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Undesired coupling to the surrounding environment destroys long-range correlations in quantum processors and hinders coherent evolution in the nominally available computational space. This noise is an outstanding challenge when leveraging the computation power of near-term quantum processors 1 . It has been shown that benchmarking random circuit sampling with cross-entropy benchmarking can provide an estimate of the effective size of the Hilbert space coherently available 2-8 . Nevertheless, quantum algorithms' outputs can be trivialized by noise, making them susceptible to classical computation spoofing. Here, by implementing an algorithm for random circuit sampling, we demonstrate experimentally that two phase transitions are observable with cross-entropy benchmarking, which we explain theoretically with a statistical model. The first is a dynamical transition as a function of the number of cycles and is the continuation of the anti-concentration point in the noiseless case. The second is a quantum phase transition controlled by the error per cycle; to identify it analytically and experimentally, we create a weak-link model, which allows us to vary the strength of the noise versus coherent evolution. Furthermore, by presenting a random circuit sampling experiment in the weak-noise phase with 67 qubits at 32 cycles, we demonstrate that the computational cost of our experiment is beyond the capabilities of existing classical supercomputers. Our experimental and theoretical work establishes the existence of transitions to a stable, computationally complex phase that is reachable with current quantum processors., (© 2024. The Author(s).)

Engineered dissipative reservoirs have the potential to steer many-body quantum systems toward correlated steady states useful for quantum simulation of high-temperature superconductivity or quantum magnetism. Using up to 49 superconducting qubits, we prepared low-energy states of the transverse-field Ising model through coupling to dissipative auxiliary qubits. In one dimension, we observed long-range quantum correlations and a ground-state fidelity of 0.86 for 18 qubits at the critical point. In two dimensions, we found mutual information that extends beyond nearest neighbors. Lastly, by coupling the system to auxiliaries emulating reservoirs with different chemical potentials, we explored transport in the quantum Heisenberg model. Our results establish engineered dissipation as a scalable alternative to unitary evolution for preparing entangled many-body states on noisy quantum processors.

Systems of correlated particles appear in many fields of modern science and represent some of the most intractable computational problems in nature. The computational challenge in these systems arises when interactions become comparable to other energy scales, which makes the state of each particle depend on all other particles 1 . The lack of general solutions for the three-body problem and acceptable theory for strongly correlated electrons shows that our understanding of correlated systems fades when the particle number or the interaction strength increases. One of the hallmarks of interacting systems is the formation of multiparticle bound states 2-9 . Here we develop a high-fidelity parameterizable fSim gate and implement the periodic quantum circuit of the spin-½ XXZ model in a ring of 24 superconducting qubits. We study the propagation of these excitations and observe their bound nature for up to five photons. We devise a phase-sensitive method for constructing the few-body spectrum of the bound states and extract their pseudo-charge by introducing a synthetic flux. By introducing interactions between the ring and additional qubits, we observe an unexpected resilience of the bound states to integrability breaking. This finding goes against the idea that bound states in non-integrable systems are unstable when their energies overlap with the continuum spectrum. Our work provides experimental evidence for bound states of interacting photons and discovers their stability beyond the integrability limit., (© 2022. The Author(s).)

Inherent symmetry of a quantum system may protect its otherwise fragile states. Leveraging such protection requires testing its robustness against uncontrolled environmental interactions. Using 47 superconducting qubits, we implement the one-dimensional kicked Ising model, which exhibits nonlocal Majorana edge modes (MEMs) with [Formula: see text] parity symmetry. We find that any multiqubit Pauli operator overlapping with the MEMs exhibits a uniform late-time decay rate comparable to single-qubit relaxation rates, irrespective of its size or composition. This characteristic allows us to accurately reconstruct the exponentially localized spatial profiles of the MEMs. Furthermore, the MEMs are found to be resilient against certain symmetry-breaking noise owing to a prethermalization mechanism. Our work elucidates the complex interplay between noise and symmetry-protected edge modes in a solid-state environment.

Interactions in quantum systems can spread initially localized quantum information into the exponentially many degrees of freedom of the entire system. Understanding this process, known as quantum scrambling, is key to resolving several open questions in physics. Here, by measuring the time-dependent evolution and fluctuation of out-of-time-order correlators, we experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor. We engineer quantum circuits that distinguish operator spreading and operator entanglement and experimentally observe their respective signatures. We show that whereas operator spreading is captured by an efficient classical model, operator entanglement in idealized circuits requires exponentially scaled computational resources to simulate. These results open the path to studying complex and practically relevant physical observables with near-term quantum processors.

