Pyramid diffractive optical networks for unidirectional image magnification and demagnification

Diffractive deep neural networks (D2NNs) are composed of successive transmissive layers optimized using supervised deep learning to all-optically implement various computational tasks between an input and output field-of-view. Here, we present a pyramid-structured diffractive optical network design (which we term P-D2NN), optimized specifically for unidirectional image magnification and demagnification. In this design, the diffractive layers are pyramidally scaled in alignment with the direction of the image magnification or demagnification. This P-D2NN design creates high-fidelity magnified or demagnified images in only one direction, while inhibiting the image formation in the opposite direction-achieving the desired unidirectional imaging operation using a much smaller number of diffractive degrees of freedom within the optical processor volume. Furthermore, the P-D2NN design maintains its unidirectional image magnification/demagnification functionality across a large band of illumination wavelengths despite being trained with a single wavelength. We also designed a wavelength-multiplexed P-D2NN, where a unidirectional magnifier and a unidirectional demagnifier operate simultaneously in opposite directions, at two distinct illumination wavelengths. Furthermore, we demonstrate that by cascading multiple unidirectional P-D2NN modules, we can achieve higher magnification factors. The efficacy of the P-D2NN architecture was also validated experimentally using terahertz illumination, successfully matching our numerical simulations. P-D2NN offers a physics-inspired strategy for designing task-specific visual processors.

Ultrafast observation of the abnormal time delay of femtosecond laser pulses in a quartz crystal

Light with different frequencies has different propagation speeds when propagating in a medium. Nonlinear optics indicates that the refractive index of the medium also varies with the intensity of light. In this article, we have discovered an anomalous slow light phenomenon that is independent of light intensity through multi-frame ultrafast imaging. The experimental results show that when coaxial 800-nm and 400-nm pulses simultaneously enter the quartz crystal, the time delay between the 800-nm and 400-nm laser pulses is up to 5 times the normal value calculated by the dispersion theory. Moreover, this delay is independent of the laser intensity, indicating that the anomalous slow light phenomenon does not originate from refractive index changes in nonlinear optics. This abnormal time delay effect may find more applications in different fields, and its physical mechanism still needs further exploration.

Direct electromagnetic information processing with planar diffractive neural network

Diffractive neural network in electromagnetic wave-driven system has attracted great attention due to its ultrahigh parallel computing capability and energy efficiency. However, recent neural networks based on the diffractive framework still face the bottlenecks of misalignment and relatively large size limiting their further applications. Here, we propose a planar diffractive neural network (pla-NN) with a highly integrated and conformal architecture to achieve direct signal processing in the microwave frequency. On the basis of printed circuit fabrication process, the misalignment could be effectively circumvented while enabling flexible extension for multiple conformal and stacking designs. We first conduct validation on the fashion-MNIST dataset and experimentally build up a system using the proposed network architecture for direct recognition of different geometry structures in the electromagnetic space. We envision that the presented architecture, once combined with the advanced dynamic maneuvering techniques and flexible topology, would exhibit unlimited potentials in the areas of high-performance computing, wireless sensing, and flexible wearable electronics.

Reconfigurable quantum photonic circuits based on quantum dots

Quantum photonic integrated circuits, composed of linear-optical elements, offer an efficient way for encoding and processing quantum information on-chip. At their core, these circuits rely on reconfigurable phase shifters, typically constructed from classical components such as thermo- or electro-optical materials, while quantum solid-state emitters such as quantum dots are limited to acting as single-photon sources. Here, we demonstrate the potential of quantum dots as reconfigurable phase shifters. We use numerical models based on established literature parameters to show that circuits utilizing these emitters enable high-fidelity operation and are scalable. Despite the inherent imperfections associated with quantum dots, such as imperfect coupling, dephasing, or spectral diffusion, we show that circuits based on these emitters may be optimized such that these do not significantly impact the unitary infidelity. Specifically, they do not increase the infidelity by more than 0.001 in circuits with up to 10 modes, compared to those affected only by standard nanophotonic losses and routing errors. For example, we achieve fidelities of 0.9998 in quantum-dot-based circuits enacting controlled-phase and - not gates without any redundancies. These findings demonstrate the feasibility of quantum emitter-driven quantum information processing and pave the way for cryogenically-compatible, fast, and low-loss reconfigurable quantum photonic circuits.

Perfect linear optics using silicon photonics

Recently there has been growing interest in using photonics to perform the linear algebra operations of neuromorphic and quantum computing applications, aiming at harnessing silicon photonics' (SiPho) high-speed and energy-efficiency credentials. Accurately mapping, however, a matrix into optics remains challenging, since state-of-the-art optical architectures are sensitive to fabrication imperfections. This leads to reduced fidelity that degrades as the insertion losses of the optical matrix nodes or the matrix dimensions increase. In this work, we present the experimental deployment of a 4 × 4 coherent crossbar (Xbar) as a silicon chip and validate experimentally its theoretically predicted fidelity restoration credentials. We demonstrate the experimental implementation of 10,000 arbitrary linear transformations achieving a record-high fidelity of 99.997% ± 0.002, limited mainly by the measurement equipment. Our work represents an integrated optical circuit providing almost unity and loss-independent fidelity in the realization of arbitrary matrices, highlighting light's credentials in resolving complex computations.

