We present an unconstrained tree-tensor-network approach to the study of lattice gauge theories in two spatial dimensions, showing how to perform numerical simulations of theories in the presence of fermionic matter and four-body magnetic terms, at zero and finite density, with periodic and open boundary conditions. We exploit the quantum-link representation of the gauge fields and demonstrate that a fermionic rishon representation of the quantum links allows us to efficiently handle the fermionic matter while finite densities are naturally enclosed in the tensor network description. We explicitly perform calculations for quantum electrodynamics in the spin-one quantum-link representation on lattice sizes of up to $16\times 16$ sites, detecting and characterizing different quantum regimes. In particular, at finite density, we detect signatures of a phase separation as a function of the bare mass values at different filling densities. The presented approach can be extended straightforwardly to three spatial dimensions.

An ultimate goal of quantum computing is to perform calculations beyond the reach of any classical computer. It is therefore imperative that useful quantum computers be very difficult to simulate classically, otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably exponentially difficult to simulate: the classical resources required grow exponentially with the number of qubits $N$ or the depth $D$ of the circuit. This difficulty has triggered recent experiments on deep, random circuits that aim to demonstrate that quantum devices may already perform tasks beyond the reach of classical computing. These real quantum computing devices, however, suffer from many sources of decoherence and imprecision which limit the degree of entanglement that can actually be reached to a fraction of its theoretical maximum. They are characterized by an exponentially decaying fidelity $\mathcal{F}\sim (1-\epsilon {)}^{ND}$ with an error rate $\epsilon$ per operation as small as $\approx 1\%$ for current devices with several dozen qubits or even smaller for smaller devices. In this work, we provide new insight on the computing capabilities of real quantum computers by demonstrating that they can be simulated at a tiny fraction of the cost that would be needed for a perfect quantum computer. Our algorithms compress the representations of quantum wave functions using matrix product states, which are able to capture states with low to moderate entanglement very accurately. This compression introduces a finite error rate $\epsilon$ so that the algorithms closely mimic the behavior of real quantum computing devices. The computing time of our algorithm increases only linearly with $N$ and $D$ in sharp contrast with exact simulation algorithms. We illustrate our algorithms with simulations of random circuits for qubits connected in both one- and two-dimensional lattices. We find that $\epsilon$ can be decreased at a polynomial cost in computing power down to a minimum error ${\epsilon }_{\infty }$. Getting below ${\epsilon }_{\infty }$ requires computing resources that increase exponentially with ${\epsilon }_{\infty }/\epsilon$. For a two-dimensional array of $N=54$ qubits and a circuit with control-$Z$ gates, error rates better than state-of-the-art devices can be obtained on a laptop in a few hours. For more complex gates such as a swap gate followed by a controlled rotation, the error rate increases by a factor 3 for similar computing time. Our results suggest that, despite the high fidelity reached by quantum devices, only a tiny fraction $(\sim {10}^{-8})$ of the system Hilbert space is actually being exploited.

To what extent does Noether’s principle apply to quantum channels? Here, we quantify the degree to which imposing a symmetry constraint on quantum channels implies a conservation law and show that this relates to physically impossible transformations in quantum theory, such as time reversal and spin inversion. In this analysis, the convex structure and extremal points of the set of quantum channels symmetric under the action of a Lie group $G$ becomes essential. It allows us to derive bounds on the deviation from conservation laws under any symmetric quantum channel in terms of the deviation from closed dynamics as measured by the unitarity of the channel $\mathcal{E}$. In particular, we investigate in detail the U(1) and SU(2) symmetries related to energy and angular momentum conservation laws. In the latter case, we provide fundamental limits on how much a spin-$j_A$ system can be used to polarize a larger spin-$j_B$ system, and on how much one can invert spin polarization using a rotationally symmetric operation. Finally, we also establish novel links between unitarity, complementary channels, and purity that are of independent interest.

