Scientific Series

Tidal interactions in coalescing binary neutron stars modify the dynamics of the inspiral, and hence imprint a signature on their gravitational-wave (GW) signals in the form of an extra phase shift. We need accurate models for the tidal phase shift in order to constrain the supranuclear equation of state from observations. In previous studies, GW waveform models were typically constructed by treating the tide as a linear response to a perturbing tidal field. In this work, we incorporate non-linear corrections due to hydrodynamic three- and four-mode interactions and show how they can improve the accuracy and explanatory power of waveform models. We set up and numerically solve the coupled differential equations for the orbit and the modes, and analytically derive solutions of the system's equilibrium configuration. Our analytical solutions agree well with the numerical ones up to the merger and involve only algebraic relations, allowing for fast phase shift and waveform evaluations for different equations of state over a large parameter space. We find that, at Newtonian order, nonlinear fluid effects can enhance the tidal phase shift by  >~ 1 radian at a GW frequency of 1000 Hz, corresponding to a  10−20%  correction to the linear theory. The scale of the additional phase shift near the merger is consistent with the difference between numerical relativity and theoretical predictions that account only for the linear tide. Nonlinear fluid effects are thus important when interpreting the results of numerical relativity, and in the construction of waveform models for current and future GW detectors.

Zoom link:  https://pitp.zoom.us/j/91730134841?pwd=U0JXNHhFbWdQYno3aUpDWHRxWEtkUT09

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process over n qubits. For a wide range of distributions D on arbitrary n-qubit states, we show that this ML algorithm can learn to predict any local property of the output from the unknown process, with a small average error over input states drawn from D. The ML algorithm is computationally efficient even when the unknown process is a quantum circuit with exponentially many gates. Our algorithm combines efficient procedures for learning properties of an unknown state and for learning a low-degree approximation to an unknown observable. The analysis hinges on proving new norm inequalities, including a quantum analogue of the classical Bohnenblust-Hille inequality, which we derive by giving an improved algorithm for optimizing local Hamiltonians. Overall, our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.

Zoom link:  https://pitp.zoom.us/j/93857777354?pwd=c044blZuQVhLS200ME4vN25uaGJudz09

Conformal Regge theory predicts the existence of analytically continued CFT data for complex spin. How could this work when there are so many more local operators with large spin compared to small spin? Using planar N=4 SYM as a testground we find a simple physical picture. Local operators do organize themselves into analytic families but the continuation of the higher families have zeroes in their structure OPE constants for lower integer spins. They thus decouple. Newton's interpolation series technique is perfectly suited to this physical problem and will allow us to explore the right complex spin half-plane.

Gravitational waves with frequencies below 1 nHz are notoriously difficult to detect. With periods exceeding current experimental lifetimes, they induce slow drifts in observables rather than periodic correlations. Observables with well-known intrinsic contributions provide a means to probe this regime. In this talk, I will demonstrate the viability of using observed pulsar timing parameters to discover such ultralow frequency gravitational waves, presenting two complementary observables for which the systematic shift induced by ultralow-frequency gravitational waves can be extracted. I will then show the results of searches for both continuous and stochastic signals from supermassive black hole binaries using existing data for these observables, and demonstrate that this technique has the power to probe astrophysically-interesting strains.

Zoom Link:  https://pitp.zoom.us/j/95734210379?pwd=Wnp1cHR2QW93bksxaGlCWEZVSjRsUT09

No-go theorems (Bell, Kochen-Specker, …) formally show the departure of quantum theory from classical theory. These are formulated in the framework of ontological models and, if one accepts such framework, entail that quantum theory involves problematic (“fine-tuned”) properties. I will argue that the lesson to take from the no-go theorems is to abandon the framework of ontological models as the way to model reality. I will analyze what I believe to be the unnatural assumptions of such framework and I will propose a way to change it. The basic principle of the new notion of reality I propose is that for something to exist is for something to be recorded. I will motivate the principle and explore its consequences. In order to implement such proposal into a precise theory-independent mathematical framework I will make use of point-free topological spaces (locales). I will discuss why this new proposal should be promising for understanding quantum theory and I will present several open questions.

Zoom link:  https://pitp.zoom.us/j/91292006884?pwd=V2EzaEw5Z3NRUGd4cVdSRnlOOWFVZz09

We present an approach for representing fermionic quantum many-body states using tensor networks, by introducing a change of basis with local unitary gates obtained via compressing fermionic Gaussian states into quantum circuits. These fermionic Gaussian circuits enable efficient disentangling of low-energy states and entanglement renormalization in matrix product states/operators, significantly reducing bond dimension and improving computational efficiency. As a demonstration, we apply this approach to the 1D single impurity Anderson model through suppression of entanglement in both ground states and time-evolved low-lying excited states. We also explore the use of hierarchical compression to generate Gaussian multi-scale entanglement renormalization ansatz (GMERA) circuits and study their emergent coarse-grained physical models in terms of entanglement properties and suitability for time evolution.