Ultracompact and multifunctional integrated photonic platform

Realizing a multifunctional integrated photonic platform is one of the goals for future optical information processing, which usually requires large size to realize due to multiple integration challenges. Here, we realize a multifunctional integrated photonic platform with ultracompact footprint based on inverse design. The photonic platform is compact with 86 inverse designed-fixed couplers and 91 phase shifters. The footprint of each coupler is 4 μm by 2 μm, while the whole photonic platform is 3 mm by 0.2 mm-one order of magnitude smaller than previous designs. One-dimensional Floquet Su-Schrieffer-Heeger model and Aubry-André-Harper model are performed with measured fidelities of 97.90 (±0.52) % and 99.34 (±0.44) %, respectively. We also demonstrate a handwritten digits classification task with the test accuracy of 87% using on-chip training. Moreover, the scalability of this platform has been proved by demonstrating more complex computing tasks. This work provides an effective method to realize an ultrasmall integrated photonic platform.

Experimental Quantum Homomorphic Encryption Using a Quantum Photonic Chip

A fully homomorphic encryption system enables computation on encrypted data without the necessity for prior decryption. This facilitates the seamless establishment of a secure quantum channel, bridging the server and client components, and thereby providing the client with secure access to the server's substantial computational capacity for executing quantum operations. However, traditional homomorphic encryption systems lack scalability, programmability, and stability. In this Letter, we experimentally demonstrate a proof-of-concept implementation of a homomorphic encryption scheme on a compact quantum chip, verifying the feasibility of using photonic chips for quantum homomorphic encryption. Our work not only provides a solution for circuit expansion, addressing the longstanding challenge of scalability while significantly reducing the size of quantum network infrastructure, but also lays the groundwork for the development of highly sophisticated quantum fully homomorphic encryption systems.

An atomic boson sampler

A boson sampler implements a restricted model of quantum computing. It is defined by the ability to sample from the distribution resulting from the interference of identical bosons propagating according to programmable, non-interacting dynamics1. An efficient exact classical simulation of boson sampling is not believed to exist, which has motivated ground-breaking boson sampling experiments in photonics with increasingly many photons2-12. However, it is difficult to generate and reliably evolve specific numbers of photons with low loss, and thus probabilistic techniques for postselection7 or marked changes to standard boson sampling10-12 are generally used. Here, we address the above challenges by implementing boson sampling using ultracold atoms13,14 in a two-dimensional, tunnel-coupled optical lattice. This demonstration is enabled by a previously unrealized combination of tools involving high-fidelity optical cooling and imaging of atoms in a lattice, as well as programmable control of those atoms using optical tweezers. When extended to interacting systems, our work demonstrates the core abilities required to directly assemble ground and excited states in simulations of various Hubbard models15,16.

Empowering high-dimensional optical fiber communications with integrated photonic processors

Mode-division multiplexing (MDM) in optical fibers enables multichannel capabilities for various applications, including data transmission, quantum networks, imaging, and sensing. However, high-dimensional optical fiber systems, usually necessity bulk-optics approaches for launching different orthogonal fiber modes into the optical fiber, and multiple-input multiple-output digital electronic signal processing at the receiver to undo the arbitrary mode scrambling introduced by coupling and transmission in a multi-mode fiber. Here we show that a high-dimensional optical fiber communication system can be implemented by a reconfigurable integrated photonic processor, featuring kernels of multichannel mode multiplexing transmitter and all-optical descrambling receiver. Effective mode management can be achieved through the configuration of the integrated optical mesh. Inter-chip MDM optical communications involving six spatial- and polarization modes was realized, despite the presence of unknown mode mixing and polarization rotation in the circular-core optical fiber. The proposed photonic integration approach holds promising prospects for future space-division multiplexing applications.

A von-Neumann-like photonic processor and its application in studying quantum signature of chaos

Photonic quantum computation plays an important role and offers unique advantages. Two decades after the milestone work of Knill-Laflamme-Milburn, various architectures of photonic processors have been proposed, and quantum advantage over classical computers has also been demonstrated. It is now the opportune time to apply this technology to real-world applications. However, at current technology level, this aim is restricted by either programmability in bulk optics or loss in integrated optics for the existing architectures of processors, for which the resource cost is also a problem. Here we present a von-Neumann-like architecture based on temporal-mode encoding and looped structure on table, which is capable of multimode-universal programmability, resource-efficiency, phase-stability and software-scalability. In order to illustrate these merits, we execute two different programs with varying resource requirements on the same processor, to investigate quantum signature of chaos from two aspects: the signature behaviors exhibited in phase space (13 modes), and the Fermi golden rule which has not been experimentally studied in quantitative way before (26 modes). The maximal program contains an optical interferometer network with 1694 freely-adjustable phases. Considering current state-of-the-art, our architecture stands as the most promising candidate for real-world applications.

Programmable Photonic Time Circuits for Highly Scalable Universal Unitaries

Programmable photonic circuits (PPCs) have garnered substantial interest for their potential in facilitating deep learning accelerations and universal quantum computations. Although photonic computation using PPCs offers ultrafast operation, energy-efficient matrix calculations, and room-temperature quantum states, its poor scalability hinders integration. This challenge arises from the temporally one-shot operation of propagating light in conventional PPCs, resulting in a light-speed increase in device footprints. Here we propose the concept of programmable photonic time circuits, utilizing time-cycle-based computations analogous to gate cycling in the von Neumann architecture and quantum computation. Our building block is a reconfigurable SU(2) time gate, consisting of two resonators with tunable resonances, and coupled via time-coded dual-channel gauge fields. We demonstrate universal U(N) operations with high fidelity using an assembly of the SU(2) time gates, substantially improving scalability from O(N^{2}) to O(N) in terms of both the footprint and the number of gates. This result paves the way for PPC implementation in very large-scale integration.

