Scientific Series

A brief introduction to entanglement of multipartite pure quantum states will be given. As the Bell states are known to be maximally entangled among all two-qubit quantum states, a natural question arises: What is the most entangled state for the quantum system consisting of N sub-systems with d levels each? The answer depends on the entanglement measure selected, but already for four-qubit system, there is no state which displays maximal entanglement with respect to all three possible splittings of the systems into two pairs of qubits.

To construct strongly entangled multipartite quantum states one can use various mathematical techniques involving combinatorial designs, topological methods related to knot theory or the Majorana (stellar) representation of permutation symmetric quantum states.
 

We will discuss the recent advances involving programmable, coherent manipulation of quantum many-body systems using atom arrays excited into Rydberg states. Specifically, we will describe our recent technical upgrades that now allow the control over 200 atoms in two-dimensional arrays. Recent results involving the realization  of exotic phases of matter, study of quantum phase transitions and  exploration of  their non-equilibrium dynamics will be presented. In particular, we will report on realization and probing of quantum spin liquid states - the exotic states of matter have thus far evaded direct experimental detection. Finally,  realization and testing  of quantum optimization algorithms using such systems will be discussed.

The quantum gravity path integral involves a sum over topologies. Superficially, this feature is similar to Feynman diagrams of quantum field theory and the genus expansion of worldsheet string theory. There are however some key differences. While the standard construction leads to the non-abelian algebra of quantum fields, the quantum gravity path integral has been argued to define an abelian algebra associated with partition function type observables. We will discuss these issues and argue that one needs to make certain discrete choices to construct a Hilbert space from path integrals that sum over topologies. In particular, the natural choices for quantum gravity differ from those used to construct QFTs as we shall illustrate in the context of one-dimensional models.

Far-infrared spectroscopy can reveal secrets of galaxy evolution and heavy-element enrichment throughout cosmic time, and astronomers worldwide are designing cryogenic space telescopes for far-IR spectroscopy. The most challenging aspect is a far-IR detector which is both exquisitely sensitive (limited by the zodiacal-light noise in a narrow band (lambda/delta lambda ~1000)) and array able to tens of thousands of pixels. The quantum capacitance detector (QCD) being developed at MDL, is a 50mK device adapted from quantum computing applications in which photon-produced free electrons in a superconductor tunnel into a small capacitive island embedded in a resonant circuit. The QCD has optically-measured noise equivalent power (NEP) of 2x10-20 W Hz-1/2 at 1.5THz under 10-19W of optical loading, making it the most sensitive far-IR detector ever demonstrated. The QCD has further demonstrated individual far-IR photon counting, confirming the exquisite sensitivity and suitability for cryogenic space astrophysics. In this lecture, the development of the Quantum Capacitance detector will be highlighted, from inception through proof of concept devices, culminating with the demonstration of single photon detection. Current development efforts will be discussed.

The growing gravitational wave dataset makes black hole population studies possible. In this talk I will demonstrate how such studies can be used to study particle and nuclear physics. The key insight is that a wide range of initial stellar masses leave no compact remnant, due to the physics of pair-instability; the unpopulated space in the stellar graveyard is known as the black hole mass gap (BHMG). New physics can dramatically alter the late stages of stellar evolution and shift the BHMG, when it acts as an additional source of energy (loss) or modifies the equation of state. I will demonstrate how these predictions can be tested with the gravitational wave observations by the LIGO/Virgo collaboration, and show what we can already infer from GWTC-2. 

We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter.  These different "symmetry-protected topological" phases are characterized by protected (gapless) surface states.  After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries.  I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.

The Hartle-Hawking-Vilenkin state is defined on mini-superspace and is semiclassically related to inflationary theory.  However, the state suffers a few problems connected to the path integral of Euclidean or the Lorentzian measure of metrics.  In this talk, we will explore a way around these issues by working in the (Ashtekar) connection representation, a real Kodama-Chern-Simons state.  We find a generalized "Fourier Transform" that related the Chern-Simons-Kodama state to the Hartle-Hawking state beyond mini-superspace.  We end with some discussion and open ended questions for cosmology and quantum gravity.

