The hardware is the software.

Human brains and bodies are not hardware running software: the hardware is the software. We reason that because the physics of artificial intelligence hardware and of human biological "hardware" is distinct, neuromorphic engineers need to be selective in the inspiration we take from neuroscience.

Quantum-noise-limited optical neural networks operating at a few quanta per activation.

A practical limit to energy efficiency in computation is ultimately from noise, with quantum noise [1] as the fundamental floor. Analog physical neural networks [2], which hold promise for improved energy efficiency and speed compared to digital electronic neural networks, are nevertheless typically operated in a relatively high-power regime so that the signal-to-noise ratio (SNR) is large (>10). We study optical neural networks [3] operated in the limit where all layers except the last use only a single photon to cause a neuron activation. In this regime, activations are dominated by quantum noise from the fundamentally probabilistic nature of single-photon detection. We show that it is possible to perform accurate machine-learning inference in spite of the extremely high noise (signal-to-noise ratio ~ 1). We experimentally demonstrated MNIST handwritten-digit classification with a test accuracy of 98% using an optical neural network with a hidden layer operating in the single-photon regime; the optical energy used to perform the classification corresponds to 0.008 photons per multiply-accumulate (MAC) operation, which is equivalent to 0.003 attojoules of optical energy per MAC. Our experiment also used >40× fewer photons per inference than previous state-of-the-art low-optical-energy demonstrations [4, 5] to achieve the same accuracy of >90%. Our training approach, which directly models the system's stochastic behavior, might also prove useful with non-optical ultra-low-power hardware.

An optical neural network using less than 1 photon per multiplication.

Deep learning has become a widespread tool in both science and industry. However, continued progress is hampered by the rapid growth in energy costs of ever-larger deep neural networks. Optical neural networks provide a potential means to solve the energy-cost problem faced by deep learning. Here, we experimentally demonstrate an optical neural network based on optical dot products that achieves 99% accuracy on handwritten-digit classification using ~3.1 detected photons per weight multiplication and ~90% accuracy using ~0.66 photons (~2.5 × 10-19 J of optical energy) per weight multiplication. The fundamental principle enabling our sub-photon-per-multiplication demonstration-noise reduction from the accumulation of scalar multiplications in dot-product sums-is applicable to many different optical-neural-network architectures. Our work shows that optical neural networks can achieve accurate results using extremely low optical energies.

Deep physical neural networks trained with backpropagation.

Deep-learning models have become pervasive tools in science and engineering. However, their energy requirements now increasingly limit their scalability1. Deep-learning accelerators2-9 aim to perform deep learning energy-efficiently, usually targeting the inference phase and often by exploiting physical substrates beyond conventional electronics. Approaches so far10-22 have been unable to apply the backpropagation algorithm to train unconventional novel hardware in situ. The advantages of backpropagation have made it the de facto training method for large-scale neural networks, so this deficiency constitutes a major impediment. Here we introduce a hybrid in situ-in silico algorithm, called physics-aware training, that applies backpropagation to train controllable physical systems. Just as deep learning realizes computations with deep neural networks made from layers of mathematical functions, our approach allows us to train deep physical neural networks made from layers of controllable physical systems, even when the physical layers lack any mathematical isomorphism to conventional artificial neural network layers. To demonstrate the universality of our approach, we train diverse physical neural networks based on optics, mechanics and electronics to experimentally perform audio and image classification tasks. Physics-aware training combines the scalability of backpropagation with the automatic mitigation of imperfections and noise achievable with in situ algorithms. Physical neural networks have the potential to perform machine learning faster and more energy-efficiently than conventional electronic processors and, more broadly, can endow physical systems with automatically designed physical functionalities, for example, for robotics23-26, materials27-29 and smart sensors30-32.

Engineering a Kerr-Based Deterministic Cubic Phase Gate via Gaussian Operations.

We propose a deterministic, measurement-free implementation of a cubic phase gate for continuous-variable quantum information processing. In our scheme, the applications of displacement and squeezing operations allow us to engineer the effective evolution of the quantum state propagating through an optical Kerr nonlinearity. Under appropriate conditions, we show that the input state evolves according to a cubic phase Hamiltonian, and we find that the cubic phase gate error decreases inverse quartically with the amount of quadrature squeezing, even in the presence of linear loss. We also show how our scheme can be adapted to deterministically generate a nonclassical approximate cubic phase state with high fidelity using a ratio of native nonlinearity to linear loss of only 10^{-4}, indicating that our approach may be experimentally viable in the near term even on all-optical platforms, e.g., using quantum solitons in pulsed nonlinear nanophotonics.

Quantum Computation of Electronic Transitions Using a Variational Quantum Eigensolver.

We develop an extension of the variational quantum eigensolver (VQE) algorithm-multistate contracted VQE (MC-VQE)-that allows for the efficient computation of the transition energies between the ground state and several low-lying excited states of a molecule, as well as the oscillator strengths associated with these transitions. We numerically simulate MC-VQE by computing the absorption spectrum of an ab initio exciton model of an 18-chromophore light-harvesting complex from purple photosynthetic bacteria.

Experimental investigation of performance differences between coherent Ising machines and a quantum annealer.

Physical annealing systems provide heuristic approaches to solving combinatorial optimization problems. Here, we benchmark two types of annealing machines-a quantum annealer built by D-Wave Systems and measurement-feedback coherent Ising machines (CIMs) based on optical parametric oscillators-on two problem classes, the Sherrington-Kirkpatrick (SK) model and MAX-CUT. The D-Wave quantum annealer outperforms the CIMs on MAX-CUT on cubic graphs. On denser problems, however, we observe an exponential penalty for the quantum annealer [exp(-αDW N 2)] relative to CIMs [exp(-αCIM N)] for fixed anneal times, both on the SK model and on 50% edge density MAX-CUT. This leads to a several orders of magnitude time-to-solution difference for instances with over 50 vertices. An optimal-annealing time analysis is also consistent with a substantial projected performance difference. The difference in performance between the sparsely connected D-Wave machine and the fully-connected CIMs provides strong experimental support for efforts to increase the connectivity of quantum annealers.

Large-Scale, Quantitative Protein Assays on a High-Throughput DNA Sequencing Chip.

High-throughput DNA sequencing techniques have enabled diverse approaches for linking DNA sequence to biochemical function. In contrast, assays of protein function have substantial limitations in terms of throughput, automation, and widespread availability. We have adapted an Illumina high-throughput sequencing chip to display an immense diversity of ribosomally translated proteins and peptides and then carried out fluorescence-based functional assays directly on this flow cell, demonstrating that a single, widely available high-throughput platform can perform both sequencing-by-synthesis and protein assays. We quantified the binding of the M2 anti-FLAG antibody to a library of 1.3 × 104 variant FLAG peptides, exploring non-additive effects of combinations of mutations and discovering a "superFLAG" epitope variant. We also measured the enzymatic activity of 1.56 × 105 molecular variants of full-length human O6-alkylguanine-DNA alkyltransferase (SNAP-tag). This comprehensive corpus of catalytic rates revealed amino acid interaction networks and cooperativity, linked positive cooperativity to structural proximity, and revealed ubiquitous positively cooperative interactions with histidine residues.

Destabilization of Local Minima in Analog Spin Systems by Correction of Amplitude Heterogeneity.

The relaxation of binary spins to analog values has been the subject of much debate in the field of statistical physics, neural networks, and more recently quantum computing, notably because the benefits of using an analog state for finding lower energy spin configurations are usually offset by the negative impact of the improper mapping of the energy function that results from the relaxation. We show that it is possible to destabilize trapping sets of analog states that correspond to local minima of the binary spin Hamiltonian by extending the phase space to include error signals that correct amplitude inhomogeneity of the analog spin states and controlling the divergence of their velocity. Performance of the proposed analog spin system in finding lower energy states is competitive against state-of-the-art heuristics.

Comprehensive and quantitative mapping of RNA-protein interactions across a transcribed eukaryotic genome.

RNA-binding proteins (RBPs) control the fate of nearly every transcript in a cell. However, no existing approach for studying these posttranscriptional gene regulators combines transcriptome-wide throughput and biophysical precision. Here, we describe an assay that accomplishes this. Using commonly available hardware, we built a customizable, open-source platform that leverages the inherent throughput of Illumina technology for direct biophysical measurements. We used the platform to quantitatively measure the binding affinity of the prototypical RBP Vts1 for every transcript in the Saccharomyces cerevisiae genome. The scale and precision of these measurements revealed many previously unknown features of this well-studied RBP. Our transcribed genome array (TGA) assayed both rare and abundant transcripts with equivalent proficiency, revealing hundreds of low-abundance targets missed by previous approaches. These targets regulated diverse biological processes including nutrient sensing and the DNA damage response, and implicated Vts1 in de novo gene "birth." TGA provided single-nucleotide resolution for each binding site and delineated a highly specific sequence and structure motif for Vts1 binding. Changes in transcript levels in vts1Δ cells established the regulatory function of these binding sites. The impact of Vts1 on transcript abundance was largely independent of where it bound within an mRNA, challenging prevailing assumptions about how this RBP drives RNA degradation. TGA thus enables a quantitative description of the relationship between variant RNA structures, affinity, and in vivo phenotype on a transcriptome-wide scale. We anticipate that TGA will provide similarly comprehensive and quantitative insights into the function of virtually any RBP.

A coherent Ising machine for 2000-node optimization problems.

The analysis and optimization of complex systems can be reduced to mathematical problems collectively known as combinatorial optimization. Many such problems can be mapped onto ground-state search problems of the Ising model, and various artificial spin systems are now emerging as promising approaches. However, physical Ising machines have suffered from limited numbers of spin-spin couplings because of implementations based on localized spins, resulting in severe scalability problems. We report a 2000-spin network with all-to-all spin-spin couplings. Using a measurement and feedback scheme, we coupled time-multiplexed degenerate optical parametric oscillators to implement maximum cut problems on arbitrary graph topologies with up to 2000 nodes. Our coherent Ising machine outperformed simulated annealing in terms of accuracy and computation time for a 2000-node complete graph.

A fully programmable 100-spin coherent Ising machine with all-to-all connections.

Unconventional, special-purpose machines may aid in accelerating the solution of some of the hardest problems in computing, such as large-scale combinatorial optimizations, by exploiting different operating mechanisms than those of standard digital computers. We present a scalable optical processor with electronic feedback that can be realized at large scale with room-temperature technology. Our prototype machine is able to find exact solutions of, or sample good approximate solutions to, a variety of hard instances of Ising problems with up to 100 spins and 10,000 spin-spin connections.

Ultrafast optical control of individual quantum dot spin qubits.

Single spins in semiconductor quantum dots form a promising platform for solid-state quantum information processing. The spin-up and spin-down states of a single electron or hole, trapped inside a quantum dot, can represent a single qubit with a reasonably long decoherence time. The spin qubit can be optically coupled to excited (charged exciton) states that are also trapped in the quantum dot, which provides a mechanism to quickly initialize, manipulate and measure the spin state with optical pulses, and to interface between a stationary matter qubit and a 'flying' photonic qubit for quantum communication and distributed quantum information processing. The interaction of the spin qubit with light may be enhanced by placing the quantum dot inside a monolithic microcavity. An entire system, consisting of a two-dimensional array of quantum dots and a planar microcavity, may plausibly be constructed by modern semiconductor nano-fabrication technology and could offer a path toward chip-sized scalable quantum repeaters and quantum computers. This article reviews the recent experimental developments in optical control of single quantum dot spins for quantum information processing. We highlight demonstrations of a complete set of all-optical single-qubit operations on a single quantum dot spin: initialization, an arbitrary SU(2) gate, and measurement. We review the decoherence and dephasing mechanisms due to hyperfine interaction with the nuclear-spin bath, and show how the single-qubit operations can be combined to perform spin echo sequences that extend the qubit decoherence from a few nanoseconds to several microseconds, more than 5 orders of magnitude longer than the single-qubit gate time. Two-qubit coupling is discussed, both within a single chip by means of exchange coupling of nearby spins and optically induced geometric phases, as well as over longer-distances. Long-distance spin-spin entanglement can be generated if each spin can emit a photon that is entangled with the spin, and these photons are then interfered. We review recent work demonstrating entanglement between a stationary spin qubit and a flying photonic qubit. These experiments utilize the polarization- and frequency-dependent spontaneous emission from the lowest charged exciton state to single spin Zeeman sublevels.

Complete tomography of a high-fidelity solid-state entangled spin-photon qubit pair.

Entanglement between stationary quantum memories and photonic qubits is crucial for future quantum communication networks. Although high-fidelity spin-photon entanglement was demonstrated in well-isolated atomic and ionic systems, in the solid-state, where massively parallel, scalable networks are most realistically conceivable, entanglement fidelities are typically limited due to intrinsic environmental interactions. Distilling high-fidelity entangled pairs from lower-fidelity precursors can act as a remedy, but the required overhead scales unfavourably with the initial entanglement fidelity. With spin-photon entanglement as a crucial building block for entangling quantum network nodes, obtaining high-fidelity entangled pairs becomes imperative for practical realization of such networks. Here we report the first results of complete state tomography of a solid-state spin-photon-polarization-entangled qubit pair, using a single electron-charged indium arsenide quantum dot. We demonstrate record-high fidelity in the solid-state of well over 90%, and the first (99.9%-confidence) achievement of a fidelity that will unambiguously allow for entanglement distribution in solid-state quantum repeater networks.

Downconversion quantum interface for a single quantum dot spin and 1550-nm single-photon channel.

Long-distance quantum communication networks require appropriate interfaces between matter qubit-based nodes and low-loss photonic quantum channels. We implement a downconversion quantum interface, where the single photons emitted from a semiconductor quantum dot at 910 nm are downconverted to 1560 nm using a fiber-coupled periodically poled lithium niobate waveguide and a 2.2-µm pulsed pump laser. The single-photon character of the quantum dot emission is preserved during the downconversion process: we measure a cross-correlation g(2)(τ = 0) = 0.17 using resonant excitation of the quantum dot. We show that the downconversion interface is fully compatible with coherent optical control of the quantum dot electron spin through the observation of Rabi oscillations in the downconverted photon counts. These results represent a critical step towards a long-distance hybrid quantum network in which subsystems operating at different wavelengths are connected through quantum frequency conversion devices and 1.5-µm quantum channels.

Quantum-dot spin-photon entanglement via frequency downconversion to telecom wavelength.

Long-distance quantum teleportation and quantum repeater technologies require entanglement between a single matter quantum bit (qubit) and a telecommunications (telecom)-wavelength photonic qubit. Electron spins in III-V semiconductor quantum dots are among the matter qubits that allow for the fastest spin manipulation and photon emission, but entanglement between a single quantum-dot spin qubit and a flying (propagating) photonic qubit has yet to be demonstrated. Moreover, many quantum dots emit single photons at visible to near-infrared wavelengths, where silica fibre losses are so high that long-distance quantum communication protocols become difficult to implement. Here we demonstrate entanglement between an InAs quantum-dot electron spin qubit and a photonic qubit, by frequency downconversion of a spontaneously emitted photon from a singly charged quantum dot to a wavelength of 1,560 nanometres. The use of sub-10-picosecond pulses at a wavelength of 2.2 micrometres in the frequency downconversion process provides the necessary quantum erasure to eliminate which-path information in the photon energy. Together with previously demonstrated indistinguishable single-photon emission at high repetition rates, the present technique advances the III-V semiconductor quantum-dot spin system as a promising platform for long-distance quantum communication.

Pulsed nuclear pumping and spin diffusion in a single charged quantum dot.

We report the observation of a feedback process between the nuclear spins in a single charged quantum dot under coherently pulsed optical excitation and its trion transition. The optical pulse sequence intersperses resonant narrow-band pumping for spin initialization with off-resonant ultrafast pulses for coherent electron-spin rotation. A hysteretic sawtooth pattern in the free-induction decay of the single electron spin is observed; a mathematical model indicates a competition between optical nuclear pumping and nuclear spin-diffusion. This effect allows dynamic tuning of the electron Larmor frequency to a value determined by the pulse timing, potentially allowing more complex coherent control operations.

In-plane resistivity anisotropy in an underdoped iron arsenide superconductor.

High-temperature superconductivity often emerges in the proximity of a symmetry-breaking ground state. For superconducting iron arsenides, in addition to the antiferromagnetic ground state, a small structural distortion breaks the crystal's C(4 )rotational symmetry in the underdoped part of the phase diagram. We reveal that the representative iron arsenide Ba(Fe(1)(-x)Co(x))(2)As(2) develops a large electronic anisotropy at this transition via measurements of the in-plane resistivity of detwinned single crystals, with the resistivity along the shorter b axis rho(b) being greater than rho(a). The anisotropy reaches a maximum value of ~2 for compositions in the neighborhood of the beginning of the superconducting dome. For temperatures well above the structural transition, uniaxial stress induces a resistivity anisotropy, indicating a substantial nematic susceptibility.