An official website of the United States government
Abstract Models of nonlinear quantum computation based on deterministic positive trace‐preserving (PTP) channels and evolution equations are investigated. The models are defined in any finite Hilbert space, but the main results are for dimension . For every normalizable linear or nonlinear positive map ϕ on bounded linear operatorsX, there is an associated normalized PTP channel . Normalized PTP channels include unitary mean field theories, such as the Gross–Pitaevskii equation for interacting bosons, as well as models of linear and nonlinear dissipation. They classify into four types, yielding three distinct forms of nonlinearity whose computational power are explored. In the qubit case, these channels support Bloch ball torsion and other distortions studied previously, where it has been shown that such nonlinearity can be used to increase the separation between a pair of close qubit states, suggesting an exponential speedup for state discrimination. Building on this idea, the authors argue that this operation can be made robust to noise by using dissipation to induce a bifurcation to a novel phase where a pair of attracting fixed points create an intrinsically fault‐tolerant nonlinear state discriminator.
more »
« less
Nonlinear speed-ups in ultracold quantum gases
Abstract Quantum mechanics is an inherently linear theory. However, collective effects in many body quantum systems can give rise to effectively nonlinear dynamics. In the present work, we analyze whether and to what extent such nonlinear effects can be exploited to enhance the rate of quantum evolution. To this end, we compute a suitable version of the quantum speed limit for numerical and analytical examples. We find that the quantum speed limit grows with the strength of the nonlinearity, yet it does not trivially scale with the “degree” of nonlinearity. This is numerically demonstrated for the parametric harmonic oscillator obeying Gross-Pitaevskii and Kolomeisky dynamics, and analytically for expanding boxes under Gross-Pitaevskii dynamics.
more »
« less
- Award ID(s):
- 2010127
- PAR ID:
- 10478232
- Publisher / Repository:
- IOP Publishing
- Date Published:
- Journal Name:
- Europhysics Letters
- Volume:
- 140
- Issue:
- 4
- ISSN:
- 0295-5075
- Page Range / eLocation ID:
- 48001
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Quantum fluids exhibit quantum mechanical effects at the macroscopic level, which contrast strongly with classical fluids. Gain-dissipative solid-state exciton-polaritons systems are promising emulation platforms for complex quantum fluid studies at elevated temperatures. Recently, halide perovskite polariton systems have emerged as materials with distinctive advantages over other room-temperature systems for future studies of topological physics, non-Abelian gauge fields, and spin-orbit interactions. However, the demonstration of nonlinear quantum hydrodynamics, such as superfluidity and Čerenkov flow, which is a consequence of the renormalized elementary excitation spectrum, remains elusive in halide perovskites. Here, using homogenous halide perovskites single crystals, we report, in both one- and two-dimensional cases, the complete set of quantum fluid phase transitions from normal classical fluids to scatterless polariton superfluids and supersonic fluids—all at room temperature, clear consequences of the Landau criterion. Specifically, the supersonic Čerenkov wave pattern was observed at room temperature. The experimental results are also in quantitative agreement with theoretical predictions from the dissipative Gross-Pitaevskii equation. Our results set the stage for exploring the rich non-equilibrium quantum fluid many-body physics at room temperature and also pave the way for important polaritonic device applications.more » « less
-
Abstract We investigate a micro-scale model of superfluidity derived by Pitaevskii (1959Sov. Phys. JETP8282–7) to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model involves the nonlinear Schrödinger equation (NLS) and the Navier–Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. Depending on the nature of the nonlinearity in the NLS, we prove global/almost global existence of solutions to this system in —strong in wavefunction and velocity, and weak in density.more » « less
-
Abstract We examine a micro-scale model of superfluidity derived by Pitaevskii (Sov. Phys. JETP 8:282-287, 1959) which describes the interacting dynamics between superfluid He-4 and its normal fluid phase. This system consists of the nonlinear Schrödinger equation and the incompressible, inhomogeneous Navier-Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. The coupling permits mass/momentum/energy transfer between the phases, and accounts for the conversion of superfluid into normal fluid. We prove the existence of global weak solutions in$${\mathbb {T}}^3$$ for a power-type nonlinearity, beginning from small initial data. The main challenge is to control the inter-phase mass transfer in order to ensure the strict positivity of the normal fluid density, while obtaining time-independent a priori estimates.more » « less
-
We propose a new nonlinear preconditioned conjugate gradient (PCG) method in real arithmetic for computing the ground states of rotational Bose--Einstein condensate, modeled by the Gross--Pitaevskii equation. Our algorithm presents a few improvements of the PCG method in complex arithmetic studied by Antoine, Levitt, and Tang [J. Comput. Phys., 343 (2017), pp. 92--109]. We show that the special structure of the energy functional $$E(\phi)$$ and its gradient with respect to $$\phi$$ can be fully exploited in real arithmetic to evaluate them more efficiently. We propose a simple approach for fast evaluation of the energy functional, which enables exact line search. Most importantly, we derive the discrete Hessian operator of the energy functional and propose a shifted Hessian preconditioner for PCG, with which the ideal preconditioned Hessian has favorable eigenvalue distributions independent of the mesh size. This suggests that PCG with our ideal Hessian preconditioner is expected to exhibit mesh size-independent asymptomatic convergence behavior. In practice, our preconditioner is constructed by incomplete Cholesky factorization of the shifted discrete Hessian operator based on high-order finite difference discretizations. Numerical experiments in two-dimensional (2D) and three-dimensional (3D) domains show the efficiency of fast energy evaluation, the robustness of exact line search, and the improved convergence of PCG with our new preconditioner in iteration counts and runtime, notably for more challenging rotational BEC problems with high nonlinearity and rotational speed.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1209/0295-5075/ac9fed