General-purpose programmable photonic processor for advanced radiofrequency applications

A general-purpose photonic processor can be built integrating a silicon photonic programmable core in a technology stack comprising an electronic monitoring and controlling layer and a software layer for resource control and programming. This processor can leverage the unique properties of photonics in terms of ultra-high bandwidth, high-speed operation, and low power consumption while operating in a complementary and synergistic way with electronic processors. These features are key in applications such as next-generation 5/6 G wireless systems where reconfigurable filtering, frequency conversion, arbitrary waveform generation, and beamforming are currently provided by microwave photonic subsystems that cannot be scaled down. Here we report the first general-purpose programmable processor with the remarkable capability to implement all the required basic functionalities of a microwave photonic system by suitable programming of its resources. The processor is fabricated in silicon photonics and incorporates the full photonic/electronic and software stack.

Deep photonic network platform enabling arbitrary and broadband optical functionality

Expanding applications in optical communications, computing, and sensing continue to drive the need for high-performance integrated photonic components. Designing these on-chip systems with arbitrary functionality requires beyond what is possible with physical intuition, for which machine learning-based methods have recently become popular. However, computational demands for physically accurate device simulations present critical challenges, significantly limiting scalability and design flexibility of these methods. Here, we present a highly-scalable, physics-informed design platform for on-chip optical systems with arbitrary functionality, based on deep photonic networks of custom-designed Mach-Zehnder interferometers. Leveraging this platform, we demonstrate ultra-broadband power splitters and a spectral duplexer, each designed within two minutes. The devices exhibit state-of-the-art experimental performance with insertion losses below 0.66 dB, and 1-dB bandwidths exceeding 120 nm. This platform provides a tractable path towards systematic, large-scale photonic system design, enabling custom power, phase, and dispersion profiles for high-throughput communications, quantum information processing, and medical/biological sensing applications.

Quantum interference of pulsed time-bin entanglement generated from silicon ring resonator

We demonstrate a pulsed operation of an entangled photon pair source that is based on a silicon ring resonator. Time-bin entangled photon pairs at telecommunication wavelengths are generated via spontaneous four-wave mixing, which is excited by a pulsed pump laser. The entanglement between the generated photon pair is analyzed by using asymmetric Mach-Zehnder interferometers followed by single-photon detectors, resulting in non-classical interference with a visibility exceeding a classical limit. The reason for the degradation of the interference visibility is discussed using the theoretical model with experimental parameters. Our experimental results show successful pulsed generation of entanglement, which represents an important step towards a synchronized quantum network based on silicon photonics.

Programmable high-dimensional Hamiltonian in a photonic waveguide array

Waveguide lattices offer a compact and stable platform for a range of applications, including quantum walks, condensed matter system simulation, and classical and quantum information processing. However, to date, waveguide lattice devices have been static and designed for specific applications. We present a programmable waveguide array in which the Hamiltonian terms can be individually electro-optically tuned to implement various Hamiltonian continuous-time evolutions on a single device. We used a single array with 11 waveguides in lithium niobate, controlled via 22 electrodes, to perform a range of experiments that realized the Su-Schriffer-Heeger model, the Aubrey-Andre model, and Anderson localization, which is equivalent to over 2500 static devices. Our architecture's micron-scale local electric fields overcome the cross-talk limitations of thermo-optic phase shifters in other platforms such as silicon, silicon-nitride, and silica. Electro-optic control allows for ultra-fast and more precise reconfigurability with lower power consumption, and with quantum input states, our platform can enable the study of multiple condensed matter quantum dynamics with a single device.

Realization of photon correlations beyond the linear optics limit

Linear optical transformations of multiple single-photon inputs are fundamental for the development of photonic quantum technologies. Various nonclassical correlations can already be observed directly in states generated using only single-photon inputs and linear optics transformations. However, some quantum correlations require additional operations, and states that exhibit such correlations are classified as non-Fock states. Here, we demonstrate the generation of a two-photon three-mode non-Fock state that exhibits conditional quantum coherences that can only be achieved by non-Fock states. We determine the fidelity of the non-Fock state based on experimentally observed conditional visibilities that characterize the state and compare the result to the fidelity bounds for different classes of Fock and non-Fock states. Our experimental verification of the non-Fock character of the state provides insights into the technological requirements needed to achieve nonclassical correlations in multiphoton quantum optics.

Synchronous micromechanically resonant programmable photonic circuits

Programmable photonic integrated circuits (PICs) are emerging as powerful tools for control of light, with applications in quantum information processing, optical range finding, and artificial intelligence. Low-power implementations of these PICs involve micromechanical structures driven capacitively or piezoelectrically but are often limited in modulation bandwidth by mechanical resonances and high operating voltages. Here we introduce a synchronous, micromechanically resonant design architecture for programmable PICs and a proof-of-principle 1×8 photonic switch using piezoelectric optical phase shifters. Our design purposefully exploits high-frequency mechanical resonances and optically broadband components for larger modulation responses on the order of the mechanical quality factor Qm while maintaining fast switching speeds. We experimentally show switching cycles of all 8 channels spaced by approximately 11 ns and operating at 4.6 dB average modulation enhancement. Future advances in micromechanical devices with high Qm, which can exceed 10000, should enable an improved series of low-voltage and high-speed programmable PICs.

Auto-calibrating universal programmable photonic circuits: hardware error-correction and defect resilience

It is recently shown that discrete N × N linear unitary operators can be represented by interlacing N + 1 phase shift layers with a fixed intervening operator such as discrete fractional Fourier transform (DFrFT). Here, we show that introducing perturbations to the intervening operations does not compromise the universality of this architecture. Furthermore, we show that this architecture is resilient to defects in the phase shifters as long as no more than one faulty phase shifter is present in each layer. These properties enable post-fabrication auto-calibration of such universal photonic circuits, effectively compensating for fabrication errors and defects in phase components.