The light-matter interaction can be utilized to qualitatively alter physical properties of materials. Recent theoretical and experimental studies have explored this possibility of controlling matter by light based on driving many-body systems via strong classical electromagnetic radiation, leading to a time-dependent Hamiltonian for electronic or lattice degrees of freedom. To avoid inevitable heating, pump-probe setups with ultrashort laser pulses have so far been used to study transient light-induced modifications in materials. Here, we pursue yet another direction of controlling quantum matter by modifying quantum fluctuations of its electromagnetic environment. In contrast to earlier proposals on light-enhanced electron-electron interactions, we consider a dipolar quantum many-body system embedded in a cavity composed of metal mirrors and formulate a theoretical framework to manipulate its equilibrium properties on the basis of quantum light-matter interaction. We analyze hybridization of different types of the fundamental excitations, including dipolar phonons, cavity photons, and plasmons in metal mirrors, arising from the cavity confinement in the regime of strong light-matter interaction. This hybridization qualitatively alters the nature of the collective excitations and can be used to selectively control energy-level structures in a wide range of platforms. Most notably, in quantum paraelectrics, we show that the cavity-induced softening of infrared optical phonons enhances the ferroelectric phase in comparison with the bulk materials. Our findings suggest an intriguing possibility of inducing a superradiant-type transition via the light-matter coupling without external pumping. We also discuss possible applications of the cavity-induced modifications in collective excitations to molecular materials and excitonic devices.

We introduce a dynamical picture, referred to as correlation picture, which connects a correlated bipartite state to its uncorrelated counterpart. This picture allows us to derive an exact dynamical equation for a general open-system dynamics with system-environment correlations included. This exact dynamics is in the form of a Lindblad-like equation even in the presence of initial system-environment correlations. For explicit calculations, we also develop a weak-correlation expansion that allows us to introduce systematic perturbative approximations. This expansion provides approximate master equations that can feature advantages over existing weak-coupling techniques. As a special case, we derive a Markovian master equation, which is different from existing approaches. We compare our equations with corresponding standard weak-coupling equations using two examples, for which our correlation-picture formalism is more accurate, or at least as accurate as the weak-coupling equations.

Continuously monitoring the environment of a quantum many-body system reduces the entropy of (purifies) the reduced density matrix of the system, conditional on the outcomes of the measurements. We show that, for mixed initial states, a balanced competition between measurements and entangling interactions within the system can result in a dynamical purification phase transition between (i) a phase that locally purifies at a constant system-size-independent rate and (ii) a “mixed” phase where the purification time diverges exponentially in the system size. The residual entropy density in the mixed phase implies the existence of a quantum error-protected subspace, where quantum information is reliably encoded against the future nonunitary evolution of the system. We show that these codes are of potential relevance to fault-tolerant quantum computation as they are often highly degenerate and satisfy optimal trade-offs between encoded information densities and error thresholds. In spatially local models in $1+1$ dimensions, this phase transition for mixed initial states occurs concurrently with a recently identified class of entanglement phase transitions for pure initial states. The purification transition studied here also generalizes to systems with long-range interactions, where conventional notions of entanglement transitions have to be reformulated. We numerically explore this transition for monitored random quantum circuits in $1+1$ dimensions and all-to-all models. Unlike in pure initial states, the mutual information of an initially completely mixed state in $1+1$ dimensions grows sublinearly in time due to the formation of the error-protected subspace. Purification dynamics is likely a more robust probe of the transition in experiments, where imperfections generically reduce entanglement and drive the system towards mixed states. We describe the motivations for studying this novel class of nonequilibrium quantum dynamics in the context of advanced quantum computing platforms and fault-tolerant quantum computation.

In the past decades, it was recognized that quantum chaos, which is essential for the emergence of statistical mechanics and thermodynamics, manifests itself in the effective description of the eigenstates of chaotic Hamiltonians through random matrix ensembles and the eigenstate thermalization hypothesis. Standard measures of chaos in quantum many-body systems are level statistics and the spectral form factor. In this work, we show that the norm of the adiabatic gauge potential, the generator of adiabatic deformations between eigenstates, serves as a much more sensitive measure of quantum chaos. We are able to detect transitions from integrable to chaotic behavior at perturbation strengths orders of magnitude smaller than those required for standard measures. Using this alternative probe in two generic classes of spin chains, we show that the chaotic threshold decreases exponentially with system size and that one can immediately detect integrability-breaking (chaotic) perturbations by analyzing infinitesimal perturbations even at the integrable point. In some cases, small integrability breaking is shown to lead to anomalously slow relaxation of the system, exponentially long in system size.