The discovery of topological order has revised the understanding of quantum matter and provided the theoretical foundation for many quantum error–correcting codes. Realizing topologically ordered states has proven to be challenging in both condensed matter and synthetic quantum systems. We prepared the ground state of the toric code Hamiltonian using an efficient quantum circuit on a superconducting quantum processor. We measured a topological entanglement entropy near the expected value of –ln2 and simulated anyon interferometry to extract the braiding statistics of the emergent excitations. Furthermore, we investigated key aspects of the surface code, including logical state injection and the decay of the nonlocal order parameter. Our results demonstrate the potential for quantum processors to provide insights into topological quantum matter and quantum error correction.

A promising approach to study condensed-matter systems is to simulate them on an engineered quantum platform 1-4 . However, the accuracy needed to outperform classical methods has not been achieved so far. Here, using 18 superconducting qubits, we provide an experimental blueprint for an accurate condensed-matter simulator and demonstrate how to investigate fundamental electronic properties. We benchmark the underlying method by reconstructing the single-particle band structure of a one-dimensional wire. We demonstrate nearly complete mitigation of decoherence and readout errors, and measure the energy eigenvalues of this wire with an error of approximately 0.01 rad, whereas typical energy scales are of the order of 1 rad. Insight into the fidelity of this algorithm is gained by highlighting the robust properties of a Fourier transform, including the ability to resolve eigenenergies with a statistical uncertainty of 10 -4 rad. We also synthesize magnetic flux and disordered local potentials, which are two key tenets of a condensed-matter system. When sweeping the magnetic flux we observe avoided level crossings in the spectrum, providing a detailed fingerprint of the spatial distribution of local disorder. By combining these methods we reconstruct electronic properties of the eigenstates, observing persistent currents and a strong suppression of conductance with added disorder. Our work describes an accurate method for quantum simulation 5,6 and paves the way to study new quantum materials with superconducting qubits.

Monolayers of molybdenum and tungsten dichalcogenides are direct bandgap semiconductors, which makes them promising for optoelectronic applications. In particular, van der Waals heterostructures consisting of monolayers of MoS2 sandwiched between atomically thin hexagonal boron nitride (hBN) and graphene electrodes allows one to obtain light emitting quantum wells (LEQWs) with low-temperature external quantum efficiency (EQE) of 1%. However, the EQE of MoS2- and MoSe2-based LEQWs shows behavior common for many other materials: it decreases fast from cryogenic conditions to room temperature, undermining their practical applications. Here we compare MoSe2 and WSe2 LEQWs. We show that the EQE of WSe2 devices grows with temperature, with room temperature EQE reaching 5%, which is 250× more than the previous best performance of MoS2 and MoSe2 quantum wells in ambient conditions. We attribute such different temperature dependences to the inverted sign of spin-orbit splitting of conduction band states in tungsten and molybdenum dichalcogenides, which makes the lowest-energy exciton in WSe2 dark.

We evaluate binding energies of trions X±, excitons bound by a donor or acceptor charge X^{D(A)}, and overcharged acceptors or donors in two-dimensional atomic crystals by mapping the three-body problem in two dimensions onto one particle in a three-dimensional potential treatable by a purposely developed boundary-matching-matrix method. We find that in monolayers of transition metal dichalcogenides the dissociation energy of X^{±} is typically much larger than that of localized exciton complexes, so that trions are more resilient to heating, despite the fact that their recombination line in optics is less redshifted from the exciton line than the line of X^{D(A)}.

We show that the transport and thermodynamic properties of a singly connected disordered conductor exhibit quantum Aharonov-Bohm oscillations as a function of the total magnetic flux through the sample. The oscillations are associated with the interference contribution from a special class of electron trajectories confined to the surface of the sample.

We consider chiral electrons moving along the one-dimensional helical edge of a two-dimensional topological insulator and interacting with a disordered chain of Kondo impurities. Assuming the electron-spin couplings of random anisotropies, we map this system to the problem of the pinning of the charge density wave by the disordered potential. This mapping proves that arbitrary weak anisotropic disorder in coupling of chiral electrons with spin impurities leads to the Anderson localization of the edge states.

We introduce the notion of the strongly correlated band insulator (SCI), where the lowest energy excitations are collective modes (excitons) rather than the single particles. We construct controllable 1/N expansion for SCI to describe their observable properties. A remarkable example of the SCI is bilayer graphene which is shown to be tunable between the SCI and usual weak coupling regime.

We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to the existence of long-range hops. We find that the critical wave functions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T invariant the states are critical for all values of the parameters. Otherwise, there can be a "metal-insulator" transition between this "ordinary" diffusion and the Levy flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified nonlinear supermatrix σ model.

The superconductor-insulator transition (SIT) in regular arrays of Josephson junctions is studied at low temperatures. We derived an imaginary time Ginzburg-Landau-type action properly describing the Coulomb interaction. The renormalization group analysis at zero temperature T=0 in the space dimensionality d=3 shows that the SIT is always of the first order. At finite T, a tricritical point separates the lines of the first- and second-order phase transitions. The same conclusion holds for d=2 if the mutual capacitance is larger than the distance between junctions.