Experimental certification of contextuality, coherence, and dimension in a programmable universal photonic processor

Quantum superposition of high-dimensional states enables both computational speed-up and security in cryptographic protocols. However, the exponential complexity of tomographic processes makes certification of these properties a challenging task. In this work, we experimentally certify coherence witnesses tailored for quantum systems of increasing dimension using pairwise overlap measurements enabled by a six-mode universal photonic processor fabricated with a femtosecond laser writing technology. In particular, we show the effectiveness of the proposed coherence and dimension witnesses for qudits of dimensions up to 5. We also demonstrate advantage in a quantum interrogation task and show it is fueled by quantum contextuality. Our experimental results testify to the efficiency of this approach for the certification of quantum properties in programmable integrated photonic platforms.

Programmable MZI based on a silicon photonic MEMS-tunable delay line

We report on a scalable and programmable integrated Mach-Zehnder interferometer (MZI) with a tunable free spectral range (FSR) and extinction ratio (ER). For the tunable path of the MZI, we designed and utilized a tunable delay line having high flexibility based on silicon photonic microelectromechanical systems (MEMS). By utilizing MEMS, the length of the delay line can be geometrically modified. In this way, there is no optical loss penalty other than the waveguide propagation loss as the number of tunable steps increases. Therefore, our device is more scalable in terms of optical loss than the previous approaches based on cascaded MZIs. In addition, the tuning energy required to reconfigure the length is only 8.46 pJ.

Multi-wavelength diffractive neural network with the weighting method

Recently, the diffractive deep neural network (D2NN) has demonstrated the advantages to achieve large-scale computational tasks in terms of high speed, low power consumption, parallelism, and scalability. A typical D2NN with cascaded diffractive elements is designed for monochromatic illumination. Here, we propose a framework to achieve the multi-wavelength D2NN (MW-D2NN) based on the method of weight coefficients. In training, each wavelength is assigned a specific weighting and their output planes construct the wavelength weighting loss function. The trained MW-D2NN can implement the classification of images of handwritten digits at multi-wavelength incident beams. The designed 3-layers MW-D2NN achieves a simulation classification accuracy of 83.3%. We designed a 1-layer MW-D2NN. The simulation and experiment classification accuracy are 71.4% and 67.5% at RGB wavelengths. Furthermore, the proposed MW-D2NN can be extended to intelligent machine vision systems for multi-wavelength and incoherent illumination.

Integrated Bragg grating filters based on silicon-Sb2Se3 with non-volatile bandgap engineering capability

Integrated optical filters show outstanding capability in integrated reconfigurable photonic applications, including wavelength division multiplexing (WDM), programmable photonic processors, and on-chip quantum photonic networks. Present schemes for reconfigurable filters either have a large footprint or suffer from high static power consumption, hindering the development of reconfigurable photonic integrated systems. Here, a reconfigurable hybrid Bragg grating filter is elaborately designed through a precise, modified coupling mode theory. It is also experimentally presented by integrating non-volatile phase change material (PCM) Sb2Se3 on silicon to realize compact, low-loss, and broadband engineering operations. The fabricated filter holds a compact footprint of 0.5 µm × 43.5 µm and maintains a low insertion loss of < 0.5 dB after multiple levels of engineering to achieve crystallization. The filter is able to switch from a low-loss transmission state to the Bragg reflection state, making it a favorable solution for large-scale reconfigurable photonic circuits. With a switching extinction ratio over 30 dB at 1504.85 nm, this hybrid filter breaks the tradeoff between insertion loss and tuning range. These results reveal its potential as a new candidate for a basic element in large-scale non-volatile reconfigurable systems.

Time-Domain Universal Linear-Optical Operations for Universal Quantum Information Processing

We demonstrate universal and programmable three-mode linear-optical operations in the time domain by realizing a scalable dual-loop optical circuit suitable for universal quantum information processing (QIP). The programmability, validity, and deterministic operation of our circuit are demonstrated by performing nine different three-mode operations on squeezed-state pulses, fully characterizing the outputs with variable measurements, and confirming their entanglement. Our circuit can be scaled up just by making the outer loop longer and also extended to universal quantum computers by incorporating feed forward systems. Thus, our work paves the way to large-scale universal optical QIP.

Recent progress in quantum photonic chips for quantum communication and internet

Recent years have witnessed significant progress in quantum communication and quantum internet with the emerging quantum photonic chips, whose characteristics of scalability, stability, and low cost, flourish and open up new possibilities in miniaturized footprints. Here, we provide an overview of the advances in quantum photonic chips for quantum communication, beginning with a summary of the prevalent photonic integrated fabrication platforms and key components for integrated quantum communication systems. We then discuss a range of quantum communication applications, such as quantum key distribution and quantum teleportation. Finally, the review culminates with a perspective on challenges towards high-performance chip-based quantum communication, as well as a glimpse into future opportunities for integrated quantum networks.

Transferable learning on analog hardware

While analog neural network (NN) accelerators promise massive energy and time savings, an important challenge is to make them robust to static fabrication error. Present-day training methods for programmable photonic interferometer circuits, a leading analog NN platform, do not produce networks that perform well in the presence of static hardware errors. Moreover, existing hardware error correction techniques either require individual retraining of every analog NN (which is impractical in an edge setting with millions of devices), place stringent demands on component quality, or introduce hardware overhead. We solve all three problems by introducing one-time error-aware training techniques that produce robust NNs that match the performance of ideal hardware and can be exactly transferred to arbitrary highly faulty photonic NNs with hardware errors up to five times larger than present-day fabrication tolerances.

