We show how to accurately study two-dimensional quantum critical phenomena using infinite projected entangled-pair states (iPEPS). We identify the presence of a finite correlation length in the optimal iPEPS approximation to Lorentz-invariant critical states which we use to perform a finite correlation length scaling analysis to determine critical exponents. This is analogous to the one-dimensional finite entanglement scaling with infinite matrix product states. We provide arguments why this approach is also valid in 2D by identifying a class of states that, despite obeying the area law of entanglement, seems hard to describe with iPEPS. We apply these ideas to interacting spinless fermions on a honeycomb lattice and obtain critical exponents which are in agreement with quantum Monte Carlo results. Furthermore, we introduce a new scheme to locate the critical point without the need of computing higher-order moments of the order parameter. Finally, we also show how to obtain an improved estimate of the order parameter in gapless systems, with the 2D Heisenberg model as an example.

It is an open question how well tensor network states in the form of an infinite projected entangled-pair states (iPEPS) tensor network can approximate gapless quantum states of matter. Here we address this issue for two different physical scenarios: (i) a conformally invariant $(2+1)d$ quantum critical point in the incarnation of the transverse-field Ising model on the square lattice and (ii) spontaneously broken continuous symmetries with gapless Goldstone modes exemplified by the $S=1/2$ antiferromagnetic Heisenberg and $XY$ models on the square lattice. We find that the energetically best wave functions display finite correlation lengths and we introduce a powerful finite correlation length scaling framework for the analysis of such finite bond dimension (finite-$D$) iPEPS states. The framework is important (i) to understand the mild limitations of the finite-$D$ iPEPS manifold in representing Lorentz-invariant, gapless many-body quantum states and (ii) to put forward a practical scheme in which the finite correlation length $\xi (D)$ combined with field theory inspired formulas can be used to extrapolate the data to infinite correlation length, i.e., to the thermodynamic limit. The finite correlation length scaling framework opens the way for further exploration of quantum matter with an (expected) Lorentz-invariant, massless low-energy description, with many applications ranging from condensed matter to high-energy physics.

Traditional computational methods for studying quantum many-body systems are “forward methods,” which take quantum models, i.e., Hamiltonians, as input and produce ground states as output. However, such forward methods often limit one’s perspective to a small fraction of the space of possible Hamiltonians. We introduce an alternative computational “inverse method,” the eigenstate-to-Hamiltonian construction (EHC), that allows us to better understand the vast space of quantum models describing strongly correlated systems. EHC takes as input a wave function $|{\psi }_T⟩$ and produces as output Hamiltonians for which $|{\psi }_T⟩$ is an eigenstate. This is accomplished by computing the quantum covariance matrix, a quantum mechanical generalization of a classical covariance matrix. EHC is widely applicable to a number of models and, in this work, we consider seven different examples. Using the EHC method, we construct a parent Hamiltonian with a new type of antiferromagnetic ground state, a parent Hamiltonian with two different targeted degenerate ground states, and large classes of parent Hamiltonians with the same ground states as well-known quantum models, such as the Majumdar-Ghosh model, the XX chain, the Heisenberg chain, the Kitaev chain, and a 2D BdG model. EHC gives an alternative inverse approach for studying quantum many-body phenomena.

We analyze the effect of quenched disorder on spin-$1/2$ quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-$1/2$ moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-$1/2$ magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin $1/2$ per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of ${\mathrm{YbMgGaO}}_4$, a recently discovered triangular lattice spin-$1/2$ insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on ${\mathrm{YbMgGaO}}_4$ and related materials.

It is vital to minimize the impact of errors for near-future quantum devices that will lack the resources for full fault tolerance. Two quantum error mitigation (QEM) techniques have been introduced recently, namely, error extrapolation [Y. Li and S. C. Benjamin, Phys. Rev. X 7, 021050 (2017); K. Temme et al., Phys. Rev. Lett. 119, 180509 (2017)] and quasiprobability decomposition [K. Temme et al., Phys. Rev. Lett. 119, 180509 (2017)]. To enable practical implementation of these ideas, here we account for the inevitable imperfections in the experimentalist’s knowledge of the error model itself. We describe a protocol for systematically measuring the effect of errors so as to design efficient QEM circuits. We find that the effect of localized Markovian errors can be fully eliminated by inserting or replacing some gates with certain single-qubit Clifford gates and measurements. Finally, having introduced an exponential variant of the extrapolation method we contrast the QEM techniques using exact numerical simulation of up to 19 qubits in the context of a “swap” test circuit. Our optimized methods dramatically reduce the circuit’s output error without increasing the qubit count.

