Seminars from 2023

A quantum computer attains computational advantage when outperforming the best classical computers running the best-known algorithms on well-defined tasks. We report quantum computational advantage using Borealis, a photonic processor offering dynamic programmability on all gates implemented. We carry out Gaussian boson sampling (GBS) on 216 squeezed modes entangled with three-dimensional connectivity, 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.

The ultra-strong coupling regime in light-matter interactions requires non-perturbative methods, for example, to calculate the radiation emitted from an atom. In this talk, I will discuss how star-to-chain transformations may be utilised for such tasks, when combined with methods based on matrix product or Gaussian states, respectively. Being well known in the study of open quantum systems, we demonstrate that the approach allows us to also treat field observables – both in vacuum states and thermal states of the field. As applications, here I consider giant atoms in the ultra-strong coupling regime [1], and the emission from a uniformly accelerated emitter in the Unruh effect [2].
[1] D. D. Noachtar, JK, R. H. Jonsson, “Nonperturbative treatment of giant atoms using chain transformations”, PRA 106, 013702 (2022).[2] R. H. Jonsson, JK, “Chain-mapping methods for relativistic light-matter interactions”, in preparation (2023).

Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network statesVanishing gradients can pose substantial obstacles for high-dimensionaloptimization problems. Here we consider energy minimization problems forquantum many-body systems with extensive Hamiltonians, which can be studied onclassical computers or in the form of variational quantum eigensolvers onquantum computers. Barren plateaus correspond to scenarios where the averageamplitude of the energy gradient decreases exponentially with increasing systemsize. This occurs, for example, for quantum neural networks and for brickwallquantum circuits when the depth increases polynomially in the system size. Herewe show that the variational optimization problems for matrix product states,tree tensor networks, and the multiscale entanglement renormalization ansatzare free of barren plateaus. The derived scaling properties for the gradientvariance provide an analytical guarantee for the trainability of randomlyinitialized tensor network states (TNS) and motivate certain initializationschemes. In a suitable representation, unitary tensors that parametrize the TNSare sampled according to the uniform Haar measure. We employ a Riemannianformulation of the gradient based optimizations which simplifies the analyticalevaluation.

I will introduce a family of dual-unitary circuits (QCAs) in 1+1 dimensions which are invariant under Lorentz and scale transformations. With the same dual unitaries I will construct tensor-network states for this 1+1 model and interpret them as spatial slices of curved 2+1 discrete geometries. These tensor-network states satisfy the Ryu-Takayanagi relationship between entanglement and geometry, but they provide much more, they contain a complete description of the geometry which includes the interior of black holes, a feature that is not so stransparent in standard AdS/CFT. The dynamics of the circuit induces a natural dynamics on these geometries which reproduces gravitational phenomena like gravitational time dilation, the formation of black holes and the growth of their throat.

In this talk, I will discuss several aspects of critical quantum metrology, that is the estimation of parameters of many-body systems close to a quantum critical point. We will first derive a no-go result stating that any non-adaptive measurement strategy will fail to exploit quantum critical enhancement (i.e. precision beyond the shot-noise limit) for a sufficiently large number of particles. We will then consider different adaptive strategies that can overcome this no-go bound, and illustrate their performance in the estimation of (i) a magnetic field using as a probe a 1D spin Ising chain and (ii) the coupling strength in a Bose-Hubbard square lattice. Finally, and if time allows, I will also present on-going efforts to the understanding of the form of optimal interacting spin networks for measuring low temperatures and magnetic fields. This talk is based on arXiv:2211.07688, and also party on arXiv:2211.01934.

We study the incoherent transport of bosonic particles through a one dimensional lattice with different left and right hopping rates, as modelled by the asymmetric simple inclusion process (ASIP). Specifically, we show that as the current passing through this system increases, a transition occurs, which is signified by the appearance of a characteristic zigzag pattern in the stationary density profile near the boundary. In this highly unusual transport phase, the local particle distribution alternates on every site between a thermal distribution and a Bose-condensed state with broken U(1)-symmetry. Furthermore, we show that the onset of this phase is closely related to the so-called non-Hermitian skin effect and coincides with an exceptional point in the spectrum of density fluctuations. Therefore, this effect establishes a direct connection between quantum transport, non-equilibrium condensation phenomena and non-Hermitian topology, which can be probed in cold-atom experiments or in systems with long-lived photonic, polaritonic and plasmonic excitations.