Demonstration of a Bosonic Quantum Classifier with Data Reuploading

In a single qubit system, a universal quantum classifier can be realized using the data reuploading technique. In this study, we propose a new quantum classifier applying this technique to bosonic systems and successfully demonstrate it using a silicon-based photonic integrated circuit. We established a theory of quantum machine learning algorithm applicable to bosonic systems and implemented a programmable optical circuit combined with an interferometer. Learning and classification using part of the implemented optical quantum circuit with uncorrelated two photons resulted in a classification with a success probability of 94±0.8% in the proof of principle experiment. As this method can be applied to an arbitrary two-mode N-photon system, further development of optical quantum classifiers, such as extensions to quantum entangled and multiphoton states, is expected in the future.

Quantum simulation of thermodynamics in an integrated quantum photonic processor

One of the core questions of quantum physics is how to reconcile the unitary evolution of quantum states, which is information-preserving and time-reversible, with evolution following the second law of thermodynamics, which, in general, is neither. The resolution to this paradox is to recognize that global unitary evolution of a multi-partite quantum state causes the state of local subsystems to evolve towards maximum-entropy states. In this work, we experimentally demonstrate this effect in linear quantum optics by simultaneously showing the convergence of local quantum states to a generalized Gibbs ensemble constituting a maximum-entropy state under precisely controlled conditions, while introducing an efficient certification method to demonstrate that the state retains global purity. Our quantum states are manipulated by a programmable integrated quantum photonic processor, which simulates arbitrary non-interacting Hamiltonians, demonstrating the universality of this phenomenon. Our results show the potential of photonic devices for quantum simulations involving non-Gaussian states.

High-speed thin-film lithium niobate quantum processor driven by a solid-state quantum emitter

Scalable photonic quantum computing architectures pose stringent requirements on photonic processing devices. The needs for low-loss high-speed reconfigurable circuits and near-deterministic resource state generators are some of the most challenging requirements. Here, we develop an integrated photonic platform based on thin-film lithium niobate and interface it with deterministic solid-state single-photon sources based on quantum dots in nanophotonic waveguides. The generated photons are processed with low-loss circuits programmable at speeds of several gigahertz. We realize a variety of key photonic quantum information processing functionalities with the high-speed circuits, including on-chip quantum interference, photon demultiplexing, and reprogrammability of a four-mode universal photonic circuit. These results show a promising path forward for scalable photonic quantum technologies by merging integrated photonics with solid-state deterministic photon sources in a heterogeneous approach to scaling up.

Fast reconstruction of programmable integrated interferometers

Programmable linear optical interferometers are important for classical and quantum information technologies, as well as for building hardware-accelerated artificial neural networks. Recent results showed the possibility of constructing optical interferometers that could implement arbitrary transformations of input fields even in the case of high manufacturing errors. The building of detailed models of such devices drastically increases the efficiency of their practical use. The integral design of interferometers complicates its reconstruction since the internal elements are hard to address. This problem can be approached by using optimization algorithms [Opt. Express29, 38429 (2021)10.1364/OE.432481]. In this paper, we present what we believe to be a novel efficient algorithm based on linear algebra only, which does not use computationally expensive optimization procedures. We show that this approach makes it possible to perform fast and accurate characterization of high-dimensional programmable integrated interferometers. Moreover, the method provides access to the physical characteristics of individual interferometer layers.

Strong second-harmonic generation by sublattice polarization in non-uniformly strained monolayer graphene

Despite the potential of graphene for building a variety of quantum photonic devices, its centrosymmetric nature forbids the observation of second harmonic generation (SHG) for developing second-order nonlinear devices. To activate SHG in graphene, extensive research efforts have been directed towards disrupting graphene's inversion symmetry using external stimuli like electric fields. However, these methods fail to engineer graphene's lattice symmetry, which is the root cause of the forbidden SHG. Here, we harness strain engineering to directly manipulate graphene's lattice arrangement and induce sublattice polarization to activate SHG. Surprisingly, the SHG signal is boosted 50-fold at low temperatures, which can be explained by resonant transitions between strain-induced pseudo-Landau levels. The second-order susceptibility of strained graphene is found to be larger than that of hexagonal boron nitride with intrinsic broken inversion symmetry. Our demonstration of strong SHG in strained graphene offers promising possibilities for developing high-efficiency nonlinear devices for integrated quantum circuits.

Experimentally realized in situ backpropagation for deep learning in photonic neural networks

Integrated photonic neural networks provide a promising platform for energy-efficient, high-throughput machine learning with extensive scientific and commercial applications. Photonic neural networks efficiently transform optically encoded inputs using Mach-Zehnder interferometer mesh networks interleaved with nonlinearities. We experimentally trained a three-layer, four-port silicon photonic neural network with programmable phase shifters and optical power monitoring to solve classification tasks using "in situ backpropagation," a photonic analog of the most popular method to train conventional neural networks. We measured backpropagated gradients for phase-shifter voltages by interfering forward- and backward-propagating light and simulated in situ backpropagation for 64-port photonic neural networks trained on MNIST image recognition given errors. All experiments performed comparably to digital simulations ([Formula: see text]94% test accuracy), and energy scaling analysis indicated a route to scalable machine learning.

Hardware Error Correction for MZI-Based Matrix Computation

With the rapid development of artificial intelligence, the electronic system has fallen short of providing the needed computation speed. It is believed that silicon-based optoelectronic computation may be a solution, where Mach-Zehnder interferometer (MZI)-based matrix computation is the key due to its advantages of simple implementation and easy integration on a silicon wafer, but one of the concerns is the precision of the MZI method in the actual computation. This paper will identify the main hardware error sources of MZI-based matrix computation, summarize the available hardware error correction methods from the perspective of the entire MZI meshes and a single MZI device, and propose a new architecture that will largely improve the precision of MZI-based matrix computation without increasing the size of the MZI's mesh, which may lead to a fast and accurate optoelectronic computing system.

