branching provide us the only known coherent definition of objective probability. I illustrate this argument with a toy many-worlds theory known as Kent's universe, and discuss its limitations when applied to the usual Many-Worlds interpretation of quantum mechanics.

I'll also argue that subjective probabilities are unproblematic in the many-worlds setting by showing how the usual decision-theoretical axioms apply there, and finish by showing that together with a proper definition of measurement they suffice to derive the Born rule.