We predict a nonequilibrium critical phenomenon in the space-time density evolution of a fermionic gas above the temperature of transition into the superfluid phase. On the BCS side of the Bose-Einstein condensation-BCS crossover, the evolution of a localized density disturbance exhibits a negative echo at the point of the initial inhomogeneity. Approaching the Bose-Einstein condensation side, this effect competes with the slow spreading of the density of bosonic molecules. However, even here the echo dominates for large enough times. This effect may be used as an experimental tool to locate the position of the transition.

Quenched disorder in graphene is characterized by 5 constants and experiences the logarithmic renormalization even from the spatial scales smaller than the Fermi wavelength. We derive and solve renormalization group equations (RGEs) describing the system at such scales. At larger scales, we derive a nonlinear supermatrix sigma model completely describing localization and crossovers between different ensembles. The parameters of this sigma model are determined by the solutions of the RGEs.

A resonant level strongly coupled to a local phonon under nonequilibrium conditions is investigated. The nonequilibrium Hartree-Fock approximation is shown to correspond to approximating the steady state density matrix by delta functions at field values to which the local dynamics relaxes in a semiclassical limit. If multiple solutions exist, all are shown to make nonvanishing contributions to physical quantities: multistability does not exist. Departures from equilibrium are shown to produce decoherence, preventing the formation of a polaron feature in the spectral function. The formalism also applies to the nonequilibrium Kondo problem.

We observe a new type of magneto-oscillations in the photovoltage and the longitudinal resistance of a two-dimensional electron system. The oscillations are induced by microwave radiation and are periodic in magnetic field. The period is determined by the microwave frequency, the electron density, and the distance between potential probes. The phenomenon is accounted for by interference of coherently excited edge magnetoplasmons in the contact regions and offers perspectives for developing new tunable microwave and terahertz detection schemes and spectroscopic techniques.

Under a strong ac drive the zero-frequency linear response dissipative resistivity rho(d)(j=0) of a homogeneous state is allowed to become negative. We show that such a state is absolutely unstable. The only time-independent state of a system with a rho(d)(j=0)<0 is characterized by a current which almost everywhere has a magnitude j(0) fixed by the condition that the nonlinear dissipative resistivity rho(d)(j(2)(0))=0. As a result, the dissipative component of the dc-electric field vanishes. The total current may be varied by rearranging the current pattern appropriately with the dissipative component of the dc-electric field remaining zero. This result, together with the calculation of Durst et al., indicating the existence of regimes of applied ac microwave field and dc magnetic field where rho(d)(j=0)<0, explains the zero-resistance state observed by Mani et al. and Zudov et al.

We study the mechanism of nuclear spin relaxation in quantum dots due to the electron exchange with the 2D gas. We show that the nuclear spin relaxation rate 1/T(1) is dramatically affected by the Coulomb blockade (CB) and can be controlled by gate voltage. In the case of strong spin-orbit (SO) coupling the relaxation rate is maximal in the CB valleys, whereas for the weak SO coupling the maximum of 1/T(1) is near the CB peaks.

The effects of interplay between spin-orbit coupling and Zeeman splitting on weak localization and universal conductance fluctuations in lateral semiconductor quantum dots are analyzed: All possible symmetry classes of corresponding random matrix theories are listed and crossovers between them achievable by sweeping magnetic field and changing the dot parameters are described. We also suggest experiments to measure the spin-orbit coupling constants.

We consider mesoscopic fluctuations of Coulomb drag transresistivity between two layers at a Landau level filling factor nu = 1/2 each. We find that, at low temperatures, sample to sample fluctuations exceed both the ensemble average and the corresponding fluctuations at B = 0. At the experimentally relevant temperatures, the variance of the transresistivity is proportional to T(-1/2). We find the dependence of this variance on density and magnetic field to reflect the attachment of two flux quanta to each electron.

A two-channel Kondo (2CK) non-Fermi liquid state in a metal resulting from the interaction between electrons and structural defects modeled by double-well potentials (DWP) is revisited. Account only of the two lowest states in DWP is known to lead to rather low Kondo temperature, T(K). We prove that the contribution of higher excited states reduces T(K), if all of the intermediate states are taken into account. Prefactor in T(K) is shown to be determined by the spacing between the second and the third levels epsilon(3) in DWP rather than by the electron Fermi energy epsilon(F). Since epsilon(3)<

This paper is devoted to study of the classical-to-quantum crossover of the shot noise in chaotic systems. This crossover is determined by the ratio of the particle dwell time in the system, tau(d), to the characteristic time for diffraction t(E) approximately lambda(-1)|lnh, where lambda is the Lyapunov exponent. The shot noise vanishes when t(E)>>tau(d), while it reaches a universal value in the opposite limit. Thus, the Lyapunov exponent of chaotic mesoscopic systems may be found by shot noise measurements.