Quantum acoustics explores the non-classical dynamics of vibrating mechanical systems –– pendulums oscillating at exceedingly high frequencies with vanishingly small amplitudes [1]. It constitutes an entirely new platform for implementing quantum technologies, and offers to cooperate with optical and electronic components to form a new paradigm of hybrid quantum systems. However, at the moment quantum acoustics lacks a central component that enabled the success of the optical or electronic platforms –– a source of a quantum nonlinearity. In this talk I will show two platforms which can implement this key characteristic: strain-coupled transitions between states of an NV which form an acoustic two-level system [3], and a molecular vibration with strong anharmonicity [4]. [1] M. Aspelmeyer et al., “Cavity optomechanics,” Rev. Mod. Phys. 86, 1391 (2014).[2] D. Lee et al., “Topical review: spins and mechanics in diamond,” J. Opt. 19, 033001 (2017).[3] M. K. Schmidt et al., “Acoustic diamond resonators with ultra-small mode volumes,” Phys. Rev. Research 2, 033153 (2021).[4] M. K. Schmidt and M. J. Steel, “Molecular optomechanics in the anharmonic regime,” in preparation.

Waveguides allow interconnecting systems at long distances with low losses, the most successful example being the optical fiber-based worldwide internet. In quantum optics, one can use waveguides to couple distant quantum emitters via a common electromagnetic mode, a field known as waveguide quantum electrodynamics (wQED). As we test the limits of such systems, standard quantum optical effects must be revisited and revised. In this talk, I will discuss theoretical considerations and physical effects that arise when two distant two-level systems interact through a waveguide. In particular, I will present novel phenomena such as radiation beyond standard superradiance, formation of bound states in the continuum, entanglement-dependent directional emission, and spontaneous entanglement generation.

Quantum systems of many interacting particles appear in numerous branches of physics, from condensed matter to statistical or high energy physics. Their study, however, is often very complicated due to the high dimensions of the Hilbert spaces involved.The field of quantum information brings a new perspective to the study of those systems. Through it, we can rigorously analyze whether specific physical problems are fundamentally complex, and will require a quantum computer, or whether they can be solved efficiently with (classical) numerical means.In this talk, we show how many interesting properties about many-body systems both in equilibrium and out of it can be computed in polynomial time, with provable efficiency guarantees. In particular, we focus on the classical simulation of Gibbs or thermal states, and on the simulation of arbitrary dynamics for short times. We do this through the frameworks of tensor network methods, as well as cluster expansions, which highlight how fundamental physical features, such as locality, constrain the complexity of quantum systems.

I will review the use of cluster expansion to bound the complexity of some quantum tasks

The dynamics of a qubit that is swept repeatedly through anavoided crossing is known as Landau-Zener-Stückelberg-Majorana(LZSM) interference. Lately it is used for demonstrating quantumcoherence as well as for determining qubit parameters such as theT2 time. One method for recording these interference patterns isdispersive readout performed by measuring the transmission of acavity coupled to the qubit. I will present a universaltheory for dispersive readout of quantum systems in and out ofequilibrium. It is based on the backaction of the measuredsystem to the cavity obtained with non-equilibrium linearresponse theory, which provides the signal in terms of a systemsusceptibility [1] as well as resonance conditions that relatethe cavity transmission to spectral properties and Berry phases.Examples are the readout of detuned qubits and thermallyexcited multi-level systems. For ac-driven quantum systems, weidentify the relevant Fourier component of the susceptibility andintroduce a computational scheme based on Floquet theory. Thetheory is applied to LZSM interference in Si/SiGe double quantumdots, where the interference patterns exhibit a harp-likestructure stemming from the valley degree of freedom [2].Moreover, the sub-structure of the LZSM pattern allows one todraw conclusions about the steady-state populations of theFloquet states [3,4].

Quantum processors have great potential to solve computationally intractable problems, and to deepen our understanding of complex quantum systems. Yet, mapping of an initial spin-state to a general target quantum state, one of the central functions of the processor, often requires the application of numerous high-fidelity entangling operations. As the number of such two-qubit operations scales exponentially with the number of spins, efficient implementations might benefit from techniques that extend beyond the quantum gate model and harness native resources of the physical platform. In the talk, I will present new avenues to realize quantum gates and simulations using trapped-ion systems beyond the quantum gate model. I will describe a single-step protocol to generate native, N-body entangling interactions between trapped-ion spins, using spin-dependent squeezing. Then, I will present our latest quantum simulations using simultaneous and reconfigurable spin-spin interactions, enabling the emergence and preparation of exotic phases of matter. Finally, I will outline an avenue to program a dense graph of couplings between the long-lived phonon modes in trapped-ion crystals, paving the path to programmable quantum simulations of bosonic and spin-boson systems on currently available devices.