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