LIGO's successful detection of gravitational waves has revitalized the theoretical understanding of the angular momentum carried away by gravitational radiation. An infinite-dimensional supertranslation ambiguity has presented an essential difficulty for decades of study. Recent advances were made to quantify the supertranslation ambiguity in the context of binary coalescence. In this talk, we will present the first definition of angular momentum in general relativity that is completely free from supertranslation ambiguity. The new definition of angular momentum is derived from the limit of the quasilocal angular momentum we defined previously.

We present two classical algorithms for the simulation of universal quantum circuits on n qubits constructed from c instances of Clifford gates and t arbitrary-angle Z-rotation gates such as T gates. Our algorithms complement each other by performing best in different parameter regimes. The Estimate algorithm produces an additive precision estimate of the Born rule probability of a chosen measurement outcome with the only source of run-time inefficiency being a linear dependence on the stabilizer extent (which scales like ≈1.17^t for T gates). Our algorithm is state-of-the-art for this task:

as an example, in approximately 25 hours (on a standard desktop computer), we estimated the Born rule probability to within an additive error of 0.03, for a 50 qubit, 60 non-Clifford gate quantum circuit with more than 2000 Clifford gates. The Compute algorithm calculates the probability of a chosen measurement outcome to machine precision with run-time O(2^t−r(t−r)t) where r is an efficiently computable, circuit-specific quantity. With high probability, r is very close to min{t,n−w} for random circuits with many Clifford gates, where w is the number of measured qubits. Compute can be effective in surprisingly challenging parameter regimes, e.g., we can randomly sample Clifford+T circuits with n=55, w=5, c=105 and t=80 T-gates, and then compute the Born rule probability with a run-time consistently less than 104 seconds using a single core of a standard desktop computer. We provide a C+Python implementation of our algorithms.

Statistical mechanics is the branch of physics that explains how macroscopic properties of matter emerge from the behavior of its microscopic constituents. Population ecology studies how and why populations change over time and space, primarily due to the interaction among individuals and between individuals and the environment where they thrive. Although seemingly very different, both disciplines aim to explain large-scale phenomena based on a description of their underlying drivers, and statistical mechanics tools have been largely used to formalize population ecology. For over 100 years, however, mathematical models in population ecology have relied on very strong and unrealistic assumptions about the way individuals move and get to interact with each other and with the environment. Specifically, they assume that individuals behave like the molecules of an ideal gas: following completely random trajectories through the entire area occupied by the population and only interacting with each other when their trajectories intersect. 

In this presentation, I will first discuss why mathematical models are powerful tools to understand ecological processes. Then, I will show how traditional models of population dynamics emerge from ideal gas assumptions for individual movement and briefly touch on our recent efforts to refine those models combining more elaborated tools from statistical physics, random walk theory, and GPS tracking data of natural populations.

In this talk I will discuss the application of the so-called “consistency relations” for large scale structures to the study of primordial non-Gaussianities of the local f_NL type. I will first introduce the consistency relations themselves, commenting on some important aspects and underlying assumptions. I will then verify them (and their violation) using N-body simulations for the matter density in the Universe. This proves consistency relations to be a promising tool to apply in the forthcoming large scale structures surveys. I will conclude describing some work in progress aimed at finding a practical recipe to constrain f_NL from these relations.

We propose a new type of critical quantum liquids, dubbed Stiefel liquids, based on 2+1 dimensional Wess-Zumino-Witten models on target space SO(N)/SO(4). We show that the well known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N = 5 and N = 6, respectively. Furthermore, we conjecture that Stiefel liquids with N > 6 are non-Lagrangian, in the sense that the theories do not (at least not easily) admit any weakly-coupled UV completion. Such non-Lagrangian states are beyond the paradigm of parton gauge theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of mean-field construction also makes it difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders.