Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases.

Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

Infinite switch simulated tempering in force (FISST).

Many proteins in cells are capable of sensing and responding to piconewton-scale forces, a regime in which conformational changes are small but significant for biological processes. In order to efficiently and effectively sample the response of these proteins to small forces, enhanced sampling techniques will be required. In this work, we derive, implement, and evaluate an efficient method to simultaneously sample the result of applying any constant pulling force within a specified range to a molecular system of interest. We start from simulated tempering in force, whereby force is added as a linear bias on a collective variable to the system's Hamiltonian, and the coefficient is taken as a continuous auxiliary degree of freedom. We derive a formula for an average collective-variable-dependent force, which depends on a set of weights learned on-the-fly throughout a simulation, that reflect the limit where force varies infinitely quickly. Simulation data can then be used to retroactively compute averages of any observable at any force within the specified range. This technique is based on recent work deriving similar equations for infinite switch simulated tempering in temperature, which showed that the infinite switch limit is the most efficient for sampling. Here, we demonstrate that our method accurately samples molecular systems at all forces within a user defined force range simultaneously and show how it can serve as an enhanced sampling tool for cases where the pulling direction destabilizes states that have low free-energy at zero-force. This method is implemented in and freely distributed with the PLUMED open-source sampling library, and hence can be readily applied to problems using a wide range of molecular dynamics software packages.

Quantum supremacy using a programmable superconducting processor.

The promise of quantum computers is that certain computational tasks might be executed exponentially faster on a quantum processor than on a classical processor1. A fundamental challenge is to build a high-fidelity processor capable of running quantum algorithms in an exponentially large computational space. Here we report the use of a processor with programmable superconducting qubits2-7 to create quantum states on 53 qubits, corresponding to a computational state-space of dimension 253 (about 1016). Measurements from repeated experiments sample the resulting probability distribution, which we verify using classical simulations. Our Sycamore processor takes about 200 seconds to sample one instance of a quantum circuit a million times-our benchmarks currently indicate that the equivalent task for a state-of-the-art classical supercomputer would take approximately 10,000 years. This dramatic increase in speed compared to all known classical algorithms is an experimental realization of quantum supremacy8-14 for this specific computational task, heralding a much-anticipated computing paradigm.

Neural-Network Approach to Dissipative Quantum Many-Body Dynamics.

In experimentally realistic situations, quantum systems are never perfectly isolated and the coupling to their environment needs to be taken into account. Often, the effect of the environment can be well approximated by a Markovian master equation. However, solving this master equation for quantum many-body systems becomes exceedingly hard due to the high dimension of the Hilbert space. Here we present an approach to the effective simulation of the dynamics of open quantum many-body systems based on machine-learning techniques. We represent the mixed many-body quantum states with neural networks in the form of restricted Boltzmann machines and derive a variational Monte Carlo algorithm for their time evolution and stationary states. We document the accuracy of the approach with numerical examples for a dissipative spin lattice system.

Observation of the Crossover from Photon Ordering to Delocalization in Tunably Coupled Resonators.

Networks of nonlinear resonators offer intriguing perspectives as quantum simulators for nonequilibrium many-body phases of driven-dissipative systems. Here, we employ photon correlation measurements to study the radiation fields emitted from a system of two superconducting resonators in a driven-dissipative regime, coupled nonlinearly by a superconducting quantum interference device, with cross-Kerr interactions dominating over on-site Kerr interactions. We apply a parametrically modulated magnetic flux to control the linear photon hopping rate between the two resonators and its ratio with the cross-Kerr rate. When increasing the hopping rate, we observe a crossover from an ordered to a delocalized state of photons. The presented coupling scheme is intrinsically robust to frequency disorder and may therefore prove useful for realizing larger-scale resonator arrays.

Surface Chemistry-Mediated Near-Infrared Emission of Small Coinage Metal Nanoparticles.

From size-dependent luminescence to localized surface plasmon resonances, the optical properties that emerge from common materials with nanoscale dimensions have been revolutionary. As nanomaterials get smaller, they approach molecular electronic structures, and this transition from bulk to molecular electronic properties is a subject of far-reaching impact. One class of nanomaterials that exhibit particularly interesting optoelectronic features at this size transition are coinage metal (i.e., group 11 elements copper, silver, and gold) nanoparticles with core diameters between approximately 1 to 3 nm (∼25-200 atoms). Coinage metal nanoparticles can exhibit red or near-infrared photoluminescence features that are not seen in either their molecular or larger nanoscale counterparts. This emission has been exploited both as a probe of electronic behavior at the nanoscale as well as in critical applications such as biological imaging and chemical sensing. Interestingly, it has been demonstrated that their photoluminescence figures of merit such as emission quantum yield, energy, and lifetime are largely independent of particle diameter. Instead, emission from particles at this size range depends heavily on the particle surface chemistry, which includes both its metallic composition and the capping ligand architecture. The strong influence of surface chemistry on these emergent optoelectronic phenomena has powerful implications for both the study and use of these particles, primarily due to the theoretically limitless possible surface ligand architectures and metallic compositions. In this Account, we highlight recent work that studies and uses surface chemistry-mediated photoluminescence from coinage metal nanoparticles. Specifically, we emphasize the distinct, as well as synergistic, roles of the nanoparticle capping ligand and the nanoparticle core for controlling and/or enhancing their near-infrared photoluminescence. We then discuss the implications of surface chemistry-mediated photoluminescence as it relates to downstream applications such as energy transfer, sensing, and biological imaging. We conclude by discussing current challenges that remain in the field, including opportunities to develop new particle synthetic routes, analytical tools, and physical frameworks with which to understand small nanoparticle emission. Taken together, we anticipate that these materials will be foundational both in understanding the unique transition from molecular to bulk electronic structures and in the development of nanomaterials that leverage this transition.

Ligand mediated evolution of size dependent magnetism in cobalt nanoclusters.

We use density functional theory to model the impact of a ligand shell on the magnetic properties of CoN (15 ≤ N ≤ 55) nanoclusters. We study three different ligand shells on each nanocluster core size, each known to have different electronic interactions with the surface: pure Cl ligand shells (X-type), pure PH3 ligand shells (L-type), and two component ligand shells with mixtures of Cl and PH3 ligands. The simulations show that the identity, arrangement, and total coverage of the ligand shell controls the distribution of local magnetic moments across the CoN core. On the surface of an unpassivated CoN nanocluster, the Co-Co coordination number (CN) is known to determine the local magnetic moments. Upon the introduction of a ligand, the Co-Co CN remains important, however the nature of the metal-ligand bond changes the extent to which increasing Co-Co CN quenches magnetism. Further, we identify an additional and significant long-range impact on local magnetic moments (LMM) from the PH3 ligand shells. Thus, we establish important design principles of magnetic nanoclusters, where ligand shell chemistry mediates the distribution of LMMs across a CoNLM nanocluster, allowing a route to rational design of specific magnetic properties.

Parametric Oscillation, Frequency Mixing, and Injection Locking of Strongly Coupled Nanomechanical Resonator Modes.

We study locking phenomena of two strongly coupled, high quality factor nanomechanical resonator modes to a common parametric drive at a single drive frequency in different parametric driving regimes. By controlled dielectric gradient forces we tune the resonance frequencies of the flexural in-plane and out-of-plane oscillation of the high stress silicon nitride string through their mutual avoided crossing. For the case of the strong common parametric drive signal-idler generation via nondegenerate parametric two-mode oscillation is observed. Broadband frequency tuning of the very narrow linewidth signal and idler resonances is demonstrated. When the resonance frequencies of the signal and idler get closer to each other, partial injection locking, injection pulling, and complete injection locking to half of the drive frequency occurs depending on the pump strength. Furthermore, satellite resonances, symmetrically offset from the signal and idler by their beat note, are observed, which can be attributed to degenerate four-wave mixing in the highly nonlinear mechanical oscillations.

Observation of uniform ligand environments and (31)P-(197)Au coupling in phosphine-terminated Au nanoparticles.

Here, we use solution and solid-state (31)P NMR to study the ligand environment of water soluble, phosphine-terminated gold nanoparticles. The resulting spectra indicate that particle-bound phosphine ligands occupy an unexpectedly monodisperse ligand environment. This uniformity then facilitates one of the first descriptions of distinct (31)P-(197)Au coupling in colloidal nanoparticles.

Ligand-Mediated "Turn On," High Quantum Yield Near-Infrared Emission in Small Gold Nanoparticles.

Small gold nanoparticles (∼1.4-2.2 nm core diameters) exist at an exciting interface between molecular and metallic electronic structures. These particles have the potential to elucidate fundamental physical principles driving nanoscale phenomena and to be useful in a wide range of applications. Here, we study the optoelectronic properties of aqueous, phosphine-terminated gold nanoparticles (core diameter = 1.7 ± 0.4 nm) after ligand exchange with a variety of sulfur-containing molecules. No emission is observed from these particles prior to ligand exchange, however the introduction of sulfur-containing ligands initiates photoluminescence. Further, small changes in sulfur substituents produce significant changes in nanoparticle photoluminescence features including quantum yield, which ranges from 0.13 to 3.65% depending on substituent. Interestingly, smaller ligands produce the most intense, highest energy, narrowest, and longest-lived emissions. Radiative lifetime measurements for these gold nanoparticle conjugates range from 59 to 2590 µs, indicating that even minor changes to the ligand substituent fundamentally alter the electronic properties of the luminophore itself. These results isolate the critical role of surface chemistry in the photoluminescence of small metal nanoparticles and largely rule out other mechanisms such as discrete (Au(I)-S-R)n impurities, differences in ligand densities, and/or core diameters. Taken together, these experiments provide important mechanistic insight into the relationship between gold nanoparticle near-infrared emission and pendant ligand architectures, as well as demonstrate the pivotal role of metal nanoparticle surface chemistry in tuning and optimizing emergent optoelectronic features from these nanostructures.

Copper Induces a Core Plasmon in Intermetallic Au(144,145)-xCux(SR)60 Nanoclusters.

The electronic structure and optical absorption spectra of intermetallic thiol-stabilized gold-copper clusters, having 144-145 metal atoms and 60 thiols, were studied by ab initio computations. The widely known icosahedral-based cluster model from the work of Lopez-Acevedo et al. (2009) was used, and clusters doped with one to 30 copper atoms were considered. When doped inside the metal core, copper induces dramatic changes in the optical spectrum as compared to the previously studied all-gold Au144(SR)60. An intense broad absorption peak develops in the range 535-587 nm depending on the amount of doping and doping sites. This result agrees very well with recent experiments by the Dass group for Au144-xCux(SR)60 (x ≤ 23). The analysis of the peaks shows a collective plasmon-like dipole oscillation of the electron density in the metal core. Internal charge transfer from copper to gold and an almost perfect alignment of the upper edges of Cu(3d) and Au(5d) bands are observed in the metal core, contributing to the plasmon-like absorption. The calculations also predict energetically preferable doping of the ligand layer by copper, but such clusters are nonplasmonic.

Quantum state engineering with circuit electromechanical three-body interactions.

We propose a hybrid system with quantum mechanical three-body interactions between photons, phonons, and qubit excitations. These interactions take place in a circuit quantum electrodynamical architecture with a superconducting microwave resonator coupled to a transmon qubit whose shunt capacitance is free to mechanically oscillate. We show that this system design features a three-mode polariton-mechanical mode and a nonlinear transmon-mechanical mode interaction in the strong coupling regime. Together with the strong resonator-transmon interaction, these properties provide intriguing opportunities for manipulations of this hybrid quantum system. We show, in particular, the feasibility of cooling the mechanical motion down to its ground state and preparing various nonclassical states including mechanical Fock and cat states and hybrid tripartite entangled states.

Quantitative analysis of thiolated ligand exchange on gold nanoparticles monitored by 1H NMR spectroscopy.

We use nuclear magnetic resonance spectroscopy methods to quantify the extent of ligand exchange between different types of thiolated molecules on the surface of gold nanoparticles. Specifically, we determine ligand density values for single-moiety ligand shells and then use these data to describe ligand exchange behavior with a second, thiolated molecule. Using these techniques, we identify trends in gold nanoparticle functionalization efficiency with respect to ligand type, concentration, and reaction time as well as distinguish between functionalization pathways where the new ligand may either replace the existing ligand shell (exchange) or add to it ("backfilling"). Specifically, we find that gold nanoparticles functionalized with thiolated macromolecules, such as poly(ethylene glycol) (1 kDa), exhibit ligand exchange efficiencies ranging from 70% to 95% depending on the structure of the incoming ligand. Conversely, gold nanoparticles functionalized with small-molecule thiolated ligands exhibit exchange efficiencies as low as 2% when exposed to thiolated molecules under identical exchange conditions. Taken together, the reported results provide advances in the fundamental understanding of mixed ligand shell formation and will be important for the preparation of gold nanoparticles in a variety of biomedical, optoelectronic, and catalytic applications.

Synchronized switching in a josephson junction crystal.

We consider a superconducting coplanar waveguide resonator where the central conductor is interrupted by a series of uniformly spaced Josephson junctions. The device forms an extended medium that is optically nonlinear on the single photon level with normal modes that inherit the full nonlinearity of the junctions but are nonetheless accessible via the resonator ports. For specific plasma frequencies of the junctions, a set of normal modes clusters in a narrow band and eventually becomes entirely degenerate. Upon increasing the intensity of a red detuned drive on these modes, we observe a sharp and synchronized switching from low-occupation quantum states to high-occupation classical fields, accompanied by a pronounced jump from low to high output intensity.

Single-photon transistor in circuit quantum electrodynamics.

We introduce a circuit quantum electrodynamical setup for a "single-photon" transistor. In our approach photons propagate in two open transmission lines that are coupled via two interacting transmon qubits. The interaction is such that no photons are exchanged between the two transmission lines but a single photon in one line can completely block or enable the propagation of photons in the other line. High on-off ratios can be achieved for feasible experimental parameters. Our approach is inherently scalable as all photon pulses can have the same pulse shape and carrier frequency such that output signals of one transistor can be input signals for a consecutive transistor.

Photon solid phases in driven arrays of nonlinearly coupled cavities.

We introduce and study the properties of an array of QED cavities coupled by nonlinear elements, in the presence of photon leakage and driven by a coherent source. The nonlinear couplings lead to photon hopping and to nearest-neighbor Kerr terms. By tuning the system parameters, the steady state of the array can exhibit a photon crystal associated with a periodic modulation of the photon blockade. In some cases, the crystalline ordering may coexist with phase synchronization. The class of cavity arrays we consider can be built with superconducting circuits of existing technology.

Photoluminescent gold-copper nanoparticle alloys with composition-tunable near-infrared emission.

Discrete gold nanoparticles with diameters between 2 and 3 nm show remarkable properties including enhanced catalytic behavior and photoluminescence. However, tunability of these properties is limited by the tight size range within which they are observed. Here, we report the synthesis of discrete, bimetallic gold-copper nanoparticle alloys (diameter ≅ 2-3 nm) which display photoluminescent properties that can be tuned by changing the alloy composition. Electron microscopy, X-ray photoelectron spectroscopy, inductively coupled plasma mass spectrometry, and pulsed-field gradient stimulated echo (1)H NMR measurements show that the nanoparticles are homogeneous, discrete, and crystalline. Upon varying the composition of the nanoparticles from 0% to 100% molar ratio copper, the photoluminescence maxima shift from 947 to 1067 nm, with excitation at 360 nm. The resulting particles exhibit brightness values (molar extinction coefficient (ε) × quantum yield (Φ)) that are more than an order of magnitude larger than the brightest near-infrared-emitting lanthanide complexes and small-molecule probes evaluated under similar conditions.

Quantum information processing with nanomechanical qubits.

We introduce an approach to quantum information processing where the information is stored in the motional degrees of freedom of nanomechanical devices. The qubits of our approach are formed by the two lowest energy levels of mechanical resonators, which are tuned to be strongly anharmonic by suitable electrostatic fields. Single qubit rotations are conducted by radio-frequency voltage pulses that are applied to individual resonators. Two-qubit entangling gates in turn are implemented via a coupling of two qubits to a common optical resonance of a high finesse cavity. We find that gate fidelities exceeding 99% can be achieved for realistic experimental parameters.

Polariton crystallization in driven arrays of lossy nonlinear resonators.

We investigate the steady states of a lossy array of nonlinear optical resonators that are driven by lasers and interact via mutual photon tunneling. For weak nonlinearities, we find two-mode squeezing of polaritons in modes whose quasimomenta match the relative phases of the laser drives. For strong nonlinearities the spatial polariton density-density correlations indicate that the polaritons crystallize and are predominantly found at a specific distance from each other despite being injected by a coherent light source and damped by the environment.