Large Baseline Optical Imaging Assisted by Single Photons and Linear Quantum Optics

In this Letter, we show that by combining quantum metrology and networking tools, it is possible to extend the baseline of an interferometric optical telescope and thus improve diffraction-limited imaging of point source positions. The quantum interferometer is based on single-photon sources, linear optical circuits, and efficient photon number counters. Surprisingly, with thermal (stellar) sources of low photon number per mode and high transmission losses across the baseline, the detected photon probability distribution still retains a large amount of Fisher information about the source position, allowing for a significant improvement in the resolution of positioning point sources, on the order of 10  μas. Our proposal can be implemented with current technology. In particular, our proposal does not require experimental optical quantum memories.

Characterizing quantum circuits with qubit functional configurations

We develop a systematic framework for characterizing all quantum circuits with qubit functional configurations. The qubit functional configuration is a mathematical structure that can classify the properties and behaviors of quantum circuits collectively. Major benefits of classifying quantum circuits in this way include: 1. All quantum circuits can be classified into corresponding types; 2. Each type characterizes important properties (such as circuit complexity) of the quantum circuits belonging to it; 3. Each type contains a huge collection of possible quantum circuits allowing systematic investigation of their common properties. We demonstrate the theory's application to analyzing the hardware-efficient ansatzes of variational quantum algorithms. For potential applications, the functional configuration theory may allow systematic understanding and development of quantum algorithms based on their functional configuration types.

Heavy tails and pruning in programmable photonic circuits for universal unitaries

Developing hardware for high-dimensional unitary operators plays a vital role in implementing quantum computations and deep learning accelerations. Programmable photonic circuits are singularly promising candidates for universal unitaries owing to intrinsic unitarity, ultrafast tunability and energy efficiency of photonic platforms. Nonetheless, when the scale of a photonic circuit increases, the effects of noise on the fidelity of quantum operators and deep learning weight matrices become more severe. Here we demonstrate a nontrivial stochastic nature of large-scale programmable photonic circuits-heavy-tailed distributions of rotation operators-that enables the development of high-fidelity universal unitaries through designed pruning of superfluous rotations. The power law and the Pareto principle for the conventional architecture of programmable photonic circuits are revealed with the presence of hub phase shifters, allowing for the application of network pruning to the design of photonic hardware. For the Clements design of programmable photonic circuits, we extract a universal architecture for pruning random unitary matrices and prove that "the bad is sometimes better to be removed" to achieve high fidelity and energy efficiency. This result lowers the hurdle for high fidelity in large-scale quantum computing and photonic deep learning accelerators.

Single-photon detection using high-temperature superconductors

The detection of individual quanta of light is important for quantum communication, fluorescence lifetime imaging, remote sensing and more. Due to their high detection efficiency, exceptional signal-to-noise ratio and fast recovery times, superconducting-nanowire single-photon detectors (SNSPDs) have become a critical component in these applications. However, the operation of conventional SNSPDs requires costly cryocoolers. Here we report the fabrication of two types of high-temperature superconducting nanowires. We observe linear scaling of the photon count rate on the radiation power at the telecommunications wavelength of 1.5 μm and thereby reveal single-photon operation. SNSPDs made from thin flakes of Bi₂Sr₂CaCu₂O_8+δ exhibit a single-photon response up to 25 K, and for SNSPDs from La_1.55Sr_0.45CuO₄/La₂CuO₄ bilayer films, this response is observed up to 8 K. While the underlying detection mechanism is not fully understood yet, our work expands the family of materials for SNSPD technology beyond the liquid helium temperature limit and suggests that even higher operation temperatures may be reached using other high-temperature superconductors.

Quantum Interference between Fundamentally Different Processes Is Enabled by Shaped Input Wavefunctions

This work presents a general framework for quantum interference between processes that can involve different fundamental particles or quasi-particles. This framework shows that shaping input wavefunctions is a versatile and powerful tool for producing and controlling quantum interference between distinguishable pathways, beyond previously explored quantum interference between indistinguishable pathways. Two examples of quantum interference enabled by shaping in interactions between free electrons, bound electrons, and photons are presented: i) the vanishing of the zero-loss peak by destructive quantum interference when a shaped electron wavepacket couples to light, under conditions where the electron's zero-loss peak otherwise dominates; ii) quantum interference between free electron and atomic (bound electron) spontaneous emission processes, which can be significant even when the free electron and atom are far apart, breaking the common notion that a free electron and an atom must be close by to significantly affect each other's processes. Conclusions show that emerging quantum wave-shaping techniques unlock the door to greater versatility in light-matter interactions and other quantum processes in general.

MXene-Nanoflakes-Enabled All-Optical Nonlinear Activation Function for On-Chip Photonic Deep Neural Networks

2D metal carbides and nitrides (MXene) are promising material platforms for on-chip neural networks owing to their nonlinear saturable absorption effect. The localized surface plasmon resonances in metallic MXene nanoflakes may play an important role in enhancing the electromagnetic absorption; however, their contribution is not determined due to the lack of a precise understanding of its localized surface plasmon behavior. Here, a saturable absorber made of MXene thin film and a silicon waveguide with MXene flakes overlayer are developed to perform neuromorphic tasks. The proposed configurations are reconfigurable and can therefore be adjusted for various applications without the need to modify the physical structure of the proposed MXene-based activator configurations via tuning the wavelength of operation. The capability and feasibility of the obtained results of machine-learning applications are confirmed via handwritten digit classification task, with near 99% accuracy. These findings can guide the design of advanced ultrathin saturable absorption materials on a chip for a broad range of applications.

