Publications

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Many bounded versions of undecidable problems are NP-hard

Andreas Klingler, Mirte van der Eyden, Sebastian Stengele, Tobias Reinhart, Gemma de las Cuevas

SciPost Phys. 14, 173 (2023) · published 29 June 2023 | · pdf

Several physically inspired problems have been proven undecidable; examples are the spectral gap problem and the membership problem for quantum correlations. Most of these results rely on reductions from a handful of undecidable problems, such as the halting problem, the tiling problem, the Post correspondence problem or the matrix mortality problem. All these problems have a common property: they have an NP-hard bounded version. This work establishes a relation between undecidable unbounded problems and their bounded NP-hard versions. Specifically, we show that NP-hardness of a bounded version follows easily from the reduction of the unbounded problems. This leads to new and simpler proofs of the NP-hardness of bounded version of the Post correspondence problem, the matrix mortality problem, the positivity of matrix product operators, the reachability problem, the tiling problem, and the ground state energy problem. This work sheds light on the intractability of problems in theoretical physics and on the computational consequences of bounding a parameter.
Flux-tunable hybridization in a double quantum dot interferometer

Christian G. Prosko, Ivan Kulesh, Michael Chan, Lin Han, Di Xiao, Candice Thomas, Michael J. Manfra, Srijit Goswami, Filip K. Malinowski

SciPost Phys. 17, 074 (2024) · published 6 September 2024 | · pdf

Quantum interference of electron tunneling occurs in any system where multiple tunneling paths connect states. This unavoidably arises in two-dimensional semiconducting qubit arrays, and must be controlled as a prerequisite for the manipulation and readout of hybrid topological and parity qubits. Studying a loop formed by two quantum dots, we demonstrate a magnetic-flux-tunable hybridization between two electronic levels, an irreducibly simple system where quantum interference is expected to occur. Using radio-frequency reflectometry of the dots’ gate electrodes we extract an interdot coupling exhibiting oscillations with a periodicity of one flux quantum. In different tunneling regimes we benchmark the oscillations’ contrast, and find their amplitude varies with the charge state of the quantum dots. These results establish the feasibility and limitations of parity readout of qubits with tunnel couplings tuned by flux.
Revisiting the flavor violating decays of the Tau and Mu leptons in the Standard Model with massive neutrinos

Gerardo Hernández Tomé

SciPost Phys. Proc. 1, 017 (2019) · published 19 February 2019 | · pdf

The flavor violating leptonic decays of the $\tau$ and $\mu$ leptons into three lighter charged leptons are revisited in the framework the Standard Model with massive neutrinos. In contrast to the previous prediction, we have found strongly suppressed rates for the $\tau^-\to \mu^- \ell^+ \ell^-$ ($\ell=\mu, e$) decays. Our results are in good agreement with the approximation of neglecting masses and momenta of the external particles in the loop integrals made in the first computation for the $\mu^- \to e^-e^+ e^-$ decay.
Internal Levin-Wen models

Vincentas Mulevičius, Ingo Runkel, Thomas Voß

SciPost Phys. 17, 088 (2024) · published 24 September 2024 | · pdf

Levin--Wen models are a class of two-dimensional lattice spin models with a Hamiltonian that is a sum of commuting projectors, which describe topological phases of matter related to Drinfeld centres. We generalise this construction to lattice systems internal to a topological phase described by an arbitrary modular fusion category $\mathcal{C}$. The lattice system is defined in terms of an orbifold datum $\mathbb{A}$ in $\mathcal{C}$, from which we construct a state space and a commuting-projector Hamiltonian $H_{\mathbb{A}}$ acting on it. The topological phase of the degenerate ground states of $H_{\mathbb{A}}$ is characterised by a modular fusion category $\mathcal{C}_\mathbb{A}$ defined directly in terms of $\mathbb{A}$. By choosing different $\mathbb{A}$'s for a fixed $\mathcal{C}$, one obtains precisely all phases which are Witt-equivalent to $\mathcal{C}$. As special cases we recover the Kitaev and the Levin--Wen lattice models from instances of orbifold data in the trivial modular fusion category of vector spaces, as well as phases obtained by anyon condensation in a given phase $\mathcal{C}$.
Connected correlations in partitioning protocols: A case study and beyond

Saverio Bocini

SciPost Phys. 15, 027 (2023) · published 25 July 2023 | · pdf

The assumption of local relaxation in inhomogeneous quantum quenches allows to compute asymptotically the expectation value of local observables via hydrodynamic arguments known as generalized hydrodynamics (GHD). In this work we address formally the question of when an observable is local enough to be described by GHD using the playground of partitioning protocols and non-interacting time evolution. We show that any state evolving under a quadratic Hamiltonian can be described via a set of decoupled dynamical fields such that one of those fields can be identified with a space-time-dependent generalisation of the root density. By studying the contribution to a connected spin correlation of each of those fields independently, we derive the locality conditions under which an observable can be described using the root density only. That shows both the regime of validity for hydrodynamic approaches that aim at describing the asymptotic value of observables in term of the root density only, such as GHD, and the locality conditions necessary for Gaussianification to occur.
Bistabilities and domain walls in weakly open quantum systems