Quantum mechanics implies that a single photon can be in the superposition of two distant spatial modes and enable nonlocal interferences. The most vivid example is the two-photon coalescence on a $50:50$ beam splitter, known as Hong-Ou-Mandel interference. In the past decade, this experiment has been used to characterize the suitability of different single-photon sources for linear optical quantum gates. This characterization alone cannot guarantee the suitability of the photons in a scalable quantum network. As for a deeper insight, we perform a number of nonclassical interference measurements of single photons emitted by a single organic molecule that are optimized by an atomic Faraday filter. Our measurements reveal near unity visibility of the quantum interference, and a one-port correlation measurement proves the ideal Fourier limited nature of our single-photon source. A delayed choice quantum eraser allows us to observe a constructive interference between the photons, and a Hong-Ou-Mandel peak is formed additionally to the commonly observed dip. These experiments comprehensively characterize the involved photons for their use in a future quantum Internet, and they attest to the fully efficient interaction of the molecular photons with a next subsequent quantum node. They can be adapted to other emitters and will allow us to gain insights to their applicability for quantum information processing. We introduce a quality number that describes the photon’s properties for their use in a quantum network; this states that effectively 97% of the utilized molecular photons can be used in a scalable quantum optical system and interact with other quantum nodes. The experiments are based on a hybridization of solid state quantum optics, atomic systems, and all-optical quantum information processing.

Quantum spin dephasing is caused by inhomogeneous coupling to the environment, with resulting limits to the measurement time and precision of spin-based sensors. The effects of spin dephasing can be especially pernicious for dense ensembles of electronic spins in the solid state, such as nitrogen-vacancy (NV) color centers in diamond. We report the use of two complementary techniques, spin-bath driving, and double quantum coherence magnetometry, to enhance the inhomogeneous spin dephasing time ($T_2^{*}$) for NV ensembles by more than an order of magnitude. In combination, these quantum control techniques (i) eliminate the effects of the dominant NV spin ensemble dephasing mechanisms, including crystal strain gradients and dipolar interactions with paramagnetic bath spins, and (ii) increase the effective NV gyromagnetic ratio by a factor of two. Applied independently, spin-bath driving and double quantum coherence magnetometry elucidate the sources of spin ensemble dephasing over a wide range of NV and bath spin concentrations. These results demonstrate the longest reported $T_2^{*}$ in a solid-state electronic spin ensemble at room temperature and outline a path towards NV-diamond dc magnetometers with broadband femtotesla sensitivity.

We construct examples of translationally invariant solvable models of strongly correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regimes with local quantum criticality and marginal-Fermi-liquid behavior. In the marginal-Fermi-liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi surfaces. The self-energy has a singular frequency dependence but lacks momentum dependence, reminiscent of a dynamical mean-field-theory-like behavior but in dimensions $d<\infty$. In the low-temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi surface in the non-Fermi-liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse-grained descriptions of a class of intermediate-scale non-Fermi-liquid behavior in generic correlated metals.

In bilayer graphene, electrostatic confinement can be realized by a suitable design of top and back gate electrodes. We measure electronic transport through a bilayer graphene quantum dot, which is laterally confined by gapped regions and connected to the leads via $p$-$n$ junctions. Single electron and hole occupancy is realized and charge carriers $n=1,2,\dots 50$ can be filled successively into the quantum system with charging energies exceeding 10 meV. For the lowest quantum states, we can clearly observe valley and Zeeman splittings with a spin g-factor of $g_s\approx 2$. In the low-field limit, the valley splitting depends linearly on the perpendicular magnetic field and is in qualitative agreement with calculations.

Quantum-classical hybrid algorithms are emerging as promising candidates for near-term practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground-state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a cross-platform benchmark for multiqubit quantum simulators.

Manifestations of quantum interference effects in macroscopic objects are rare. Weak localization is one of the few examples of such effects showing up in the electron transport through solid state. Here, we show that weak localization becomes prominent also in optical spectroscopy via detection of the electron spin dynamics. In particular, we find that weak localization controls the free electron spin relaxation in semiconductors at low temperatures and weak magnetic fields by slowing it down by almost a factor of two in $n$-doped GaAs in the metallic phase. The weak localization effect on the spin relaxation is suppressed by moderate magnetic fields of approximately 1 T, which destroy the interference of electron trajectories, and by increasing the temperature. The weak localization suppression causes an anomalous decrease of the longitudinal electron spin relaxation time $T_1$ with magnetic field, in stark contrast with the well-known magnetic-field-induced increase in $T_1$. This is consistent with transport measurements, which show the same variation of resistivity with magnetic field. Our discovery opens up a vast playground to explore quantum magnetotransport effects optically in the spin dynamics.

