Publications

Order by: publication date number of citations

• Quantum hypothesis testing in many-body systems

  Jan de Boer, Victor Godet, Jani Kastikainen, Esko Keski-Vakkuri

  SciPost Phys. Core 4, 019 (2021) · published 23 June 2021 | Toggle abstract · pdf

  One of the key tasks in physics is to perform measurements in order to determine the state of a system. Often, measurements are aimed at determining the values of physical parameters, but one can also ask simpler questions, such as "is the system in state A or state B?". In quantum mechanics, the latter type of measurements can be studied and optimized using the framework of quantum hypothesis testing. In many cases one can explicitly find the optimal measurement in the limit where one has simultaneous access to a large number $n$ of identical copies of the system, and estimate the expected error as $n$ becomes large. Interestingly, error estimates turn out to involve various quantum information theoretic quantities such as relative entropy, thereby giving these quantities operational meaning. In this paper we consider the application of quantum hypothesis testing to quantum many-body systems and quantum field theory. We review some of the necessary background material, and study in some detail the situation where the two states one wants to distinguish are parametrically close. The relevant error estimates involve quantities such as the variance of relative entropy, for which we prove a new inequality. We explore the optimal measurement strategy for spin chains and two-dimensional conformal field theory, focusing on the task of distinguishing reduced density matrices of subsystems. The optimal strategy turns out to be somewhat cumbersome to implement in practice, and we discuss a possible alternative strategy and the corresponding errors.

  7 citations

• Generalized eigenproblem without fermion doubling for Dirac fermions on a lattice

  M. J. Pacholski, G. Lemut, J. Tworzydło, C. W. J. Beenakker

  SciPost Phys. 11, 105 (2021) · published 14 December 2021 | Toggle abstract · pdf

  The spatial discretization of the single-cone Dirac Hamiltonian on the surface of a topological insulator or superconductor needs a special "staggered" grid, to avoid the appearance of a spurious second cone in the Brillouin zone. We adapt the Stacey discretization from lattice gauge theory to produce a generalized eigenvalue problem, of the form ${\mathcal H}\psi=E {\mathcal P}\psi$, with Hermitian tight-binding operators ${\mathcal H}$, ${\mathcal P}$, a locally conserved particle current, and preserved chiral and symplectic symmetries. This permits the study of the spectral statistics of Dirac fermions in each of the four symmetry classes A, AII, AIII, and D.

  7 citations

• NISQ Algorithm for Hamiltonian simulation via truncated Taylor series

  Jonathan Wei Zhong Lau, Tobias Haug, Leong Chuan Kwek, Kishor Bharti

  SciPost Phys. 12, 122 (2022) · published 8 April 2022 | Toggle abstract · pdf

  Simulating the dynamics of many-body quantum systems is believed to be one of the first fields that quantum computers can show a quantum advantage over classical computers. Noisy intermediate-scale quantum (NISQ) algorithms aim at effectively using the currently available quantum hardware. For quantum simulation, various types of NISQ algorithms have been proposed with individual advantages as well as challenges. In this work, we propose a new algorithm, truncated Taylor quantum simulator (TQS), that shares the advantages of existing algorithms and alleviates some of the shortcomings. Our algorithm does not have any classical-quantum feedback loop and bypasses the barren plateau problem by construction. The classical part in our hybrid quantum-classical algorithm corresponds to a quadratically constrained quadratic program (QCQP) with a single quadratic equality constraint, which admits a semidefinite relaxation. The QCQP based classical optimization was recently introduced as the classical step in quantum assisted eigensolver (QAE), a NISQ algorithm for the Hamiltonian ground state problem. Thus, our work provides a conceptual unification between the NISQ algorithms for the Hamiltonian ground state problem and the Hamiltonian simulation. We recover differential equation-based NISQ algorithms for Hamiltonian simulation such as quantum assisted simulator (QAS) and variational quantum simulator (VQS) as particular cases of our algorithm. We test our algorithm on some toy examples on current cloud quantum computers. We also provide a systematic approach to improve the accuracy of our algorithm.

  7 citations

• Simulating Floquet topological phases in static systems

  Selma Franca, Fabian Hassler, Ion Cosma Fulga

  SciPost Phys. Core 4, 007 (2021) · published 15 April 2021 | Toggle abstract · pdf

  We show that scattering from the boundary of static, higher-order topological insulators (HOTIs) can be used to simulate the behavior of (time-periodic) Floquet topological insulators. We consider D-dimensional HOTIs with gapless corner states which are weakly probed by external waves in a scattering setup. We find that the unitary reflection matrix describing back-scattering from the boundary of the HOTI is topologically equivalent to a (D-1)-dimensional nontrivial Floquet operator. To characterize the topology of the reflection matrix, we introduce the concept of `nested' scattering matrices. Our results provide a route to engineer topological Floquet systems in the lab without the need for external driving. As benefit, the topological system does not to suffer from decoherence and heating.

