Seminars from 2023

Theoretical models describing quantum metrology schemes and the corresponding experimental demonstrations have so far mainly described step-by-step protocols that involve the preparation of the sensor into a carefully engineered quantum state; interaction of the sensor with an external (unknown) field and measurement of the sensor to retrieve information about the signal. However, the process of preparation can sometimes be lengthy and require fine tuning in time. The main goal of this project is to contribute to this challenge by using many-body interactions to entangle the state while the field encodes its information into it. In this way the process of preparing the state is eliminated along with the different challenges that come with it.

Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states Vanishing gradients can pose substantial obstacles for high-dimensional optimization problems. Here we consider energy minimization problems for quantum many-body systems with extensive Hamiltonians, which can be studied on classical computers or in the form of variational quantum eigensolvers on quantum computers. Barren plateaus correspond to scenarios where the average amplitude of the energy gradient decreases exponentially with increasing system size. This occurs, for example, for quantum neural networks and for brickwall quantum circuits when the depth increases polynomially in the system size. Here we show that the variational optimization problems for matrix product states, tree tensor networks, and the multiscale entanglement renormalization ansatz are free of barren plateaus. The derived scaling properties for the gradient variance provide an analytical guarantee for the trainability of randomly initialized tensor network states (TNS) and motivate certain initialization schemes. In a suitable representation, unitary tensors that parametrize the TNS are sampled according to the uniform Haar measure. We employ a Riemannian formulation of the gradient based optimizations which simplifies the analytical evaluation.

The dynamics of a qubit that is swept repeatedly through an avoided crossing is known as Landau-Zener-Stückelberg-Majorana (LZSM) interference. Lately it is used for demonstrating quantum coherence as well as for determining qubit parameters such as the T2 time. One method for recording these interference patterns is dispersive readout performed by measuring the transmission of a cavity coupled to the qubit. I will present a universal theory for dispersive readout of quantum systems in and out of equilibrium. It is based on the backaction of the measured system to the cavity obtained with non-equilibrium linear response theory, which provides the signal in terms of a system susceptibility [1] as well as resonance conditions that relate the cavity transmission to spectral properties and Berry phases. Examples are the readout of detuned qubits and thermally excited multi-level systems. For ac-driven quantum systems, we identify the relevant Fourier component of the susceptibility and introduce a computational scheme based on Floquet theory. The theory is applied to LZSM interference in Si/SiGe double quantum dots, where the interference patterns exhibit a harp-like structure stemming from the valley degree of freedom [2]. Moreover, the sub-structure of the LZSM pattern allows one to draw conclusions about the steady-state populations of the Floquet states [3,4].

There are multiple ways one can use tools from belief propagation for tensor networks, and these enable addressing a much larger scale of problem than usually possible – be it number of tensors or bond dimension. We introduce one algorithm that uses such tools, along with combining Schrodinger and Heisenberg pictures, to approximately simulate quantum dynamics on arbitrary graphs. We demonstrate the method on IBM’s recent 127 qubit ‘kicked Ising’ experiment, showing that it provides fast and converged results. The underlying compression and contraction primitives should be useful in a very wide range of settings.

Penning traps allow charged particles to be confined for long periods, without the use of time-varying fields. This gives rise to many advantageous properties for quantum science. I will give an overview of the fundamental aspects of trapping and operation of Penning traps, as well as describing applications to precision measurement, quantum simulation, and finally quantum computation.

Unlike their fermionic counterparts, systems of non-interacting bosons appear to lack any ability to support symmetry-protected topological (SPT) phases. In this talk, we report the emergence of non-trivial signatures of genuine SPT physics in metastable Markovian bosonic systems. Beginning with the closed-system setting, we discuss the main obstructions towards realizing SPT physics with non-interacting bosons and place a specific emphasis on the key differences with well-known examples of topological bosonic band structures, e.g., in photonic arrays. We then take the plunge into the open (Markovian) system setting in the hope to circumvent these obstructions and uncover convincing SPT signatures. Inspired by topological free fermions, we precisely characterize the properties any bosonic SPT signature must have, and consequentially, determine the class of bosonic dynamics that can support them: namely, those generated by topologically metastable quadratic bosonic Lindbladians. Such systems are shown to support tight analogues of Majorana fermions, which we deem “Majorana bosons”, and, when number symmetry is present, their U(1)-symmetric counterparts. Along the way, we discuss the subtle distinction between symmetry generators and conserved quantities in dissipative settings and present a nontrivial correspondence between these objects for non-interacting bosons. We further explore several models exemplifying they realm of potential realizations of these signatures and explore connections with topological amplification, the non-Hermitian skin effect, and non-reciprocal transport. Finally, we discuss observable consequences of topological metastability in the form of zero-frequency power-spectral peaks and long-lived, macroscopically separated (in space), quantum correlations.

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

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.

Everett’s many worlds interpretation (MWI) is one of the most widely discussed topics in contemporary fundamental science, yet discussions of it most often remain at a superficial and qualitative level. The goal of this talk is to convince you that a more quantitative discussion is needed and possible using tools from statistical mechanics. To this end, I start by introducing the MWI and its problems. I then review the decoherent histories formalism, which allows to address various problems of the MWI. Based on it, the following two (mostly numerical) results are discussed. First, I argue that the basic mechanism of decoherence are slow and coarse observables of isolated non-integrable many-body systems. Those show exponentially suppressed interference effects as a function of the particle number of the system, if probed a few times. However, things start to change drastically for very long histories (e.g., many repetitions in a quantum coin flip experiment). The “branches” of the many worlds “tree” then suddenly acquire a non-trivial structure, with decoherence surviving only on a very small subset of branches. Remarkably, those surviving classical branches are exactly those that sample frequencies according to Born’s rule.