Experimental Boson Sampling Enabling Cryptographic One-Way Function

Boson sampling is a computational problem, which is commonly believed to be a representative paradigm for attaining the milestone of quantum advantage. So far, massive efforts have been made to the experimental large-scale boson sampling for demonstrating this milestone, while further applications of the machines remain a largely unexplored area. Here, we investigate experimentally the efficiency and security of a cryptographic one-way function that relies on coarse-grained boson sampling, in the framework of a photonic boson-sampling machine fabricated by a femtosecond laser direct writing technique. Our findings demonstrate that the implementation of the function requires moderate sample sizes, which can be over 4 orders of magnitude smaller than the ones predicted by the Chernoff bound; whereas for numbers of photons n≥3 and bins d∼poly(m,n), the same output of the function cannot be generated by nonboson samplers. Our Letter is the first experimental study that deals with the potential applications of boson sampling in the field of cryptography and paves the way toward additional studies in this direction.

Ultrahigh-responsivity waveguide-coupled optical power monitor for Si photonic circuits operating at near-infrared wavelengths

A phototransistor is a promising candidate as an optical power monitor in Si photonic circuits since the internal gain of photocurrent enables high responsivity. However, state-of-the-art waveguide-coupled phototransistors suffer from a responsivity of lower than 10³A/W, which is insufficient for detecting very low power light. Here, we present a waveguide-coupled phototransistor operating at a 1.3 μm wavelength, which consists of an InGaAs ultrathin channel on a Si waveguide working as a gate electrode to increase the responsivity. The Si waveguide gate underneath the InGaAs ultrathin channel enables the effective control of transistor current without optical absorption by the gate metal. As a result, our phototransistor achieved the highest responsivity of approximately 10⁶ A/W among the waveguide-coupled phototransistors, allowing us to detect light of 621 fW propagating in the Si waveguide. The high responsivity and the reasonable response time of approximately 100 μs make our phototransistor promising as an effective optical power monitor in Si photonic circuits.

Asymptotically fault-tolerant programmable photonics

Component errors limit the scaling of programmable coherent photonic circuits. These errors arise because the standard tunable photonic coupler—the Mach-Zehnder interferometer (MZI)—cannot be perfectly programmed to the cross state. Here, we introduce two modified circuit architectures that overcome this limitation: (1) a 3-splitter MZI mesh for generic errors, and (2) a broadband MZI+Crossing design for correlated errors. Because these designs allow for perfect realization of the cross state, the matrix fidelity no longer degrades with increased mesh size, allowing scaling to arbitrarily large meshes. The proposed architectures support progressive self-configuration, are more compact than previous MZI-doubling schemes, and do not require additional phase shifters. This removes a key limitation to the development of very-large-scale programmable photonic circuits.

Phase customization in photonic integrated circuits with trimmed waveguides

Accurate photon phase control on a chip is essential to improve the expandability and stability of photonic integrated circuits (PICs). Here, we propose a novel, to the best of our knowledge, on-chip static phase control method in which a modified line is added close to the normal waveguide with a lower-energy laser. By controlling the laser energy and the position and length of the modified line, the optical phase can be precisely controlled with low loss and a three-dimensional (3D) path. Customizable phase modulation ranging from 0 to 2π is performed with a precision of λ/70 in a Mach-Zehnder interferometer. The proposed method can customize high-precision control phases without changing the waveguide's original spatial path, which is expected to control the phase and solve the phase error correction problem during processing of large-scale 3D-path PICs.

Dynamical Behavior of Two Interacting Double Quantum Dots in 2D Materials for Feasibility of Controlled-NOT Operation

Two interacting double quantum dots (DQDs) can be suitable candidates for operation in the applications of quantum information processing and computation. In this work, DQDs are modeled by the heterostructure of two-dimensional (2D) MoS₂ having 1T-phase embedded in 2H-phase with the aim to investigate the feasibility of controlled-NOT (CNOT) gate operation with the Coulomb interaction. The Hamiltonian of the system is constructed by two models, namely the 2D electronic potential model and the 4×4 matrix model whose matrix elements are computed from the approximated two-level systems interaction. The dynamics of states are carried out by the Crank-Nicolson method in the potential model and by the fourth order Runge-Kutta method in the matrix model. Model parameters are analyzed to optimize the CNOT operation feasibility and fidelity, and investigate the behaviors of DQDs in different regimes. Results from both models are in excellent agreement, indicating that the constructed matrix model can be used to simulate dynamical behaviors of two interacting DQDs with lower computational resources. For CNOT operation, the two DQD systems with the Coulomb interaction are feasible, though optimization of engineering parameters is needed to achieve optimal fidelity.

Resource-efficient high-dimensional subspace teleportation with a quantum autoencoder

Quantum autoencoders serve as efficient means for quantum data compression. Here, we propose and demonstrate their use to reduce resource costs for quantum teleportation of subspaces in high-dimensional systems. We use a quantum autoencoder in a compress-teleport-decompress manner and report the first demonstration with qutrits using an integrated photonic platform for future scalability. The key strategy is to compress the dimensionality of input states by erasing redundant information and recover the initial states after chip-to-chip teleportation. Unsupervised machine learning is applied to train the on-chip autoencoder, enabling the compression and teleportation of any state from a high-dimensional subspace. Unknown states are decompressed at a high fidelity (~0.971), obtaining a total teleportation fidelity of ~0.894. Subspace encodings hold great potential as they support enhanced noise robustness and increased coherence. Laying the groundwork for machine learning techniques in quantum systems, our scheme opens previously unidentified paths toward high-dimensional quantum computing and networking.

