Publications

Order by: publication date number of citations

Entanglement classification via operator size

Qi-Feng Wu

SciPost Phys. Core 6, 063 (2023) · published 15 September 2023 | · pdf

In this work, multipartite entanglement is classified by polynomials. I show that the operator size is closely related to the entanglement structure. Given a generic quantum state, I define a series of subspaces generated by operators of different sizes acting on it. The information about the entanglement is encoded into these subspaces. With the dimension of these subspaces as coefficients, I define a polynomial which I call the entanglement polynomial. The entanglement polynomial induces a homomorphism from quantum states to polynomials. It implies that we can characterize and find the building blocks of entanglement by polynomial factorization. Two states share the same entanglement polynomial if they are equivalent under the stochastic local operations and classical communication. To calculate the entanglement polynomial practically, I construct a series of states, called renormalized states, whose ranks are related to the coefficients of the entanglement polynomial.
Cover your bases: asymptotic distributions of the profile likelihood ratio when constraining effective field theories in high-energy physics

Florian Urs Bernlochner, Daniel C. Fry, Stephen Burns Menary, Eric Persson

SciPost Phys. Core 6, 013 (2023) · published 16 March 2023 | · pdf

We investigate the asymptotic distribution of the profile likelihood ratio (PLR) when constraining effective field theories (EFTs) and show that Wilks' theorem is often violated, meaning that we should not assume the PLR to follow a $\chi^2$-distribution. We derive the correct asymptotic distributions when either one or two real EFT couplings modulate observable cross sections with a purely linear or quadratic dependence. We then discover that when both the linear and quadratic terms contribute, the PLR distribution does not have a simple form. In this case we provide a partly-numerical solution for the one-parameter case. Using a novel approach, we find that the constants which define our asymptotic distributions may be obtained experimentally using a profile of the Asimov likelihood contour. Our results may be immediately used to obtain the correct coverage when deriving real-world EFT constraints using the PLR as a test-statistic.
STEP: A tool to perform tests of smoothness on differential distributions based on expansion of polynomials

Patrick L. S. Connor, Radek Žlebčík

SciPost Phys. Core 6, 040 (2023) · published 1 June 2023 | · pdf

We motivate and describe a method based on fits with polynomials to test the smoothness of differential distributions. As a demonstration, we apply the method to several measurements of inclusive jet double-differential cross section in the jet transverse momentum and rapidity at the Tevatron and LHC. This method opens new possibilities to test the quality of differential distributions used for the extraction of physics quantities such as the strong coupling.
A general learning scheme for classical and quantum Ising machines

Ludwig Schmid, Enrico Zardini, Davide Pastorello

SciPost Phys. Core 7, 013 (2024) · published 14 March 2024 | · pdf

An Ising machine is any hardware specifically designed for finding the ground state of the Ising model. Relevant examples are coherent Ising machines and quantum annealers. In this paper, we propose a new machine learning model that is based on the Ising structure and can be efficiently trained using gradient descent. We provide a mathematical characterization of the training process, which is based upon optimizing a loss function whose partial derivatives are not explicitly calculated but estimated by the Ising machine itself. Moreover, we present some experimental results on the training and execution of the proposed learning model. These results point out new possibilities offered by Ising machines for different learning tasks. In particular, in the quantum realm, the quantum resources are used for both the execution and the training of the model, providing a promising perspective in quantum machine learning.
Real-space spectral simulation of quantum spin models: Application to generalized Kitaev models

Francisco M. O. Brito, Aires Ferreira

SciPost Phys. Core 7, 006 (2024) · published 21 February 2024 | · pdf

The proliferation of quantum fluctuations and long-range entanglement presents an outstanding challenge for the numerical simulation of interacting spin systems with exotic ground states. Here, we present a toolset of Chebyshev polynomial-based iterative methods that provides a unified framework to study the thermodynamical properties, critical behavior and dynamics of frustrated quantum spin models with controlled accuracy. Similar to previous applications of the Chebyshev spectral methods to condensed matter systems, the algorithmic complexity scales linearly with the Hilbert space dimension and the Chebyshev truncation order. Using this approach, we study two paradigmatic quantum spin models on the honeycomb lattice: the Kitaev-Heisenberg (K-H) and the Kitaev-Ising (K-I) models. We start by applying the Chebyshev toolset to compute nearest-neighbor spin correlations, specific heat and entropy of the K-H model on a 24-spin cluster. Our results are benchmarked against exact diagonalization and a popular iterative method based on thermal pure quantum states. The transitions between a variety of magnetic phases, namely ferromagnetic, Néel, zigzag and stripy antiferromagnetic and quantum spin liquid phases are obtained accurately and efficiently. We also determine the temperature dependence of the spin correlations, over more than three decades in temperature, by means of a finite temperature Chebyshev polynomial method introduced here. Finally, we report novel dynamical signatures of the quantum phase transitions in the K-I model. Our findings suggest that the efficiency, versatility and low-temperature stability of the Chebyshev framework developed here could pave the way for previously unattainable studies of quantum spin models in two dimensions.
A solvable model for graph state decoherence dynamics

