Publications

Order by: publication date number of citations

• Quantum approximate optimization for hard problems in linear algebra

  Ajinkya Borle, Vincent E. Elfving, Samuel J. Lomonaco

  SciPost Phys. Core 4, 031 (2021) · published 30 November 2021 | Toggle abstract · pdf

  The quantum approximate optimization algorithm (QAOA) by Farhi et al. is a quantum computational framework for solving quantum or classical optimization tasks. Here, we explore using QAOA for binary linear least squares (BLLS); a problem that can serve as a building block of several other hard problems in linear algebra, such as the non-negative binary matrix factorization (NBMF) and other variants of the non-negative matrix factorization (NMF) problem. Most of the previous efforts in quantum computing for solving these problems were done using the quantum annealing paradigm. For the scope of this work, our experiments were done on noiseless quantum simulators, a simulator including a device-realistic noise-model, and two IBM Q 5-qubit machines. We highlight the possibilities of using QAOA and QAOA-like variational algorithms for solving such problems, where trial solutions can be obtained directly as samples, rather than being amplitude-encoded in the quantum wavefunction. Our numerics show that even for a small number of steps, simulated annealing can outperform QAOA for BLLS at a QAOA depth of $p\leq3$ for the probability of sampling the ground state. Finally, we point out some of the challenges involved in current-day experimental implementations of this technique on cloud-based quantum computers.

  12 citations

• Classification of all $\mathcal{N}\geq 3$ moduli space orbifold geometries at rank 2

  Philip C. Argyres, Antoine Bourget, Mario Martone

  SciPost Phys. 9, 083 (2020) · published 7 December 2020 | Toggle abstract · pdf

  We classify orbifold geometries which can be interpreted as moduli spaces of four-dimensional $\mathcal{N}\geq 3$ superconformal field theories up to rank 2 (complex dimension 6). The large majority of the geometries we find correspond to moduli spaces of known theories or discretely gauged version of them. Remarkably, we find 6 geometries which are not realized by any known theory, of which 3 have an $\mathcal{N}=2$ Coulomb branch slice with a non-freely generated coordinate ring, suggesting the existence of new, exotic $\mathcal{N}=3$ theories.

  12 citations

• Essential renormalisation group

  Alessio Baldazzi, Riccardo Ben Alì Zinati, Kevin Falls

  SciPost Phys. 13, 085 (2022) · published 7 October 2022 | Toggle abstract · pdf

  We propose a novel scheme for the exact renormalisation group motivated by the desire of reducing the complexity of practical computations. The key idea is to specify renormalisation conditions for all inessential couplings, leaving us with the task of computing only the flow of the essential ones. To achieve this aim, we utilise a renormalisation group equation for the effective average action which incorporates general non-linear field reparameterisations. A prominent feature of the scheme is that, apart from the renormalisation of the mass, the propagator evaluated at any constant value of the field maintains its unrenormalised form. Conceptually, the simplifications can be understood as providing a description based only on quantities that enter expressions for physical observables since the redundant, non-physical content is automatically disregarded. To exemplify the scheme's utility, we investigate the Wilson-Fisher fixed point in three dimensions at order two in the derivative expansion. In this case, the scheme removes all order $\partial^2$ operators apart from the canonical term. Further simplifications occur at higher orders in the derivative expansion. Although we concentrate on a minimal scheme that reduces the complexity of computations, we propose more general schemes where inessential couplings can be tuned to optimise a given approximation. We further discuss the applicability of the scheme to a broad range of physical theories.

  12 citations

• Curvature induced magnonic crystal in nanowires

  Anastasiia Korniienko, Volodymyr P. Kravchuk, Oleksandr V. Pylypovskyi, Denis D. Sheka, Jeroen van den Brink, Yuri Gaididei

  SciPost Phys. 7, 035 (2019) · published 20 September 2019 | Toggle abstract · pdf

  A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devices with the geometrically tunable parameters is proposed, namely, to filter elements.

  12 citations

• Black holes, quantum chaos, and the Riemann hypothesis

  Panagiotis Betzios, Nava Gaddam, Olga Papadoulaki

  SciPost Phys. Core 4, 032 (2021) · published 10 December 2021 | Toggle abstract · pdf

  Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for a natural semiclassical regularisation and discretisation of the continuous spectrum of a quantum Hamiltonian related to the Dilation operator. We observe that the said spectrum is in correspondence with the zeros of the Riemann zeta and Dirichlet beta functions. Following ideas of Berry and Keating, this may help the pursuit of the Riemann hypothesis. It strengthens the proposal that this quantum Hamiltonian captures the near horizon dynamics of the scattering matrix of the Schwarzschild black hole, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.