Two-layer integrated photonic architectures with multiport photodetectors for high-fidelity and energy-efficient matrix multiplications

Photonic integrated circuits (PICs) are emerging as a promising tool for accelerating matrix multiplications in deep learning. Previous PIC architectures, primarily focusing on the matrix-vector multiplication (MVM), have large hardware errors that increase with the device scale. In this work, we propose a novel PIC architecture for MVM, which features an intrinsically small hardware error that does not increase with the device scale. Moreover, we further develop this concept and propose a PIC architecture for the general matrix-matrix multiplication (GEMM), which allows the GEMM to be directly performed on a photonic chip with a high energy efficiency unattainable by parallel or sequential MVMs. This work provides a promising approach to realize a high fidelity and high energy efficiency optical computing platform.

Reducing circuit complexity in optical quantum computation using 3D architectures

Integrated photonic architectures based on optical waveguides are one of the leading candidates for the future realisation of large-scale quantum computation. One of the central challenges in realising this goal is simultaneously minimising loss whilst maximising interferometric visibility within waveguide circuits. One approach is to reduce circuit complexity and depth. A major constraint in most planar waveguide systems is that beamsplitter transformations between distant optical modes require numerous intermediate SWAP operations to couple them into nearest neighbour proximity, each of which introduces loss and scattering. Here, we propose a 3D architecture which can significantly mitigate this problem by geometrically bypassing trivial intermediate operations. We demonstrate the viability of this concept by considering a worst-case 2D scenario, where we interfere the two most distant optical modes in a planar structure. Using femtosecond laser direct-writing technology we experimentally construct a 2D architecture to implement Hong-Ou-Mandel interference between its most distant modes, and a 3D one with corresponding physical dimensions, demonstrating significant improvement in both fidelity and efficiency in the latter case. In addition to improving fidelity and efficiency of individual non-adjacent beamsplitter operations, this approach provides an avenue for reducing the optical depth of circuits comprising complex arrays of beamsplitter operations.

Cryo-compatible opto-mechanical low-voltage phase-modulator integrated with superconducting single-photon detectors

Photonic integrated circuits (PICs) have enabled novel functionality in quantum optics, quantum information processing and quantum communication. PICs based on Silicon Nitride (Si₃N₄) provide low-loss passive components and are compatible with efficient superconducting nanowire single-photon detectors (SNSPDs). For realizing functional quantum photonic systems, the integration with active phase-shifters is needed which is challenging at the cryogenic temperatures needed for operating SNSPDs. Here we demonstrate a cryo-compatible phase shifter using a low-voltage opto-mechanical modulator and show joint operation with SNSPDs at 1.3 K. We achieve a half-wave voltage of 4.6 V, single-photon detection with 88% on-chip detection efficiency (OCDE) and a low timing jitter of 12.2 ps. Our approach allows for operating reconfigurable quantum photonic circuits with low dissipation in a cryogenic setting.

High-fidelity and large-scale reconfigurable photonic processor for NISQ applications

Reconfigurable linear optical networks are a key component for the development of optical quantum information processing platforms in the NISQ era and beyond. We report the implementation of such a device based on an innovative design that uses the mode mixing of a multimode fiber in combination with the programmable wavefront shaping of a SLM. The capabilities of the platform are explored in the classical regime. For up to 8 inputs and a record number of 38 outputs, we achieve fidelities in excess of 93%, and losses below 6.5dB. The device was built inside a standard server rack to allow for real world use and shows consistent performance for 2x8 circuits over a period of 10 days without re-calibration.

High-fidelity photonic quantum logic gate based on near-optimal Rydberg single-photon source

Compared to other types of qubits, photon is one of a kind due to its unparalleled advantages in long-distance quantum information exchange. Therefore, photon is a natural candidate for building a large-scale, modular optical quantum computer operating at room temperature. However, low-fidelity two-photon quantum logic gates and their probabilistic nature result in a large resource overhead for fault tolerant quantum computation. While the probabilistic problem can, in principle, be solved by employing multiplexing and error correction, the fidelity of linear-optical quantum logic gate is limited by the imperfections of single photons. Here, we report the demonstration of a linear-optical quantum logic gate with truth table fidelity of 99.84(3)% and entangling gate fidelity of 99.69(4)% post-selected upon the detection of photons. The achieved high gate fidelities are made possible by our near-optimal Rydberg single-photon source. Our work paves the way for scalable photonic quantum applications based on near-optimal single-photon qubits and photon-photon gates.

The current main source of errors for photonic quantum logic gates is the imperfections of the single photons. Here, by using high-quality photons from Rydberg atoms, the authors are able to reach 99.7% entangling gate fidelity in a photonic CNOT gate.

Dispersionless Coupling among Optical Waveguides by Artificial Gauge Field

Coupling among closely packed waveguides is a common optical phenomenon, and plays an important role in optical routing and integration. Unfortunately, this coupling property is usually sensitive to the working wavelength and structure features that hinder the broadband and robust functions. Here, we report a new strategy utilizing an artificial gauge field (AGF) to engineer the coupling dispersion and realize a dispersionless coupling among waveguides with periodically bending modulation. The AGF-induced dispersionless coupling is experimentally verified in a silicon waveguide platform, which already has well-established broadband and robust routing functions (directional coupling and splitting), suggesting potential applications in integrated photonics. As examples, we further demonstrate a three-level-cascaded AGF waveguide network to route broadband light to desired ports with an overwhelming advantage over the conventional ones in comparison. Our method provides a new route of coupling dispersion control by AGF and benefits applications that fundamentally rely on waveguide coupling.