The existence of fundamentally identical particles represents a foundational distinction between classical and quantum mechanics. Because of their exchange symmetry, identical particles can appear to be entangled—another uniquely quantum phenomenon with far-reaching practical implications. However, a long-standing debate has questioned whether identical particle entanglement is physical or merely a mathematical artifact. In this work, we provide such particle entanglement with a consistent theoretical description as a quantum resource in processes frequently encountered in optical and cold atomic systems. This leads to a plethora of applications of immediate practical impact. On the one hand, we show that the metrological advantage for estimating phase shifts in systems of identical bosons amounts to a measure of their particle entanglement, with a clear-cut operational meaning. On the other hand, we demonstrate in general terms that particle entanglement is the property resulting in directly usable mode entanglement when distributed to separated parties, with particle conservation laws in play. Application of our tools to an experimental implementation with Bose-Einstein condensates leads to the first quantitative estimation of identical particle entanglement. Further connections are revealed between particle entanglement and other resources such as optical nonclassicality and quantum coherence. Overall, this work marks a resolutive step in the ongoing debate by delivering a unifying conceptual and practical understanding of entanglement between identical particles.

Spins in gate-defined silicon quantum dots are promising candidates for implementing large-scale quantum computing. To read the spin state of these qubits, the mechanism that has provided the highest fidelity is spin-to-charge conversion via singlet-triplet spin blockade, which can be detected in situ using gate-based dispersive sensing. In systems with a complex energy spectrum, like silicon quantum dots, accurately identifying when singlet-triplet blockade occurs is hence of major importance for scalable qubit readout. In this work, we present a description of spin-blockade physics in a tunnel-coupled silicon double quantum dot defined in the corners of a split-gate transistor. Using gate-based magnetospectroscopy, we report successive steps of spin blockade and spin-blockade lifting involving spin states with total spin angular momentum up to $S=3$. More particularly, we report the formation of a hybridized spin-quintet state and show triplet-quintet and quintet-septet spin blockade, enabling studies of the quintet relaxation dynamics from which we find $T_1\sim 4\mu \mathrm{s}$. Finally, we develop a quantum capacitance model that can be applied generally to reconstruct the energy spectrum of a double quantum dot, including the spin-dependent tunnel couplings and the energy splitting between different spin manifolds. Our results allow for the possibility of using Si complementary metal-oxide-semiconductor quantum dots as a tunable platform for studying high-spin systems.

We investigate Feshbach resonances in collisions of high-spin atoms such as Er and Dy with closed-shell atoms such as Sr and Yb, using coupled-channel scattering and bound-state calculations. We consider both low-anisotropy and high-anisotropy limits. In both regimes, we find many resonances with a wide variety of widths. The wider resonances are suitable for tuning interatomic interactions, while some of the narrower resonances are highly suitable for magnetoassociation to form high-spin molecules. These molecules might be transferred to short-range states, where they would have large magnetic moments and electric dipole moments that can be induced with very low electric fields. The results offer the opportunity to study mixed quantum gases where one species is dipolar and the other is not and open up important prospects for a new field of ultracold high-spin polar molecules.

A promising route to realize entangled magnetic states combines geometrical frustration with quantum-tunneling effects. Spin-ice materials are canonical examples of frustration, and Ising spins in a transverse magnetic field are the simplest many-body model of quantum tunneling. Here, we show that the tripod-kagome lattice material ${\mathrm{Ho}}_3{\mathrm{Mg}}_2{\mathrm{Sb}}_3{\mathrm{O}}_{14}$ unites an icelike magnetic degeneracy with quantum-tunneling terms generated by an intrinsic splitting of the ${\mathrm{Ho}}^{3+}$ ground-state doublet, which is further coupled to a nuclear spin bath. Using neutron scattering and thermodynamic experiments, we observe a symmetry-breaking transition at $T^{*}\approx 0.32\mathrm{K}$ to a remarkable state with three peculiarities: a concurrent recovery of magnetic entropy associated with the strongly coupled electronic and nuclear degrees of freedom; a fragmentation of the spin into periodic and icelike components; and persistent inelastic magnetic excitations down to $T\approx 0.12\mathrm{K}$. These observations deviate from expectations of classical spin fragmentation on a kagome lattice, but can be understood within a model of dipolar kagome ice under a homogeneous transverse magnetic field, which we survey with exact diagonalization on small clusters and mean-field calculations. In ${\mathrm{Ho}}_3{\mathrm{Mg}}_2{\mathrm{Sb}}_3{\mathrm{O}}_{14}$, hyperfine interactions dramatically alter the single-ion and collective properties, and suppress possible quantum correlations, rendering the fragmentation with predominantly single-ion quantum fluctuations. Our results highlight the crucial role played by hyperfine interactions in frustrated quantum magnets and motivate further investigations of the role of quantum fluctuations on partially ordered magnetic states.