Local operations assisted by classical communication (LOCC) constitute the free operations in entanglement theory. Hence, the determination of LOCC transformations is crucial for the understanding of entanglement. We characterize here almost all LOCC transformations among pure multipartite multilevel states. Combined with the analogous results for qubit states shown by Gour et al. [J. Math. Phys. (N.Y.) 58, 092204 (2017)], this gives a characterization of almost all local transformations among multipartite pure states. We show that nontrivial LOCC transformations among generic, fully entangled, pure states are almost never possible. Thus, almost all multipartite states are isolated. They can neither be deterministically obtained from local-unitary-inequivalent (LU-inequivalent) states via local operations, nor can they be deterministically transformed to pure, fully entangled LU-inequivalent states. In order to derive this result, we prove a more general statement, namely, that, generically, a state possesses no nontrivial local symmetry. We discuss further consequences of this result for the characterization of optimal, probabilistic single-copy and probabilistic multicopy LOCC transformations and the characterization of LU-equivalence classes of multipartite pure states.

In many instances, sprays are formed from the breakup of liquid jets or sheets. We investigate the different parameters that determine the characteristic drop size in the breakup of sheets. We vary both the spraying parameters, such as the pressure and geometry of the nozzle, and the fluid parameters, such as viscosity and surface tension. The combined results show that the drop size is determined by a competition between fluid inertia and surface tension, which allows for the prediction of the drop size from the Weber number and geometry of the nozzle. Once rescaled with the average drop size, the size distribution is found to be described by a compound gamma distribution with two parameters, $n$ and $m$, with the former setting the ligament corrugation and the latter the width of the ligament size distribution. Fit values for $m$ indicate that nozzles of a conical type produce ligaments of almost equal size, while the flat fan nozzles produce broader distributed ligament sizes. Values for $n$ show that, for all nozzles, ligaments are very corrugated, which is not unexpected for such spray formation processes. By using high-speed photography of the sprays, the parameters $m$ and $n$ can be directly measured and, indeed, govern the drop-size distribution.

In vitro and in vivo spiking activity clearly differ. Whereas networks in vitro develop strong bursts separated by periods of very little spiking activity, in vivo cortical networks show continuous activity. This is puzzling considering that both networks presumably share similar single-neuron dynamics and plasticity rules. We propose that the defining difference between in vitro and in vivo dynamics is the strength of external input. In vitro, networks are virtually isolated, whereas in vivo every brain area receives continuous input. We analyze a model of spiking neurons in which the input strength, mediated by spike rate homeostasis, determines the characteristics of the dynamical state. In more detail, our analytical and numerical results on various network topologies show consistently that under increasing input, homeostatic plasticity generates distinct dynamic states, from bursting, to close-to-critical, reverberating, and irregular states. This implies that the dynamic state of a neural network is not fixed but can readily adapt to the input strengths. Indeed, our results match experimental spike recordings in vitro and in vivo: The in vitro bursting behavior is consistent with a state generated by very low network input ($<0.1\%$), whereas in vivo activity suggests that on the order of 1% recorded spikes are input driven, resulting in reverberating dynamics. Importantly, this predicts that one can abolish the ubiquitous bursts of in vitro preparations, and instead impose dynamics comparable to in vivo activity by exposing the system to weak long-term stimulation, thereby opening new paths to establish an in vivo-like assay in vitro for basic as well as neurological studies.

At ambient pressure, CrAs undergoes a first-order transition into a double-helical magnetic state at $T_N=265\mathrm{K}$, which is accompanied by a structural transition. The recent discovery of pressure-induced superconductivity in CrAs makes it important to clarify the nature of quantum phase transitions out of the coupled structural/helimagnetic order in this system. Here, we show, via neutron diffraction on the single-crystal CrAs under hydrostatic pressure ($P$), that the combined order is suppressed at $P_c\approx 10\mathrm{kbar}$, near which bulk superconductivity develops with a maximal transition temperature $T_c\approx 2\mathrm{K}$. We further show that the coupled order is also completely suppressed by phosphorus doping in ${\mathrm{CrAs}}_{1-x}{\mathrm{P}}_x$ at a critical $x_c\approx 0.05$, above which inelastic neutron scattering evidenced persistent antiferromagnetic correlations, providing a possible link between magnetism and superconductivity. In line with the presence of antiferromagnetic fluctuations near $P_c(x_c)$, the $A$ coefficient of the quadratic temperature dependence of resistivity exhibits a dramatic enhancement as $P$ ($x$) approaches $P_c(x_c)$, around which $\rho (T)$ has a non-Fermi-liquid form. Accordingly, the electronic specific-heat coefficient of ${\mathrm{CrAs}}_{1-x}{\mathrm{P}}_x$ peaks around $x_c$. These properties provide clear evidence for quantum criticality, which we interpret as originating from a nearly second-order helimagnetic quantum phase transition that is concomitant with a first-order structural transition. Our findings in CrAs highlight the distinct characteristics of quantum criticality in bad metals, thereby bringing out new insights into the physics of unconventional superconductivity such as those occurring in the high-$T_c$ iron pnictides.

