Scientific Series

Recent advances in programmable quantum devices brought to the fore the intriguing possibility of using them to realize and investigate topological quantum spin liquids (QSLs) phase. This new and exciting direction brings about important research questions on how to probe and determine the presence of such exotic, highly entangled phases. In this talk, I will discuss how to construct Z2 QSLs states as the ground state of a static Hamiltonian with only local two-qubit interactions and a transverse field, and demonstrate its realization in the classical limit at the endpoint of quantum annealing protocol, using D-Wave DW-2000Q machine . I will also demonstrate how to probe signatures of Z2 QSLs fractional statistics in quantum simulators via quasiparticle interferometry. At the end, I will show the robustness of this probe against disorders and dephasing -- effects that are generally pervasive in quantum devices nowadays.

Zoom Link: https://pitp.zoom.us/j/99207971920?pwd=N3R3YUJtWXJWVjFQWlRoZ3hYSDlMZz09

Quantum algorithms have been found which are able to solve important problems exponentially faster than any known classical algorithm. The most well known example is Shor's algorithm which would be able to break all RSA encryption if fault tolerant quantum computers existed for it to be run on. It is currently not believed that quantum computers will be able to efficiently solve NP-Complete problems, but the answer is still unknown. I present a novel quantum algorithm which is able to solve 3-SAT along with numerical simulations to see how it performs on small instances, but new methods of analyzing the complexity of quantum algorithms will need to be developed before we can say exactly how it performs. This will be the goal of my PSI essay.

Zoom Link: https://pitp.zoom.us/j/95795655548?pwd=aU5jNFhFZHEzUWpLK1FvWjd2Q1c2Zz09

We describe a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be described in this framework in a natural way. In particular, the so-called Madelung transform between the Schrödinger-type equations on wave functions and Newton's equations on densities turns out to be a Kähler map between the corresponding phase spaces, equipped with the Fubini-Study and Fisher Rao information metrics. This is a joint work with G.Misiolek and K.Modin.

Zoom Link: https://pitp.zoom.us/j/92283820673?pwd=dXQzYWppaUdBVnhtVG1TZTFQQmx4UT09

We show that if a massive (or charged) body is put in a quantum superposition of spatially separated states in the vicinity of any (Killing) the mere presence of the horizon will eventually destroy the coherence of the superposition. This occurs because, in effect, the long-range fields sourced by the superposition registers on the horizon which forces the radiation of entangling soft gravitons/photons through the horizon. This allows the horizon to harvest “which path” information about the superposition. The electromagnetic decoherence arises only when the superposed particle carries electric charge. However, since all matter sources gravity, the quantum gravitational decoherence applies to all superpositions. We provide estimates of the decoherence time for such quantum superpositions. Additionally, we show that this decoherence is distinct from--and larger than--the decoherence resulting from the presence of thermal radiation from the horizon (i.e. Hawking/Bunch-Davies/Unruh radiation). We believe that the fact that Killing horizons will eventually decohere any quantum superposition may be of fundamental significance for our understanding of the nature of black holes and horizons in quantum gravity. (Based on arXiv:2205.06279 and arXiv: 2301.00026).

Zoom link:  https://pitp.zoom.us/j/95263116767?pwd=amZ6SkROV1lxckVpdzhNbFhYc1ZiQT09

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