We report on the cancellation of quantum backaction noise in an optomechanical cavity. We perform measurements of the displacement of the microresonator, one in reflection of the cavity and one in transmission of the cavity. We show that measuring the amplitude quadrature of the light transmitted by the optomechanical cavity allows us to cancel the backaction noise between 2 and 50 kHz as a consequence of the strong optical spring present in the detuned cavity. This cancellation yields a more sensitive measurement of the microresonator’s position with a 2 dB increase in sensitivity. To confirm that the backaction is eliminated, we measure the noise in the transmission signal as a function of circulating power and use a correlation technique between two photodetectors to remove shot noise. Remaining backaction noise would be observable as a power-dependent noise floor, which is not observed. Eliminating the effects of backaction in this frequency regime is an important demonstration of a technique that could be used to mitigate the effects of backaction in interferometric gravitational wave detectors such as Advanced LIGO, VIRGO, and KAGRA.

We present a new method for the spectral characterization of pulsed twin-beam sources in the high-gain regime, using cascaded stimulated emission. We show an implementation of this method for a periodically poled potassium titanyl phosphate spontaneous parametric down-conversion source generating up to 60 photon pairs per pulse, and we demonstrate excellent agreement between our experiments and our theory. This work enables the complete and accurate experimental characterization of high-gain effects in parametric down-conversion, including self- and cross-phase modulation. Moreover, our theory allows the exploration of designs with the goal of improving the specifications of twin-beam sources for application in quantum information, computation, sampling, and metrology.

We present the first experimental determination of the intra-atomic exchange energy between the inner $4f$ and the outer $6s5d$ shells in rare-earth elements. Inelastic electron tunneling spectroscopy on individual rare-earth atoms adsorbed on metal-supported graphene reveals an element-dependent excitation, with energy between 30 and 170 meV, linearly increasing with the spin angular momentum of the $4f$ shell. This observation is possible owing to the strong spin polarization of the outer shells, characteristic of rare-earth adatoms on graphene. This polarization gives rise to a giant magnetoresistance of up to 75% observed for Dy on $\mathrm{graphene}/\mathrm{Ir}(111)$ single-atom magnets. Density functional theory calculations of the $6s5d$ shell spin polarizations and of their intra-atomic exchange constants with the $4f$ shell yield exchange energies in agreement with the experimental values. These results prove that the description of the spin dynamics in RE considering only the $4f-5d$ interaction is oversimplified. A more realistic treatment requires us to consider a multishell intra-atomic exchange in which both $6s$ and $5d$ shells are taken into account, with the $4f-6s$ contribution possibly prevailing over the $4f-5d$ one. Our findings are important for the general understanding of magnetism in rare earths, whether they are in bulk compounds or as surface adsorbed atoms and clusters. The results presented here also push for a revision of the description of the spin dynamics in rare-earth-based systems.

Laser-dressed photoemission spectroscopy has established itself as the gold standard of attosecond temporal metrology. In this technique, the attosecond structure of an extreme-ultraviolet pulse is retrieved from the wave function of the electron wave packet released during photoionization. Here, we show that this electron wave packet should rather be described using the density matrix formalism, thus allowing one to account for all processes that can affect its coherence, from the attosecond pulse generation to the photoemission and the measurement processes. Using this approach, we reconstruct experimentally a partially coherent electron wave packet with a purity of 0.11 (1 for full coherence). Comparison with theoretical models then allows us to identify the origins of this decoherence and to overcome several limitations such as beam-line instabilities or spectrometer resolution. Furthermore, we show numerically how this method gives access to the coherence and eigencomponents of complex photoelectron wave packets. It thus goes beyond the current measurement of photoionization time delays and provides a general framework for the analysis and understanding of complex photoemission processes.

