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Simulating quantum states on a classical computer is hard, typically requiring prohibitive resources in terms of memory and computational power. Efficient simulation, however, can be achieved for certain classes of quantum states, in…
We study equivariant Gromov-Witten invariants and quantum cohomology in GKM theory. Building on the localization formula, we prove that the resulting expression is independent of the choice of compatible connection, and provide an…
We initiate a study of the complexity of quantum field theories (QFTs) by proposing a measure of information contained in a QFT and its observables. We show that from minimal assertions, one is naturally led to measure complexity by two…
Over the last years the Asymptotic Safety program has matured into a serious candidate for a quantum theory of gravity compatible with observations. The rapid technical progress in computing renormalisation group flows for gravity and…
Quantum communication employs the counter-intuitive features of quantum physics to perform tasks that are im- possible in the classical world. It is crucial for testing the foundations of quantum theory and promises to rev- olutionize our…
Quantum computing with qudits, an extension of qubits to multiple levels, is a research field less mature than qubit-based quantum computing. However, qudits can offer some advantages over qubits, by representing information with fewer…
Single photon interference due to passage through a periodic grating is considered in a novel proposal for processing D-dimensional quantum systems (quDits) encoded in the spatial degrees of freedom of light. We show that free space…
Quantum computers (QC) could harbor the potential to significantly advance materials simulations, particularly at the atomistic scale involving strongly correlated fermionic systems where an accurate description of quantum many-body effects…
The developments of quantum computing algorithms and experiments for atomic scale simulations have largely focused on quantum chemistry for molecules, while their application in condensed matter systems is scarcely explored. Here we present…
Quantum simulation is a rapidly evolving tool with great potential for research at the frontiers of physics, and is particularly suited to be used in computationally intensive lattice simulations, such as problems with non-equilibrium. In…
The present paper is the companion of [1] in which we proposed a scheme that tries to derive the Quantum Field Theory (QFT) on Curved Spacetimes (CST) limit from background independent Quantum General Relativity (QGR). The constructions of…
Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies.…
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on…
This work has a methodological nature and is a set of lecture notes for undergraduate students. It is devoted to the study of the basic tools of quantum field theory on the example of the simplest cubic "toy" model. We introduce such…
The Schrieffer-Wolff transformation (SWT) is a foundational perturbative method for deriving effective Hamiltonians in quantum systems by systematically eliminating couplings between pairs of energy distant subspaces. Despite recent…
This work develops and applies the concept of mollification in order to smooth out highly oscillatory exponentials. This idea, known for quite a while in the mathematical community (mollifiers are a means to smooth distributions), is new to…
The quantum Fourier transform for discrete variable (dvQFT) is an efficient algorithm for several applications. It is usually considered for the processing of quantum bits (qubits) and its efficient implementation is obtained with two…
We present the Quantum Hamiltonian Analysis Toolkit (QHAT), a newly developed application that provides a user-friendly interface for studying Hamiltonians and performing Hamiltonian simulation on fault-tolerant quantum computers. QHAT…
Instead of formulating the states of a Quantum Field Theory (QFT) as density matrices over a single large Hilbert space, it has been proposed by Kijowski [Kijowski, 1977] to construct them as consistent families of partial density matrices,…
Mean-field theories have proven to be efficient tools for exploring diverse phases of matter, complementing alternative methods that are more precise but also more computationally demanding. Conventional mean-field theories often fall short…