Florian Lange, Achim Rosch

SciPost Phys. 9, 057 (2020) · published 21 October 2020 | · pdf

Weakly pumped systems with approximate conservation laws can be efficiently described by a generalized Gibbs ensemble if the steady state of the system is unique. However, such a description can fail if there are multiple steady state solutions, for example, a bistability. In this case domains and domain walls may form. In one-dimensional (1D) systems any type of noise (thermal or non-thermal) will in general lead to a proliferation of such domains. We study this physics in a 1D spin chain with two approximate conservation laws, energy and the $z$-component of the total magnetization. A bistability in the magnetization is induced by the coupling to suitably chosen Lindblad operators. We analyze the theory for a weak coupling strength $\epsilon$ to the non-equilibrium bath. In this limit, we argue that one can use hydrodynamic approximations which describe the system locally in terms of space- and time-dependent Lagrange parameters. Here noise terms enforce the creation of domains, where the typical width of a domain wall goes as $\sim 1/\sqrt{\epsilon}$ while the density of domain walls is exponentially small in $1/\sqrt{\epsilon}$. This is shown by numerical simulations of a simplified hydrodynamic equation in the presence of noise.
Thermodynamic Bethe Ansatz and generalised hydrodynamics in the sine-Gordon model

Botond C. Nagy, Gábor Takács, Márton Kormos

SciPost Phys. 16, 145 (2024) · published 4 June 2024 | · pdf

We set up a hydrodynamic description of the non-equilibrium dynamics of sine-Gordon quantum field theory for generic coupling. It is built upon an explicit form of the Bethe Ansatz description of general thermodynamic states, with the structure of the resulting coupled integral equations encoded in terms of graphical diagrams. The resulting framework is applied to derive results for the Drude weights of charge and energy. Quantities associated with the charge universally have fractal dependence on the coupling, which is notably absent from those associated with energy, a feature explained by the different roles played by reflective scattering in transporting these quantities. We then present far-from-equilibrium results, including explicit time evolution starting from bipartite initial states and dynamical correlation functions. Our framework can be applied to explore numerous other aspects of non-equilibrium dynamics, which opens the way to a wide array of theoretical studies and potential novel experimental predictions.
The role of atomic interactions in cavity-induced continuous time crystals

Christian Høj Johansen, Johannes Lang, Francesco Piazza

SciPost Phys. 17, 089 (2024) · published 24 September 2024 | · pdf

We consider continuous time-crystalline phases in dissipative many-body systems of atoms in cavities, focusing on the role of short-range interatomic interactions. First, we show that the latter can alter the nature of the time crystal by changing the type of the underlying critical bifurcation. Second, we characterize the heating mechanism and dynamics resulting from the short-range interactions and demonstrate that they make the time crystal inherently metastable. We argue this is generic for the broader class of dissipative time crystals in atom-cavity systems whenever the cavity loss rate is comparable to the atomic recoil energy. We observe that such a scenario for heating has several similarities to the one proposed for preheating in the early universe, where the oscillating coherent inflation field decays into a cascade of exponentially growing fluctuations. By extending approaches for dissipative dynamical systems to our many-body problem, we obtain analytical predictions for the parameters describing the phase transition and the heating rate inside the time-crystalline phase. We underpin and extend the analytical predictions of the heating rates with numerical simulations, which also show that the metastable regime exists when the inherent stochastic nature is taken into account.
Constant-time quantum algorithm for homology detection in closed curves

Nhat A. Nghiem Vu, Xianfeng David Gu, Tzu-Chieh Wei

SciPost Phys. 15, 049 (2023) · published 4 August 2023 | · pdf

Given a loop or more generally 1-cycle $r$ of size L on a closed two-dimensional manifold or surface, represented by a triangulated mesh, a question in computational topology asks whether or not it is homologous to zero. We frame and tackle this problem in the quantum setting. Given an oracle that one can use to query the inclusion of edges on a closed curve, we design a quantum algorithm for such a homology detection with a constant running time, with respect to the size or the number of edges on the loop $r$, requiring only a single usage of oracle. In contrast, classical algorithm requires $\Omega(L)$ oracle usage, followed by a linear time processing and can be improved to logarithmic by using a parallel algorithm. Our quantum algorithm can be extended to check whether two closed loops belong to the same homology class. Furthermore, it can be applied to a specific problem in the homotopy detection, namely, checking whether two curves are not homotopically equivalent on a closed two-dimensional manifold.
Experimental input from $e^+e^-$ for $a_{\mu}$ light-by-light

Yuping Guo on behalf of BESIII Collaboration

SciPost Phys. Proc. 1, 054 (2019) · published 9 May 2019 | · pdf

The anomalous magnetic momentum of the muon, $a_{\mu}$, has been measured and calculated with a precision up to $~0.5$ ppm, but there is a 3 to 4 standard deviations between these two values. The uncertainty in the calculation is dominated by the hadronic part, including the hadronic vacuum polarization and the hadronic light-by-light. The meson transition form factors and the helicity amplitudes can be used as input or constraint to the calculation of the hadronic light-by-light contribution. Latest experimental studies of the transition form factors of $\pi^0$, $\eta$, and $\eta^{*}$ and the cross-section of $\gamma\gamma^*\to\pi^+\pi-$from $e^+e^-$ collider are presented.

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