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).

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.

The generation of non-classically correlated states of light is a crucial ingredient for quantum technologies based on quantum optics. In order to achieve this, we need interfaces that induce effective interactions between individual photons. This can be realized by chirally coupling an array of two-level atoms to a waveguide. As the atoms cannot be excited twice, photons propagating through the waveguide will build up spatial correlations as they are individually absorbed and emitted by the atoms. A fundamental limit to this mechanism is the spontaneous emission of the atoms into free space. In this thesis we show, by properly considering the vacuum emission, that wave interference phenomena of the fields can protect certain modes from decaying into free space, when the array is periodic and dense enough. This phenomenon is called subradiance. Subradiance will allow for the building of special two photon correlations with fermionic characteristics, protected against losses through the propagation. We perform numerical and analytical methods to understand the relation between fermionization and subradiance.

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.

Light-matter interactions play a central role in understanding the world around us. Their study has fueled significant advances enabling the expansion of the frontiers of knowledge and the design of novel technological applications. In this context, the extension of the ideas associated with the topological phases of matter to the photonics realm stands as an exciting challenge since they can modify the way in which these interactions take place. In this talk we discuss different light-matter interaction phenomena occurring in a photonic Weyl system, i.e., a paradigmatic example of a 3D topological gapless phase. We investigate the coupling of one or more emitters to both the bulk and boundary modes of a Weyl photonic lattice. Among other things, we study the emergence of topological atom-photon bound states that mediate long-range and tunable interactions between emitters, as well as exotic ways of probing and harnessing the Fermi arc surface modes of the Weyl photonic environment. Furthermore, we show how a Weyl system hosting a pair of frequency isolated Weyl points can be implemented in a subwavelength atomic array.

Quantum metrology develops techniques that improve the measurement resolution of parameters encoded in quantum states. The quantum states of light or of trapped atomic ensembles are defined not only by the quantum state itself, but also by the shape of the modes that this state occupies. Parameters that determine a quantum optical mode include the spatial and temporal shape as well as the frequency spectrum. The estimation of these parameters is of high interest for applications in imaging, timing, positioning, and precision spectroscopy. In this talk we present a quantum theory for the estimation of mode parameters. We demonstrate that the population of suitably designed modes with nonclassical states enables quantum enhancements for the estimation of arbitrary mode parameters. We discuss applications of our results in the context of superresolution imaging and displacement sensing.

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.

We consider the use of quantum many-body systems as analog quantum simulators, and how it fares in the presence of errors, particularly when computing thermodynamic limit observables. For this purpose, we introduce the framework of stable quantum simulation tasks and fit into it known and new results for systems both in and out of equilibrium. In this context, we also discuss the notion of quantum advantage for near-term quantum simulation without error correction. Based on arXiv:2212.04924.

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.

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.

This seminar is divided in two parts. In the first half, we explore the dynamics of quantum many-body systems when certain unconventional quantities are conserved. We will show that the conservation of a charge and its associated dipole moment leads to a provable fragmentation of the Hilbert space into exponentially many disconnected sectors. In turn, this leads to novel universal hydrodynamic behavior, and can translate into non-vanishing bulk correlators and the existence of localized boundary modes akin strong zero modes, among other unexpected phenomena both in and out of equilibrium. We then show that dipole-conserving models become good approximations of strongly-tilted interacting systems, and discuss ultra-cold atoms experiments in this regime. So far measurements only appeared as a mean to probe the system of interest. Nonetheless, they can also be a useful resource to realize novel quantum phenomena. In this second half of the talk, we study the impact of measurements on the paradigmatic Ising quantum critical chain. We show that measurements can qualitatively alter long-distance correlations in a manner dependent on the measurement protocol and the nature of ancilla correlations. Measurements can, for example, modify the Ising order parameter scaling dimension and catalyze order parameter condensation. We derive numerous quantitative predictions for the behavior of correlations in select measurement outcomes, and also identify two strategies for detecting measurement-altered Ising criticality in measurement-averaged quantities. In particular we show that, in certain cases, observables can be averaged separately over measurement outcomes residing in distinct symmetry sectors; we demonstrate that these `symmetry-resolved averages’ reveal measurement effects even when considering standard linearly averaged observables. Our framework naturally adapts to more exotic quantum critical points and highlights opportunities for potential experimental realization in Rydberg arrays.

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.

Parameterized quantum circuits serve as ansätze for solving variational problems and provide a flexible paradigm for programming near-term quantum computers. Here we discuss three fundamental criteria for this paradigm to be effective: expressibility, trainability and generalisability. We will introduce these concepts and present recent analytic progress quantifying to what extent these criteria can be achieved. While more generally applicable, the discussion will be framed around the example of trying to variationally learn an unknown quantum process. We will end with some more open-ended dreaming about the applications of these ideas for experimental quantum physics and quantum compilation.