Seminars

In this talk, I will discuss one of the key properties which are responsible for the unreasonable success of classical convolutional neural networks – equivariance. It states that if the input to the neural network is shifted, then its activations translate accordingly. Developing the corresponding notion for discrete representational spaces used to describe finite-dimensional quantum systems is challenging. We generalize this notion by introducing a new framework for Sn-equivariant quantum convolutional circuits, building on and significantly generalizing Permutational Quantum Computing (PQC) formalism.

We demonstrate how to effectively apply the celebrated Okounkov-Vershik’s representation theory in machine learning and quantum physics : (1) we show how to gain a super-exponential speedup in computing the matrix elements of Sn-Fourier coefficients compared to the best known classical Fast Fourier Transform (FFT) over the symmetric group. (2) we prove that Sn Convolutional Quantum Ansätze are dense, thus expressible within each Sn-irrep block, which may serve as a universal model for potential future quantum machine learning and optimization applications. (3) we get a new proof (which is of distinctly representation-theoretic flavour) of the universality of the Quantum Approximate Optimization Algorithm. (4) our framework can be naturally applied to a wide array of problems with global SU(d) (for any integer d) symmetry. (5) We show that our ansätze are highly effective numerically by providing numerical solutions to the problem of the sign structure of the ground state of the J1-J2 antiferromagnetic Heisenberg model on the rectangular and Kagome lattices.

Observations at astronomical scales provide a strong evidence for existence of dark matter. The nature of dark matter composition, however, is still not known. Lack of detections of dark matter particles triggered multiple alternative theories. In this seminar, I will focus on dark matter candidates in form of scalar fields that couple to the Standard Model fields and yield variations of fundamental constants. In particular, variations of the fine-structure constant can be interpreted as a manifestation of dark matter fields. My presentation will be based on (Sci. Adv. 4, eaau4869 (2018)), where we use the first Earth-scale quantum sensor network based on optical atomic clocks to search for such dark matter interactions. Although no signal consistent with dark matter fields is found, we considerably improve constraints on the coupling of the dark matter fields to the Standard Model fields.

The fluctuation-dissipation theorem is a fundamental result in statistical physics that establishes a connection between the response of a system subject to a perturbation and the fluctuations associated with observables in equilibrium. Here we derive its version within a resource-theoretic framework, where one investigates optimal quantum state transitions under thermodynamic constraints. More precisely, for a fixed transformation error, we prove a relation between the minimal amount of free energy dissipated in a thermodynamic distillation process and the free energy fluctuations of the initial state of the system. Our results apply to initial states given by either asymptotically many identical pure systems or arbitrary number of independent energy-incoherent systems, and allow not only for a state transformation, but also for the change of Hamiltonian. The fluctuation-dissipation relations we derive enable us to find the optimal performance of thermodynamic protocols such as work extraction, information erasure and thermodynamically-free communication, up to second-order asymptotics in the number $N$ of processed systems. We thus provide a first rigorous analysis of these thermodynamic protocols for quantum states with coherence between different energy eigenstates in the intermediate regime of large but finite N.

This talk is based on https://arxiv.org/abs/2105.11759

The predictions of quantum theory resist generalised noncontextual explanations. In addition to the foundational relevance of this fact, the particular extent to which quantum theory violates noncontextuality limits available quantum advantage in communication and information processing. In the first part of this work, we formally define contextuality scenarios via prepare-and-measure experiments, along with the polytope of general contextual behaviours containing the set of quantum contextual behaviours. This framework allows us to recover several properties of set of quantum behaviours in these scenarios, including contextuality scenarios and associated noncontextuality inequalities that require for their violation the individual quantum preparation and measurement procedures to be mixed states and unsharp measurements. With the framework in place, we formulate novel semidefinite programming relaxations for bounding these sets of quantum contextual behaviours. Most significantly, to circumvent the inadequacy of pure states and projective measurements in contextuality scenarios, we present a novel unitary operator based semidefinite relaxation technique. We demonstrate the efficacy of these relaxations by obtaining tight upper bounds on the quantum violation of several noncontextuality inequalities and identifying novel maximally contextual quantum strategies. To further illustrate the versatility of these relaxations, we demonstrate monogamy of preparation contextuality in a tripartite setting, and present a secure semi-device independent quantum key distribution scheme powered by quantum advantage in parity oblivious random access codes.

This talk is based on Quantum 5, 484 (2021).

In this talk I will discuss some recent work with Thomas D. Galley and Flaminia Giacomini, in which we apply the formalism of generalised probabilistic theories to the study of the nature of the gravitational field. Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field. The formalism allows us to study this problem without having to make any precommitments to any particular model of gravity or ontological notions. By analysing these experiments within the framework of GPTs we prove that the following are inconsistent i) the gravitational field is the mediator of an interaction between two systems; ii) entanglement is generated between the two systems; iii) the field is classical. I will discuss the particularly interesting case which is a violation of condition (iii), a violation of which has commonly been viewed as evidence for the quantum nature of the gravitational field. From the perspective of GPTs, however, we see that there are other possibilities. That is, I will discuss other examples of non-classical but non-quantum theories which are nonetheless consistent with conditions (i) and (ii). This leaves an important open question, what evidence do we actually need in order to conclude that the gravitational field is quantum?

The indistinguishability of quantum identical particles has been widely used as a resource for the generation of entanglement. In this talk, I discuss the multipartite entanglement generation of identical particles with spatial overlap and internal state rotation, which can be realized as a linear quantum network (LQN) of identical particles. For the tripartite case, I explain schemes to generate two fundamental classes of genuine entanglement, i.e., GHZ and W classes, which are experimentally demonstrated with three photons. The tripartite entanglement class decays from the genuine entanglement to the full separability as the particles become more distinguishable from each other. To extend the tripartite results to an arbitrary N-partite case, I introduce a graph picture of LQNs, which provides a powerful tool for analyzing and designing LQNs to generate multipartite entanglement. Perfect matching diagrams (PM diagrams) in our graph picture furnish rigorous criteria for the entanglement of a given LQN and solid guidelines for designing suitable LQNs for the genuine entanglement.

This talk is based on arXiv:2101.00392 and arXiv:2104.05937.

We present the state of the art of TEDOPA (Time Evolving Density operator with Orthogonal PolynomiAls), a numerically exact simulation method for open quantum systems interacting with structured baths. We show how, by exploiting the chain mapping of the bath modes, TEDOPA is able to unleash the power of Tensor Networks methods to exponentially reduce the effective dimension of the extended system+bath state. We moreover show how the application of a thermofield-like transformation allows to efficiently extend the application of TEDOPA to open quantum systems interacting with finite temperature baths.