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Journal of Physics A: Mathematical and Theoretical - latest papers

Latest articles for Journal of Physics A: Mathematical and Theoretical

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  • Stationary acoustic black hole solutions in Bose–Einstein condensates and their Borel analysis
    In this article, we study the dynamics of a Bose–Einstein condensate (BEC) with the idea of finding solutions that could possibly correspond to the so-called acoustic (or Unruh) black/white holes. These are flows with horizons where the speed of the flow changes from sub-sonic to super-sonic. This is because sound cannot return from the supersonic to the subsonic regions. The speed of sound plays the role of the speed of light in a gravitational black hole, with an important difference being that there are excitations that can go faster than the speed of sound and therefore can escape the sonic black hole. Here, the motion of the BEC is described by the Gross–Pitaevskii equation (GPE). More specifically, we discuss singular Stationary solutions of GPE in 2D (with circular symmetry) and 3D (with spherical symmetry). We use these solutions to study the local speed of sound and magnitude of flow velocity of the condensate to determine whether they cross, indicating the potential existence of a sonic analog of a black/white hole. We discuss the numerical techniques used and also study the semi-analytical Laplace–Borel resummation of asymptotic series solutions to see how well they agree with numerical solutions. We also study how the resurgent transseries plays a role in these solutions.

  • Leveraging Hamiltonian simulation techniques to compile operations on bosonic devices
    Circuit quantum electrodynamics enables the combined use of qubits and oscillator modes. Despite a variety of available gate sets, many hybrid qubit-boson (i.e. qubit-oscillator) operations are realizable only through optimal control theory, which is oftentimes intractable and uninterpretable. We introduce an analytic approach with rigorously proven error bounds for realizing specific classes of operations via two matrix product formulas commonly used in Hamiltonian simulation, the Lie–Trotter–Suzuki and Baker–Campbell–Hausdorff product formulas. We show how this technique can be used to realize a number of operations of interest, including polynomials of annihilation and creation operators, namely for integer . We show examples of this paradigm including obtaining universal control within a subspace of the entire Fock space of an oscillator, state preparation of a fixed photon number in the cavity, simulation of the Jaynes–Cummings Hamiltonian, and simulation of the Hong-Ou-Mandel effect. This work demonstrates how techniques from Hamiltonian simulation can be applied to better control hybrid qubit-boson devices.

  • A novel approach to reduce derivative costs in variational quantum algorithms
    We present a detailed numerical study of an alternative approach, named quantum non-demolition measurement (QNDM) (Solinas et al 2023 Eur. Phys. J. D77 76), to efficiently estimate the gradients or the Hessians of a quantum observable. This is a key step and a resource-demanding task when we want to minimize the cost function associated with a quantum observable. In our detailed analysis, we account for all the resources needed to implement the QNDM approach with a fixed accuracy and compare them to the current state-of-the-art method (Mari et al 2021 Phys. Rev. A103 012405; Schuld et al 2019 Phys. Rev. A99 032331; Cerezo et al 2021 Nat. Rev. Phys.3 625). We find that the QNDM approach is more efficient, i.e. it needs fewer resources, in evaluating the derivatives of a cost function. These advantages are already clear in small dimensional systems and are likely to increase for practical implementations and more realistic situations. A significant outcome of our study is the implementation of the QNDM method in Python, provided in the supplementary material (Caletti and Minuto 2024 https://github.com/ simonecaletti/qndm-gradient). Given that most variational quantum algorithms (VQA) can be formulated within this framework, our results can have significant implications in quantum optimization algorithms and make the QNDM approach a valuable alternative to implement VQA on near-term quantum computers.

  • Minimal covariant quantum space-time
    We discuss minimal covariant quantum space-time , which is defined through the minimal doubleton representation of . An elementary definition in terms of generators and relations is given. This space is shown to admit a semi-classical interpretation as quantized twistor space , viewed as a quantized S2-bundle over a 3 + 1-dimensional FLRW space-time. In particular we find an over-complete set of (quasi-) coherent states, with a large hierarchy between the uncertainty scale and the geometric curvature scale. This provides an interesting background for the IKKT model, leading to a -extended gravitational gauge theory, which is free of ghosts due to the constraints arising from the doubleton representation.

  • Generalized incompressible fluid dynamical system interpolating between the Navier–Stokes and Burgers equations in two dimensions
    We propose a set of generalized incompressible fluid dynamical equations, which interpolates between the Burgers and Navier–Stokes equations in two dimensions and study their properties theoretically and numerically. It is well-known that under the assumption of potential flows the multi-dimensional Burgers equations are integrable in the sense they can be reduced to the heat equation, via the so-called Cole-Hopf linearization. On the other hand, it is believed that the Navier–Stokes equations do not possess such a nice property. Take, for example, the 2D Navier–Stokes equations and rotate the velocity gradient by 90 degrees, we then obtain a system which is equivalent to the Burgers equations. Based on this observation, we introduce a system of generalized incompressible fluid dynamical equations by rotating velocity gradient through a continuous angle parameter. That way we can compare properties of an integrable system with those of non-integrable ones by relating them through a continuous parameter. Using direct numerical experiments we show how the flow properties change (actually, deteriorate) when we increase the angle parameter α from 0 to . It should be noted that the case associated with least regularity, namely the Burgers equations ( ), is integrable via the heat kernel. We also formalize a perturbative treatment of the problem, which in principle yields the solution of the Navier–Stokes equations on the basis of that of the Burgers equations. The principal variation around the Burgers equations is computed numerically and is shown to agree well with the results of direct numerical simulations for some time.