Zoom link:  https://pitp.zoom.us/j/99677586832?pwd=ZGdIVGpac3pWcnhJYjlkNU16Wmlndz09

Abstract: TBD

Zoom Link: https://pitp.zoom.us/j/91979071868?pwd=Z0VWSFhJTEJFWkZRbzBtcWdtV0Ezdz09

Tom Leinster recently introduced a curious notion of entropy modulo p (https://arxiv.org/abs/1903.06961). While entropy has a certain meaning in information theory and physics, mathematically it is simply a function with certain properties. Stating these as axioms, the function is unique. Surprisingly, Leinster shows that a function obeying the same axioms can also be found for "probability distributions" over a finite field, and this function is unique too.

In quantum information, mutually unbiased bases is an important set of measurements and an example of a quantum design. While in odd prime power dimensions their construction is based on a finite field, in dimension 2^n it relies on an unpleasant Galois ring. I will replace this ring by length-2 Witt vectors whose arithmetic involves only finite field operations and Leinster's entropy mod 2. This expresses qubit mutually unbiased bases entirely in terms of a finite field and allows deriving an explicit unitary correspondence between them and the affine plane over this field.

Zoom link:  https://pitp.zoom.us/j/94032116379?pwd=TTI1RnByQnFuVHp1MytFUlJxckM4Zz09

Most people are familiar with periodic tessellations and lattices; from the floor in the PI Bistro to their favourite spin systems. In this talk, I will discuss two less familiar families of tessellations and their applications to high energy physics, condensed matter physics, and mathematics: hyperbolic tessellations and quasicrystals. After introducing the basics of regular hyperbolic lattices, I will survey constructions and surprising properties of quasicrystals (like the Penrose tiling), including their classically forbidden symmetries, long-range order, and self-similar structure. Inspired by the AdS/CFT correspondence, I will describe a mathematical relationship between hyperbolic lattices in (D+1)-dimensions and quasicrystals in D-dimensions, as well as the resolution of a conjecture by Bill Thurston. Based on work to appear with Latham Boyle.

Zoom Link: https://pitp.zoom.us/j/91876287518?pwd=NGNLOXZHa1h1cmdnMzJxQzVMVFJJdz09

Canonical transformations play fundamental roles in simplifying and solving physical systems. However, their design and implementation can be challenging in the many-particle setting. Viewing canonical transformations from the angle of learnable diffeomorphism reveals a fruitful connection to normalizing flows in machine learning. The key issue is then how to impose physical constraints such as symplecticity, unitarity, and permutation equivariance in the flow transformations. In this talk, I will present the design and application of neural canonical transformations for several physical problems. Symplectic flow identifies independent and nonlinear modes of classical Hamiltonians and natural datasets. Fermi flow variationally solves ab initio many-electron problems at finite temperatures.
Refs:
[1] Shuo-Hui Li, Chen-Xiao Dong, Linfeng Zhang, and Lei Wang, Phys. Rev. X 10, 021020 (2020)
[2]  Hao Xie, Linfeng Zhang, and Lei Wang, J. Mach. Learn. , 1, 38 (2022)

Zoom link:  https://pitp.zoom.us/j/98830940500?pwd=WjdydGY5aS9QQzk5SnI0TE1xMkwrdz09

Kronecker coefficients appear in representation of the symmetric group in the decomposition of tensor products of irreducible representations. They are notoriously difficult to compute and it is a long standing problem to find a combinatorial expression for them. 

We study the problem of computing Kronecker coefficients from quantum computational perspective. First, we show that the coefficients can be expressed as a dimension of a subspace given by intersection of two commuting, efficiently implementable projectors and relate their computation to the recently introduced quantum approximate counting class (QAPC). Using similar construction, we show that deciding positivity of Kronecker coefficients is contained in QMA. We give similar results for a related problem of approximating row sums in a character table of the symmetric group and show that its decision variant is in QMA. We then discuss two quantum algorithms - one that samples a distribution over squared characters and another one that approximates normalized Kronecker coefficients to inverse-polynomial additive error. We show that under a conjecture about average-case hardness of computing Kronecker coefficients, the resulting distribution is hard to sample from classically. 

Our work explores new structures for quantum algorithms and improved characterization of the quantum approximate counting.

Joint work with David Gossett, Sergey Bravyi, Anirban Chowdhury and Guanyu Zhu 

Zoom link:  https://pitp.zoom.us/j/95976938016?pwd=eDV3TXZReHo5UHdvZ0hIbkhXOFcxQT09

The question of whether the holomorphic collinear singularities of graviton amplitudes define a consistent chiral algebra has garnered much recent attention. I will discuss a version of this question for infinitesimal perturbations around the self-dual sector of 4d Einstein gravity. The singularities of tree amplitudes in such perturbations do form a consistent chiral algebra. However, at loop level new poles are generated, the simplest of which are described the 1-loop effective graviton vertex. These quantum corrections violate associativity of the operator product. I will argue that this failure can be traced to an anomaly in the twistor uplift of self-dual gravity. Associativity can be restored by coupling to an unusual 4th-order gravitational axion, which cancels the anomaly by a Green-Schwarz mechanism. Alternatively, the anomaly vanishes in certain theories of self-dual gravity coupled to matter, including in self-dual supergravity.

Zoom link:  https://pitp.zoom.us/j/91979544537?pwd=Ykw4Q3lRK2ZicVhCMDhlNUxFaHhlUT09