Quantum computational advantage with a programmable photonic processor.

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. No photonic machine offering programmability over all its quantum gates has demonstrated quantum computational advantage: previous machines1,2 were largely restricted to static gate sequences. Earlier photonic demonstrations were also vulnerable to spoofing3, in which classical heuristics produce samples, without direct simulation, lying closer to the ideal distribution than do samples from the quantum hardware. Here we report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling4 (GBS) on 216 squeezed modes entangled with three-dimensional connectivity5, using a time-multiplexed and photon-number-resolving architecture. On average, it would take more than 9,000 years for the best available algorithms and supercomputers to produce, using exact methods, a single sample from the programmed distribution, whereas Borealis requires only 36 µs. This runtime advantage is over 50 million times as extreme as that reported from earlier photonic machines. Ours constitutes a very large GBS experiment, registering events with up to 219 photons and a mean photon number of 125. This work is a critical milestone on the path to a practical quantum computer, validating key technological features of photonics as a platform for this goal.

Sign-Changing Photon-Mediated Atom Interactions in Multimode Cavity Quantum Electrodynamics.

Sign-changing interactions constitute a crucial ingredient in the creation of frustrated many-body systems such as spin glasses. We present here the demonstration of a photon-mediated sign-changing interaction between Bose-Einstein-condensed atoms in a confocal cavity. The interaction between two atoms is of an unusual, nonlocal form proportional to the cosine of the inner product of the atoms' position vectors. This interaction arises from the differing Gouy phase shifts of the cavity's degenerate modes. The interaction drives a nonequilibrium Dicke-type phase transition in the system leading to atomic checkerboard density-wave order. Because of the Gouy phase anomalies, the checkerboard pattern can assume either a sinelike or cosinelike character. This state is detected via the holographic imaging of the cavity's superradiant emission. Together with a companion paper [Y. Guo, V. D. Vaidya, R. M. Kroeze, R. A. Lunney, B. L. Lev, and J. Keeling, Emergent and broken symmetries of atomic self-organization arising from Gouy phases in multimode cavity QED, Phys. Rev. A 99, 053818 (2019)PLRAAN2469-992610.1103/PhysRevA.99.053818], we explore this interaction's influence on superradiant phase transitions in multimode cavities. Employing this interaction in cavity QED spin systems may enable the creation of artificial spin glasses and quantum neural networks.

Spinor Self-Ordering of a Quantum Gas in a Cavity.

We observe the joint spin-spatial (spinor) self-organization of a two-component Bose-Einstein condensate (BEC) strongly coupled to an optical cavity. This unusual nonequilibrium Hepp-Lieb-Dicke phase transition is driven by an off-resonant Raman transition formed from a classical pump field and the emergent quantum dynamical cavity field. This mediates a spinor-spinor interaction that, above a critical strength, simultaneously organizes opposite spinor states of the BEC on opposite checkerboard configurations of an emergent 2D lattice. The resulting spinor density-wave polariton condensate is observed by directly detecting the atomic spin and momentum state and by holographically reconstructing the phase of the emitted cavity field. The latter provides a direct measure of the spin state, and a spin-spatial domain wall is observed. The photon-mediated spin interactions demonstrated here may be engineered to create dynamical gauge fields and quantum spin glasses.

Supermode-density-wave-polariton condensation with a Bose-Einstein condensate in a multimode cavity.

Phase transitions, where observable properties of a many-body system change discontinuously, can occur in both open and closed systems. By placing cold atoms in optical cavities and inducing strong coupling between light and excitations of the atoms, one can experimentally study phase transitions of open quantum systems. Here we observe and study a non-equilibrium phase transition, the condensation of supermode-density-wave polaritons. These polaritons are formed from a superposition of cavity photon eigenmodes (a supermode), coupled to atomic density waves of a quantum gas. As the cavity supports multiple photon spatial modes and because the light-matter coupling can be comparable to the energy splitting of these modes, the composition of the supermode polariton is changed by the light-matter coupling on condensation. By demonstrating the ability to observe and understand density-wave-polariton condensation in the few-mode-degenerate cavity regime, our results show the potential to study similar questions in fully multimode cavities.