Jérôme Houdayer, Haggai Landa, Grégoire Misguich

SciPost Phys. Core 7, 009 (2024) · published 23 February 2024 | · pdf

We present an exactly solvable toy model for the continuous dissipative dynamics of permutation-invariant graph states of $N$ qubits. Such states are locally equivalent to an $N$-qubit Greenberger-Horne-Zeilinger (GHZ) state, a fundamental resource in many quantum information processing setups. We focus on the time evolution of the state governed by a Lindblad master equation with the three standard single-qubit jump operators, the Hamiltonian part being set to zero. Deriving analytic expressions for the expectation values of observables expanded in the Pauli basis at all times, we analyze the nontrivial intermediate-time dynamics. Using a numerical solver based on matrix product operators, we simulate the time evolution for systems with up to 64 qubits and verify a numerically exact agreement with the analytical results. We find that the evolution of the operator space entanglement entropy of a bipartition of the system manifests a plateau whose duration increases logarithmically with the number of qubits, whereas all Pauli-operator products have expectation values decaying at most in constant time.
The high-temperature expansion of the thermal sunset

Andreas Ekstedt, Johan Löfgren

SciPost Phys. Core 3, 008 (2020) · published 22 October 2020 | · pdf

We give a prescription for calculating the high-temperature expansion of the thermal sunset integral to arbitrary order. We derive all terms odd in $T$, and rederive previous results up to $\mathcal{O}(T^0) $ for both bosonic and fermionic thermal sunsets in dimensional regularisation. We perform analytical and numerical cross-checks. Intermediate steps involve integrals over three Bessel functions.
Localization control born of intertwined quasiperiodicity and non-Hermiticity

Junmo Jeon, SungBin Lee

SciPost Phys. Core 6, 077 (2023) · published 9 November 2023 | · pdf

Quasiperiodic systems are neither randomly disordered nor translationally invariant in the absence of periodic length scales. Based on their incommensurate order, novel physical properties such as critical states and self-similar wavefunctions have been actively discussed. However, in open systems generally described by the non-Hermitian Hamiltonians, it is hardly known how such quasiperiodic order would lead to new phenomena. In this work, we show that the intertwined quasiperiodicity and non-Hermiticity can give rise to striking effects: perfect delocalization of the critical and localized states to the extended states. In particular, we explore the wave function localization character in the Aubry-André-Fibonacci (AAF) model where non-reciprocal hopping phases are present. Here, the AAF model continuously interpolates the two different limits between metal to insulator transition and the critical states, and the non-Hermiticity is encoded in the hopping phase factors. Surprisingly, their interplay results in the perfect delocalization of the states, which is never allowed in quasiperiodic systems with Hermiticity. By quantifying the localization via the inverse participation ratio and the fractal dimension, we discuss that the non-Hermitian hopping phase leads to delicate control of localization characteristics of the wave function. Our work offers (1) emergent delocalization transition in quasiperiodic systems via non-Hermitian hopping phase and (2) detailed localization control of the critical states. In addition, we suggest an experimental realization of controllable localized, critical and delocalized states, using photonic crystals.
Ergodic Archimedean dimers

Henrik Schou Røising, Zhao Zhang

SciPost Phys. Core 6, 054 (2023) · published 11 August 2023 | · pdf

We study perfect matchings, or close-packed dimer coverings, of finite sections of the eleven Archimedean lattices and give a constructive proof showing that any two perfect matchings can be transformed into each other using small sets of local ring-exchange moves. This result has direct consequences for formulating quantum dimer models with a resonating valence bond ground state, i.e., a superposition of all dimer coverings compatible with the boundary conditions. On five of the composite Archimedean lattices we supplement the sufficiency proof with translationally invariant reference configurations that prove the strict necessity of the sufficient terms with respect to ergodicity. We provide examples of and discuss frustration-free deformations of the quantum dimer models on two tripartite lattices.
Stochastic field dynamics in models of spontaneous unitarity violation

Lotte Mertens, Matthijs Wesseling, Jasper van Wezel

SciPost Phys. Core 7, 012 (2024) · published 13 March 2024 | · pdf

Objective collapse theories propose a solution to the quantum measurement problem by predicting deviations from Schrödinger's equation that can be tested experimentally. A class of objective theories based on spontaneous unitarity violation was recently introduced, in which the stochastic field required for obtaining Born's rule does not depend on the state of the system being measured. Here, we classify possible models for the stochastic field dynamics in theories of spontaneous unitarity violation. We show that for correlated stochastic dynamics, the field must be defined on a closed manifold. In two or more dimensions, it is then always possible to find stochastic dynamics yielding Born's rule, independent of the state being measured or the correlation time of the stochastic field. We show that the models defined this way are all isomorphic to the definition on a two-sphere, which we propose to be a minimal physical model for the stochastic field in models of spontaneous unitarity violation.

Previous 1 ... 14 15 16 17 18 19 20 21 22 23 24 Next