Scientific Series

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

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

Optical astronomical imaging looks for better imaging quality in extreme cases of weak and subdiffraction limits. I focus on the quantum enhancement of astronomical interferometric imaging, including its fundamental limit and practical issues. For the fundamental aspects, I ignore any resource limit and noise and consider the ideal imaging problems. I show that the resolution limit can be enhanced with more carefully chosen measurement strategies and the general imaging quality can be enhanced by postprocessing the stellar photons with a quantum computer. For the practical aspects, I try to overcome the transmission loss suffered by interferometric imaging using quantum network, consider the possibility to implement a local scheme with better performance, and discuss the feasibility of decomposing thermal states into temporally localized pulses.

Scrambling of quantum information is an important feature at the root of randomization and benchmarking protocols, the onset of quantum chaos, and black-hole physics.

Unscrambling this information is possible given perfect knowledge of the scrambler [ArXiv: 1710.03363].

We show that one can retrieve the scrambled information without any previous knowledge of the scrambler, by a learning algorithm that allows the building of an efficient decoder. Surprisingly, complex quantum scramblers admit Clifford decoders: the salient properties of a scrambling unitary can be efficiently described even if exponentially complex, as long as it is not fully chaotic. This is possible because all the redundant complexity can be described as an entropy, and for non-chaotic black holes can be efficiently pushed away, just like in a refrigerator. This entropy is not due to thermal fluctuations but to the non-stabilizer behavior of the scrambler.

In the holographic approach to quantum gravity, quantum information theory plays a fundamental role in understanding how semiclassical gravity emerges from the microscopic description.  The map (sometimes called the dictionary) between these two descriptions has the structure of a quantum error correcting code.  In the context of an evaporating black hole, this code can be arbitrarily far from an isometry.  Such codes are novel from a quantum information standpoint, and their properties are not yet well understood.  I will describe a simple toy model of an evaporating black hole which allows for an explicit construction of the dictionary using the Euclidean gravity path integral.  I will also describe the sense in which this dictionary is a non-isometric code, explain its basic properties, and comment on implications for semiclassical physics in the black hole interior.

Zoom link:  https://pitp.zoom.us/j/94869738394?pwd=dGNBWXpmTTZaRSs3c0NQUDA1UkZCZz09

We revamp the constructive enumeration of 1/16-BPS states in the maximally supersymmetric Yang-Mills in four dimensions, and search for ones that are not of multi-graviton form. A handful of such states are found for gauge group SU(2) at relatively high energies, resolving a decade-old enigma. Along the way, we clarify various subtleties in the literature, and prove a non-renormalization theorem about the exactness of the cohomological enumeration in perturbation theory. We point out a giant-graviton-like feature in our results, and envision that a deep analysis of our data will elucidate the fundamental properties of black hole microstates.

Zoom link:  https://pitp.zoom.us/j/96037678536?pwd=eGdhTWF3UVN1em5uZVpJbWYyM2tzUT09