Scientific Series

 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.

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

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

Quantum theory has a temporal composition, which is expressed under many different operational frameworks. Here, points in time are imbued with a Hilbert space structure, and quantum states are passed between times through a series of experimental interventions. A multi-time quantum process, therefore, carries the same complex properties as a many-body quantum state. This invites the question: to what extent can temporal correlations be as interesting as spatial ones, and how can we access them? One particular avenue through which this structure manifests is in open quantum systems. System-environment dynamics can precipitate non-Markovian processes by which correlations persist between different times. Recently, the advent of high-fidelity quantum devices has made it possible to probe coherent quantum systems. In this talk, I will discuss my recent work in which we show how this serves as a novel test bed to capture many-time physics. We build frameworks to extract generic spatiotemporal properties of quantum stochastic processes, show how process complexity may be manipulated, and elevate user-control into the theory to make it self-consistent. Remarkably, many of these complex features are already present in naturally occurring noise, and hence the results have direct application to the development of fault-tolerant quantum devices. I will also briefly discuss some of my future research goals: the existence of exotic temporal phenomena and how emergent spatiotemporal features can be captured through renormalisation group approaches; the learnability of spacetime quantum correlations and avenues here to quantum advantage; and the taming of correlated noise in quantum devices through bespoke error suppression and error correction. 

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. In this talk, I will discuss my recent results (arXiv:2209.14353) studying the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality and show that the quantum model outperforms state-of-the-art classical models even in practice. I will also briefly discuss connections to my previous work studying the trainability of variational quantum algorithms (arXiv:2109.06957, arXiv:2205.05786).

Constraint satisfaction problems are known to always be "easy" or "hard", in the sense of being either solvable in P or being NP-complete, with no intermediate difficulty levels. The quantum analog of constraint problems, frustration-free Hamiltonians, are known to exhibit at least two more levels of complexity: QMA (for arbitrary local Hamiltonians) and MA (for stoquastic Hamiltonians). Wondering if other complexity classes can occur, we answer in the affirmative: there are interactions which can be freely arranged on qubits in any arrangement, such that the resulting frustration problem is BQP-complete, and captures exactly the difficulty of quantum computation. Simple modifications of this construction show that quantum constraint problems can be complete for QCMA and BPP as well. Based on https://arxiv.org/abs/2101.08381

A fundamental aspect of a random walk is determining when it reaches a specified threshold position for the first time.  This first-passage time, and more generally, the distribution of first passage times underlies many non-equilibrium phenomena, such as the triggering of integrate and fire neurons, the statistics of cell division, and the execution of stock options.  The computation of the first-passage time and its distribution is both simple and beautiful, with profound connections to electrostatic potential theory.  I will present some aspects of these fundamentals and then discuss applications of first-passage ideas to diverse phenomena, including stochastic search processes and a toy model of wealth sharing.

Zoom link:  https://pitp.zoom.us/j/98293478936?pwd=NTR3dWZoNElWRmd2NVJ1bzk5aC9ZQT09

The multipartite entanglement structure for the ground states of two dimensional topological phases is an interesting albeit not well understood question. Utilizing the bulk-boundary correspondence, the tripartite entanglement calculation of 2d topological phases can be reduced to that on the vertex state, defined by the boundary conditions at the interfaces between spatial regions. In this work, we use the conformal interface technique to calculate the entanglement measures of the vertex state, which include the area-law, geometrical and topological pieces, and the possible extra order one contribution. This explains our previous observation of Markov gap h=\frac{c}{3}\ln 2 in the 3-vertex state, and generalizes it to the p-vertex state as well as rational conformal field theory, and more general choices of subsystem. Finally, we support our prediction by numerical evidence. 

Zoom link:  https://pitp.zoom.us/j/93914854044?pwd=eWl3eGVLU25XUGhKbnFRSm5ab0JuUT09