The observation of an unequivocal quantum speedup remains an elusive objective for quantum computing. A more modest goal is to demonstrate a scaling advantage over a class of classical algorithms for a computational problem running on quantum hardware. The D-Wave quantum annealing processors have been at the forefront of experimental attempts to address this goal, given their relatively large numbers of qubits and programmability. A complete determination of the optimal time-to-solution using these processors has not been possible to date, preventing definitive conclusions about the presence of a scaling advantage. The main technical obstacle has been the inability to verify an optimal annealing time within the available range. Here, we overcome this obstacle using a class of problem instances constructed by systematically combining many-spin frustrated loops with few-qubit gadgets exhibiting a tunneling event—a combination that we find to promote the presence of tunneling energy barriers in the relevant semiclassical energy landscape of the full problem—and we observe an optimal annealing time using a D-Wave 2000Q processor over a range spanning up to more than 2000 qubits. We identify the gadgets as being responsible for the optimal annealing time, whose existence allows us to perform an optimal time-to-solution benchmarking analysis. We perform a comparison to several classical algorithms, including simulated annealing, spin-vector Monte Carlo, and discrete-time simulated quantum annealing (SQA), and establish the first example of a scaling advantage for an experimental quantum annealer over classical simulated annealing. Namely, we find that the D-Wave device exhibits certifiably better scaling than simulated annealing, with 95% confidence, over the range of problem sizes that we can test. However, we do not find evidence for a quantum speedup: SQA exhibits the best scaling for annealing algorithms by a significant margin. This is a finding of independent interest, since we associate SQA’s advantage with its ability to transverse energy barriers in the semiclassical energy landscape by mimicking tunneling. Our construction of instance classes with verifiably optimal annealing times opens up the possibility of generating many new such classes based on a similar principle of promoting the presence of energy barriers that can be overcome more efficiently using quantum rather than thermal fluctuations, paving the way for further definitive assessments of scaling advantages using current and future quantum annealing devices.

Recent experiments in graphene heterostructures have observed Chern insulators—integer and fractional quantum Hall states made possible by a periodic substrate potential. Here, we study theoretically that the competition between different Chern insulators, which can be tuned by the amplitude of the periodic potential, leads to a new family of quantum critical points described by ${\mathrm{QED}}_3$-Chern-Simons theory. At these critical points, $N_f$ flavors of Dirac fermions interact through an emergent U(1) gauge theory at Chern-Simons level $K$, and remarkably, the entire family (with any $N_f$ or $K$) can be realized at special values of the external magnetic field. Transitions between particle-hole conjugate Jain states realize “pure” ${\mathrm{QED}}_3$, in which multiple flavors of Dirac fermions interact with a Maxwell U(1) gauge field. The multiflavor nature of the critical point leads to an emergent $\mathrm{SU}(N_f)$ symmetry. Specifically, at the transition from a $\nu =1/3$ to $2/3$ quantum Hall state, the emergent SU(3) symmetry predicts an octet of charge density waves with enhanced susceptibilities, which is verified by DMRG numerical simulations on microscopic models applicable to graphene heterostructures. We propose experiments on Chern insulators that could resolve open questions in the study of ($2+1$)-dimensional conformal field theories and test recent duality inspired conjectures.

We use high-resolution resonant inelastic x-ray scattering (RIXS) to study a thin film of ${\mathrm{NdNiO}}_3$, a compound whose unusual spin- and bond-ordered electronic ground state has been of long-standing interest. Below the magnetic ordering temperature, we observe well-defined collective magnon excitations along different high-symmetry directions in momentum space. The magnetic spectra depend strongly on the incident photon energy, which we attribute to RIXS coupling to different local electronic configurations of the expanded and compressed ${\mathrm{NiO}}_6$ octahedra in the bond-ordered state. Both the noncollinear magnetic ground state and the observed site-dependent magnon excitations are well described by a model that assumes strong competition between the antiferromagnetic superexchange and ferromagnetic double-exchange interactions. Our study provides direct insight into the magnetic dynamics and exchange interactions of the rare-earth nickelates and demonstrates that RIXS can serve as a site-selective probe of magnetism in these and other materials.

Causal asymmetry is one of the great surprises in predictive modeling: The memory required to predict the future differs from the memory required to retrodict the past. There is a privileged temporal direction for modeling a stochastic process where memory costs are minimal. Models operating in the other direction incur an unavoidable memory overhead. Here, we show that this overhead can vanish when quantum models are allowed. Quantum models forced to run in the less-natural temporal direction not only surpass their optimal classical counterparts but also any classical model running in reverse time. This holds even when the memory overhead is unbounded, resulting in quantum models with unbounded memory advantage.