  7 citations

• Complexity of frustration: A new source of non-local non-stabilizerness

  Jovan Odavić, Tobias Haug, Gianpaolo Torre, Alioscia Hamma, Fabio Franchini, Salvatore Marco Giampaolo

  SciPost Phys. 15, 131 (2023) · published 3 October 2023 | Toggle abstract · pdf

  We advance the characterization of complexity in quantum many-body systems by examining $W$-states embedded in a spin chain. Such states show an amount of non-stabilizerness or "magic", measured as the Stabilizer Rényi Entropy, that grows logarithmically with the number of qubits/spins. We focus on systems whose Hamiltonian admits a classical point with extensive degeneracy. Near these points, a Clifford circuit can convert the ground state into a $W$-state, while in the rest of the phase to which the classical point belongs, it is dressed with local quantum correlations. Topological frustrated quantum spin-chains host phases with the desired phenomenology, and we show that their ground state's Stabilizer Rényi Entropy is the sum of that of the $W$-states plus an extensive local contribution. Our work reveals that $W$-states/frustrated ground states display a non-local degree of complexity that can be harvested as a quantum resource and has no counterpart in GHZ states/non-frustrated systems.

  7 citations

• Holographic S-fold theories at one loop

  Connor Behan

  SciPost Phys. 12, 149 (2022) · published 6 May 2022 | Toggle abstract · pdf

  A common feature of tree-level holography is that a correlator in one theory can serve as a generating function for correlators in another theory with less continuous symmetry. This is the case for a family of 4d CFTs with eight supercharges which have protected operators dual to gluons in the bulk. The most recent additions to this family were defined using S-folds which combine a spatial identification with an action of the S-duality group in type IIB string theory. Differences between these CFTs which have a dynamical origin first become manifest at one loop. To explore this phenomenon at the level of anomalous dimensions, we use the AdS unitarity method to bootstrap a one-loop double discontinuity. Compared to previous studies, the subsequent analysis is performed without any assumption about which special functions are allowed. Instead, the Casimir singular and Casimir regular terms are extracted iteratively in order to move from one Regge trajectory to the next. Our results show that anomalous dimensions in the presence of an S-fold are no longer rational functions of the spin.

  7 citations

• How to GAN Higher Jet Resolution

  Pierre Baldi, Lukas Blecher, Anja Butter, Julian Collado, Jessica N. Howard, Fabian Keilbach, Tilman Plehn, Gregor Kasieczka, Daniel Whiteson

  SciPost Phys. 13, 064 (2022) · published 23 September 2022 | Toggle abstract · pdf

  QCD-jets at the LHC are described by simple physics principles. We show how super-resolution generative networks can learn the underlying structures and use them to improve the resolution of jet images. We test this approach on massless QCD-jets and on fat top-jets and find that the network reproduces their main features even without training on pure samples. In addition, we show how a slim network architecture can be constructed once we have control of the full network performance.

  7 citations

• CrystalNets.jl: Identification of Crystal Topologies

  Lionel Zoubritzky, François-Xavier Coudert

  SciPost Chem. 1, 005 (2022) · published 17 June 2022 | Toggle abstract · pdf

  We present here an open-source Julia library for the topological identification of crystalline materials, with algorithmic and computational improvements over the previously available software in the field, resulting in a speed increase of one order of magnitude. This new algorithm and implementation can therefore be used at large scale in high-throughput screening methodologies. We have validated and benchmarked CrystalNets.jl against a diverse set of crystal databases, covering in particular metal–organic frameworks, aluminophosphates, zeolites, and other inorganic compounds.

  7 citations

• jVMC: Versatile and performant variational Monte Carlo leveraging automated differentiation and GPU acceleration

  Markus Schmitt, Moritz Reh

  SciPost Phys. Codebases 2 (2022) · published 23 August 2022 | Toggle abstract · pdf

  The introduction of Neural Quantum States (NQS) has recently given a new twist to variational Monte Carlo (VMC). The ability to systematically reduce the bias of the wave function ansatz renders the approach widely applicable. However, performant implementations are crucial to reach the numerical state of the art. Here, we present a Python codebase that supports arbitrary NQS architectures and model Hamiltonians. Additionally leveraging automatic differentiation, just-in-time compilation to accelerators, and distributed computing, it is designed to facilitate the composition of efficient NQS algorithms.

  7 citations

• A gauge theory for shallow water

  David Tong

  SciPost Phys. 14, 102 (2023) · published 9 May 2023 | Toggle abstract · pdf

  The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a $d=2+1$ dimensional Abelian gauge theory. The magnetic field corresponds to the conserved height of the fluid, while the electric charge corresponds to the conserved vorticity. In a certain linearised approximation, the shallow water equations reduce to relativistic Maxwell-Chern-Simons theory. This describes Poincaré waves. The chiral edge modes of the theory are identified as coastal Kelvin waves.

  7 citations