  12 citations

• Ruling out light axions: The writing is on the wall

  Konstantin A. Beyer, Subir Sarkar

  SciPost Phys. 15, 003 (2023) · published 10 July 2023 | Toggle abstract · pdf

  We revisit the domain wall problem for QCD axion models with more than one quark charged under the Peccei-Quinn symmetry. Symmetry breaking during or after inflation results in the formation of a domain wall network which would cause cosmic catastrophe if it comes to dominate the Universe. The network may be made unstable by invoking a "tilt" in the axion potential due to Planck scale suppressed non-renormalisable operators. Alternatively the random walk of the axion field during inflation can generate a "bias" favouring one of the degenerate vacua, but we find that this mechanism is in practice irrelevant. Consideration of the axion abundance generated by the decay of the wall network then requires the Peccei-Quinn scale to be rather low - thus e.g. ruling out the DFSZ axion with mass below $\sim$ 11 meV, where most experimental searches are in fact focused.

  12 citations

• Enhancing sensitivity to rotations with quantum solitonic currents

  P. Naldesi, J. Polo, V. Dunjko, H. Perrin, M. Olshanii, L. Amico, A. Minguzzi

  SciPost Phys. 12, 138 (2022) · published 22 April 2022 | Toggle abstract · pdf

  We study a gas of attracting bosons confined in a ring shape potential pierced by an artificial magnetic field. Because of attractive interactions, quantum analogs of bright solitons are formed. As a genuine quantum-many-body feature, we demonstrate that angular momentum fractionalization occurs and that such effect manifests on time of flight measurements. As a consequence, the matter-wave current in our system can react to very small changes of rotation or other artificial gauge fields. We work out a protocol to entangle such quantum solitonic currents, allowing to operate rotation sensors and gyroscopes to Heisenberg-limited sensitivity. Therefore, we demonstrate that the specific coherence and entanglement properties of the system can induce an enhancement of sensitivity to an external rotation.

  12 citations

• Constraining the gauge-fixed Lagrangian in minimal Landau gauge

  Axel Maas

  SciPost Phys. 8, 071 (2020) · published 1 May 2020 | Toggle abstract · pdf

  A continuum formulation of gauge-fixing resolving the Gribov-Singer ambiguity remains a challenge. Finding a Lagrangian formulation of operational resolutions in numerical lattice calculations, like minimal Landau gauge, would be one possibility. Such a formulation will here be constrained by reconstructing the Dyson-Schwinger equation for which the lattice minimal-Landau-gauge ghost propagator is a solution. It is found that this requires an additional term. As a by-product new, high precision lattice results for the ghost-gluon vertex in three and four dimensions are obtained.

  12 citations

• Comments on a state-operator correspondence for the torus

  Alexandre Belin, Jan de Boer, Jorrit Kruthoff

  SciPost Phys. 5, 060 (2018) · published 10 December 2018 | Toggle abstract · pdf

  We investigate the existence of a state-operator correspondence on the torus. This correspondence would relate states of the CFT Hilbert space living on a spatial torus to the path integral over compact Euclidean manifolds with operator insertions. Unlike the states on the sphere that are associated to local operators, we argue that those on the torus would more naturally be associated to line operators. We find evidence that such a correspondence cannot exist and in particular, we argue that no compact Euclidean path integral can produce the vacuum on the torus. Our arguments come solely from field theory and formulate a CFT version of the Horowitz-Myers conjecture for the AdS soliton.

  12 citations

• Replica approach to the generalized Rosenzweig-Porter model

  Davide Venturelli, Leticia F. Cugliandolo, Grégory Schehr, Marco Tarzia

  SciPost Phys. 14, 110 (2023) · published 12 May 2023 | Toggle abstract · pdf

  The generalized Rosenzweig-Porter model with real (GOE) off-diagonal entries arguably constitutes the simplest random matrix ensemble displaying a phase with fractal eigenstates, which we characterize here by using replica methods. We first derive analytical expressions for the average spectral density in the limit in which the size $N$ of the matrix is large but finite. We then focus on the number of eigenvalues in a finite interval and compute its cumulant generating function as well as the level compressibility, i.e., the ratio of the first two cumulants: these are useful tools to describe the local level statistics. In particular, the level compressibility is shown to be described by a universal scaling function, which we compute explicitly, when the system is probed over scales of the order of the Thouless energy. Interestingly, the same scaling function is found to describe the level compressibility of the complex (GUE) Rosenzweig-Porter model in this regime. We confirm our results with numerical tests.

  12 citations