Scientific Series

I will talk about the generalization of Berry classes for quantum lattice spin systems. It defines invariants of topologically ordered states or families thereof. In particular, its equivariant version for 2d gapped states gives the zero-temperature Hall conductance and its various generalizations. I will also discuss the construction of chiral states realizing the topological order associated with a unitary rational vertex operator algebra for which these invariants are non-trivial

Zoom link:  https://pitp.zoom.us/j/99910103969?pwd=VlVHVGRiV29iVEFyTXZyR3ovMkRaQT09

The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum mechanical wavefunction of the universe. In this talk I will discuss how we can adapt flat space bootstrapping techniques to the quantum fluctuations in the early universe, in particular showing that the requirement of unitary time evolution, colloquially the conservation of probabilities, fixes the analytic structure of the wavefunction and of all the cosmological correlators it encodes.

Zoom link:  https://pitp.zoom.us/j/95812107239?pwd=bVZMcWdHTVM0Y0tFZGMxS2FCVGF0Zz09

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, has a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). We examine the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace-preserving while the commonly-used MoorePenrose pseudoinverse may not be. Finally, we study the consequences of having imperfect knowledge about system noise and derive conditions when noise can be reduced using QEM.

Zoom link:  https://pitp.zoom.us/j/91543402893?pwd=b09IS3VWNk5KZi8ya3gzSmRKRFJidz09

A well-established approach to solving interacting quantum systems is variational Monte Carlo. There is a lot of renewed interest in it since the introduction of neural networks as a highly expressive and unbiased variational ansatz. Similar to more traditional ansätze, neural networks struggle with solving frustrated quantum systems. A conjecture has been made that the cause of these difficulties lies in the sign structures of the ground state wavefunctions. Here, we will discuss these sign structures in more detail and try to analyze how complex they really are by establishing a connection to classical Ising models.

Zoom link:  https://pitp.zoom.us/j/99087954160?pwd=Vm5zWWRFbHBwVFR1RHZMc3ptem03QT09

Recent advances in mechanical sensing technologies have led to the suggestion that heavy dark matter candidates around the Planck mass range could be detected through their gravitational interaction alone. The Windchime collaboration is developing the necessary techniques, systems, and experimental apparatus using arrays of optomechanical sensors that operate in the regime of high-bandwidth force detection, i.e., impulse metrology.  Today's sensors can be limited by the added noise due to the act of measurement itself. Techniques to go beyond this limit include squeezing of the light used for measurement and backaction evading measurement by estimating quantum non-demolition operators — typically the momentum of a mechanical resonator well above its resonance frequency. In this talk, we will discuss the theoretical limits to noise reduction using such quantum enhanced readout techniques for these optomechanical sensors.

 In holography, spacetime is emergent and its properties depend on the entanglement structure of the dual theory. An interesting question is how changes in the entanglement structure affect the bulk dual description. In this talk, I will describe how local projective measurements performed on a subregion  of the boundary theory modify the bulk dual spacetime. The post-measurement bulk is cut off by end-of-the-world branes and is dual to the complementary unmeasured region . Using a bulk calculation in —which involves a phase transition triggered by the measurement—and tensor network models of holography, I will show that the portion of bulk preserved after the measurement depends on the size of  and the state we project on. Interestingly, the post-measurement bulk includes regions that were part of the entanglement wedge of  before the measurement. Our results indicate that the effect of a measurement performed on a subregion  of the boundary is to teleport part of the bulk information contained in  into the complementary region . Finally, I will comment on applications to the eternal black hole in JT gravity (dual to the SYK thermofield double state) and the relationship between measurements and traversable wormholes.

Cosmological models and black holes belong to classes of space-time metrics defined in terms of a finite number of degrees of freedom, for which the Einstein–Hilbert action reduces to a one-dimensional mechanical model. We investigate their classical symmetries and the algebra of the corresponding Noether charges. These dynamical symmetries have a geometric interpretation, not in terms of spacetime geometry, but in terms of motion on the field space. Moreover, they interplay with the fiducial scales, introduced to regulate the homogenous model, suggesting a relationship with the boundary symmetries of the full theory.

Finally, the existence of these symmetries unravels new aspects of the physics of black holes and cosmology. It opens the way towards a rigorous group quantization of the reduced model and to the study of their holographic properties. It might have significant consequences on the propagation of test fields and the corresponding perturbation theory.

Zoom link:  https://pitp.zoom.us/j/92846533238?pwd=cERGUjd6OXB5S0ZaSzVIdVJyMHZxUT09

I will present a general bulk reconstruction technique in AdS/CFT suitable for addressing a facet of the black hole information problem: How to unambiguously predict the results of measurements performed by an infalling observer in the black hole interior.
 