We introduce the Rydberg composite, a new class of Rydberg matter where a single Rydberg atom is interfaced with a dense environment of neutral ground state atoms. The properties of the composite depend on both the Rydberg excitation, which provides the gross energetic and spatial scales, and the distribution of ground state atoms within the volume of the Rydberg wave function, which sculpt the electronic states. The latter range from the “trilobites,” for small numbers of scatterers, to delocalized and chaotic eigenstates, for disordered scatterer arrays, culminating in the dense scatterer limit in symmetry-dominated wave functions which promise good control in future experiments. We discuss one-, two-, and three-dimensional arrangements of scatterers using different theoretical methods, enabling us to obtain scaling behavior for the regular spectrum and measures of chaos and delocalization in the disordered regime. We also show that analogous quantum dot composites can elucidate in particular the dense scatterer limit. Thus, we obtain a systematic description of the composite states. The two-dimensional monolayer composite possesses the richest spectrum with an intricate band structure in the limit of homogeneous scatterers, experimentally accessible with pancake-shaped condensates.

We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at a fixed temperature and chemical potential. Our method works at a finite temperature, beyond linear response and weak system-reservoir coupling, and allows for nonquadratic interactions in the working medium. The method uses mesoscopic reservoirs, continuously damped toward thermal equilibrium, in order to represent continuum baths and a novel tensor-network algorithm to simulate the steady-state thermodynamics. Using the example of a quantum-dot heat engine, we demonstrate that our technique replicates the well-known Landauer-Büttiker theory for efficiency and power. We then go beyond the quadratic limit to demonstrate the capability of our method by simulating a three-site machine with nonquadratic interactions. Remarkably, we find that such interactions lead to power enhancement, without being detrimental to the efficiency. Furthermore, we demonstrate the capability of our method to tackle complex many-body systems by extracting the superdiffusive exponent for high-temperature transport in the isotropic Heisenberg model. Finally, we discuss transport in the gapless phase of the anisotropic Heisenberg model at a finite temperature and its connection to charge conjugation parity, going beyond the predictions of single-site boundary driving configurations.

The spectral gap problem—determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations—pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum-spin systems in two (or more) spatial dimensions: There exists no algorithm that determines in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one-dimensional spin systems are simpler than their higher-dimensional counterparts: For example, they cannot have thermal phase transitions or topological order, and there exist highly effective numerical algorithms such as the density matrix renormalization group—and even provably polynomial-time ones—for gapped 1D systems, exploiting the fact that such systems obey an entropy area law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are not possible in 1D. So does the spectral gap problem become decidable in 1D? In this paper, we prove this is not the case by constructing a family of 1D spin chains with translationally invariant nearest-neighbor interactions for which no algorithm can determine the presence of a spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable as in higher dimensions, but it also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with a constant spectral gap and nondegenerate classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behavior with dense spectrum.

We report the experimental observation of a spatiotemporal Hong-Ou-Mandel (HOM) interference of biphoton states of extremely high Schmidt number. Two-photon interference of 1500 spatial modes and a total of more than $3\times {10}^6$ spatiotemporal modes is evidenced by measuring momentum spatial coincidences, without any prior selection of the photons in time and space coincidence, between the pixels of the far-field images of two strongly multimode spontaneous parametric down-conversion (SPDC) beams propagating through a HOM interferometer. The outgoing SPDC beams are recorded on two separate detector arrays operating in the photon-counting regime. The properties of HOM interference are investigated both in the time and space domains. We show that the two-photon interference exhibits temporal and two-dimensional spatial HOM dips with visibilities of 60% and widths in good agreement with the spatiotemporal coherence properties of the biphoton state. Moreover, we demonstrate that maxima of momentum spatial coincidences are evidenced within each image, in correspondence with these dips.

We theoretically study the few- and many-body dynamics of photons in chiral waveguides. In particular, we examine pulse propagation through an ensemble of $N$ two-level systems chirally coupled to a waveguide. We show that the system supports correlated multiphoton bound states, which have a well-defined photon number $n$ and propagate through the system with a group delay scaling as $1/n^2$. This has the interesting consequence that, during propagation, an incident coherent-state pulse breaks up into different bound-state components that can become spatially separated at the output in a sufficiently long system. For sufficiently many photons and sufficiently short systems, we show that linear combinations of $n$-body bound states recover the well-known phenomenon of mean-field solitons in self-induced transparency. Our work thus covers the entire spectrum from few-photon quantum propagation, to genuine quantum many-body (atom and photon) phenomena, and ultimately the quantum-to-classical transition. Finally, we demonstrate that the bound states can undergo elastic scattering with additional photons. Together, our results demonstrate that photon bound states are truly distinct physical objects emerging from the most elementary light-matter interaction between photons and two-level emitters. Our work opens the door to studying quantum many-body physics and soliton physics with photons in chiral waveguide QED.