I will explicitly apply the method in the AdS_2/SYK correspondence. My proposal provides an internal notion of time for quantum gravitational systems that may be useful for cosmology.

We present a reduced-order surrogate model of gravitational waveforms from non-spinning binary black hole systems with comparable to large mass-ratio configurations. This surrogate model, BHPTNRSur1dq1e4, is trained on waveform data generated by point-particle black hole perturbation theory (ppBHPT) with mass ratios varying from 2.5 to 10,000. BHPTNRSur1dq1e4 can generate waveforms up to 30,500 m1(where m1 is the mass of the primary black hole), includes several more spherical harmonic modes up to \ell=10, and calibrates both dominant and subdominant modes to numerical relativity (NR) data. In the comparable mass-ratio regime, including mass ratios as low as 2.5, the gravitational waveforms generated through ppBHPT agree surprisingly well with those from NR after this simple calibration step. We argue that this scaling essentially captures higher order self-force corrections in a much simpler way. We also compare our model to recent SXS and RIT NR simulations at mass ratios ranging from 15 to 32, and find the dominant quadrupolar modes agree to better than≈10−3. We expect our model to be useful to study intermediate-mass-ratio binary systems in current and future gravitational-wave detectors. Finally, we discuss avenues for improving the model by extending its region of validity.

Zoom link:  https://pitp.zoom.us/j/99971588372?pwd=ZVUveUlNeTI1SE5iMzNnVDh0L2xkQT09

Monitored many-body systems fall broadly into two dynamical phases, ``entangling'' or ``disentangling'', separated by a transition as a function of the rate at which measurements are made on the system. Producing an analytical theory of this measurement-induced transition is an outstanding challenge. Recent work made progress in the context of tree tensor networks, which can be related to all-to-all quantum circuit dynamics with forced (postselected) measurement outcomes. So far, however, there are no exact solutions for dynamics of spin-1/2 degrees of freedom (qubits) with ``real'' measurements, whose outcome probabilities are sampled according to the Born rule. Here we define dynamical processes for qubits, with real measurements, that have a tree-like spacetime interaction graph, either collapsing or expanding the system as a function of time. The former case yields an exactly solvable measurement transition. We explore these processes analytically and numerically, exploiting the recursive structure of the tree. We compare the case of ``real'' measurements with the case of ``forced'' measurements. Both cases show a transition at a nontrivial value of the measurement strength, with the real measurement case exhibiting a smaller entangling phase. Both exhibit exponential scaling of the entanglement near the transition, but they differ in the value of a critical exponent. An intriguing difference between the two cases is that the real measurement case lies at the boundary between two distinct types of critical scaling. On the basis of our results we propose a protocol for realizing a measurement phase transition experimentally via an expansion process.

The XXZ model on the three-dimensional frustrated pyrochlore lattice describes a family of rare-earth materials showing signatures of fractionalization and no sign of ordering in the neutron-scattering experiments. The phase diagram of such XXZ model is believed to host several spin-liquid states with fascinating properties, such as emergent U(1) electrodynamics with emergent photon and possible confinement-deconfinement transition. Unfortunately, numerical studies of such lattice are hindered by three-dimensional geometry and absence of obvious small parameters.
In this talk, I will present my work [Phys. Rev. X 11, 041021] on the variational study of the pyrochlore XXZ model using the RVB-inspired and Neural-Network-inspired ansätze. They yield energies better than known results of DMRG at finite bond dimension. With these wave functions, we study the properties of frustrated phase at the Heisenberg point, and observe signatures of long-range dimer correlations.

Lastly, I will sketch the prospects of using the Programmable Rydberg Simulator platform for the study of these spin-liquid states. I will construct two possible embeddings of the pyrochlore XXZ model onto the Rydberg atoms simulator, employing the notion of spin ice and perturbative hexagon flip processes.

Zoom link:  https://pitp.zoom.us/j/99480889764?pwd=cnY2RHBjeDZvRkM2K3FlYU9OWjgxUT09

We consider two interacting systems when one is treated classically while the other remains quantum. Despite several famous no-go arguments, consistent dynamics of this coupling exist, and its most general form can be derived. We discuss the application of these dynamics to the foundations of quantum theory, and to the problem of understanding gravity when space-time is treated classically while matter has a quantum nature.

The talk will be informal and I'll review and follow on from joint work with Isaac Layton, Andrea Russo, Carlo Sparaciari, Barbara Šoda & Zachary Weller-Davies

https://arxiv.org/abs/2208.11722
https://arxiv.org/abs/2203.01982
https://arxiv.org/abs/1811.03116

Zoom link:  https://pitp.zoom.us/j/92520708199?pwd=WUowdnd4Z0k3dlU2YjVmVlAva3Q0UT09