pubs.acs.org/journal/apchd5 Perspective Machine Learning for Integrated Quantum Photonics Zhaxylyk A. Kudyshev, Vladimir M. Shalaev, and Alexandra Boltasseva* Cite This: https://dx.doi.org/10.1021/acsphotonics.0c00960 Read Online ACCESS Metrics & More Article Recommendations ABSTRACT: Realization of integrated quantum photonics is a key step toward scalable quantum applications such as quantum computing, sensing, information processing, and quantum material metrology. To enable practical quantum photonic systems, several challenges should be addressed, including (i) the realization of deterministic, bright, and stable single-photon emission operating at THz rates and at room temperatures, (ii) on-chip integration of efficient single-photon sources, and (iii) the development of deterministic and scalable nanoassembly of quantum circuitry elements. In this Perspective, we focus on the emerging field of physics- informed machine learning (ML) quantum photonics that is envisioned to play a decisive role in addressing the above challenges. Specifically, three directions of ML- assisted quantum research are discussed: (i) rapid preselection of single single- photon sources via ML-assisted quantum measurements, (ii) hybrid ML- optimization approach for developing efficient quantum circuits elements, and (iii) ML-based frameworks for developing novel deterministic assembly of on-chip quantum emitters. KEYWORDS: quantum photonics, machine learning, deep neural networks, on-chip quantum optics y utilizing quantum entanglement, a tremendous increase measurements and, in particular, the multiphoton quantum B in computational efficiency compared to any classical state tomography scale very unfavorably with the complexity of algorithm can be achieved for problems like number the photon state. There is a clear demand for single-photon factorization (exponential speedup), most optimization, and emitters (SPEs) capable of producing indistinguishable inverse design problems (quadratic speedup).1,2 While many photons and entangled photon states at room temperature physical realizations of qubits have been proposed, including and at high emission rates. Most importantly, large-scale trapped ions and atoms,3,4 superconducting circuits,5 quantum quantum circuitry integration and prototyping requires (i) dots,6 solid-state color centers,7 and photons,8 the latter offer novel rapid characterization techniques for the selection of some unique features. Photons interact very weakly with suitable quantum emitters out of large numbers of potential Downloaded via PURDUE UNIV on December 25, 2020 at 03:48:08 (UTC). ffi transparent optical media and not at all among themselves, candidates and (ii) e cient integration of the SPEs into an on- which renders the information they carry robust against chip environment. decoherence. However, the photons’ relatively weak inter- Machine learning (ML) algorithms have already shown great See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles. action with matter brings about two major issues in photonic potential for addressing the main bottlenecks in computer vision,9 natural language processing,10 speech recognition,11 quantum technologies. First, nondeterministic logical oper- 12 13 ations with photons using linear optical quantum gates put and other tasks across materials science, chemistry, laser physics,14 and microscopy.15 Recently, ML techniques have enormous overheads on the required infrastructure and fi severely limit the operation bandwidth of photonic quantum been used for the ne-tuning parameters of the semiconductor quantum devices,16,17 as well as quantum measurement information processing systems, especially when the gate 18 success rates are low. Second, single photon sources proposed optimization. Similarly, applying advanced ML algorithms so far, which utilize both quantum emitters and nonlinear to conventional methods in quantum photonics could address media, have not yet provided fast and deterministic streams of the fundamental limitations such as long characterization/read- out times, inefficient assembly, and quantum emitter perform- indistinguishable photons at room temperature. The single- photon rates in quantum emitters are limited by the spontaneous emission lifetime, while the nonlinear sources Special Issue: 20 Years of Photonics fail to produce the single-photons deterministically. Addressing Received: June 16, 2020 these issues is even more challenging when multiphoton states Revised: December 10, 2020 are required. First, the nondeterministic or slow single-photon Accepted: December 14, 2020 emission limits the speed with which such states can be prepared. Second, the time required for quantum correlation © XXXX American Chemical Society https://dx.doi.org/10.1021/acsphotonics.0c00960 A ACS Photonics XXXX, XXX, XXX−XXX ACS Photonics pubs.acs.org/journal/apchd5 Perspective Figure 1. Application of ML techniques in quantum photonics. Different quantum measurements and metrology tasks can be formulated as classification or regression problems. Based on the nature of the problem and available data set properties, different ML- and CNN-based classification/regression models can be applied. The choice of the model is dictated by the nature of the problem and required accuracy. Yet another direction where ML techniques can be used is optimization of on-chip and free-space meta-devices for quantum photonic applications. The discriminative CNNs and generative networks can be adapted for advanced multiparametric and shape/topology optimization of the meta-device designs. Active, reinforcement learning, as well as Bayesian inference algorithms, has been shown to be a promising route for automatization of quantum experiments. Such an approach can be used for the optimization of existing experimental techniques and the development of novel approaches. ance, as well as help to unlock new physics and application quantum emission can be formulated as a binary classification spaces. There are different venues within quantum photonics, problem within which the class of the emitter (“good”/“bad”) where ML techniques have great potential. Figure 1 highlights is determined based on the sparse autocorrelation measure- some of the potential applications with example problems and ment. Yet, another example is a spin-state read-out of nitrogen- corresponding ML algorithms. In this Perspective, we highlight vacancy centers (NVs) in nanodiamonds, which can be some of the key directions of the emerging field of ML assisted formulated as a binary classification (|0⟩ and |1⟩ spin states) quantum photonics. Specifically, we will cover (i) ML with the goal of minimizing the number of performed read-out techniques for quantum characterization and metrology cycles. Such problems can be addressed either by classical applications, (ii) ML-assisted quantum photonic device design machine learning algorithms (logistics regression, tree-based development, and (iii) active and reinforcement learning for models, k-nearest neighbors (kNN),19 random forest,20 novel quantum experiment development. support vector machine (SVM)21) or via convolutional neural network (CNN)-based classifiers. Along with classification ■ QUANTUM MEASUREMENT AND METROLOGY problems, quantum measurement and metrology applications Due to the statistical complexity of the signal, quantum optical can be formulated as a regression, which targets retrieving the measurements require a long collection time in order to exact value of the measurement based on the available sparse acquire complete data and to retrieve accurate results. information. The ML regression models can be used to retrieve Conventionally, statistical methods of data postprocessing the measured property of the quantum system to reduce the play an important role in the interpretation of the results of measurement time and to maintain the same level of precision. quantum measurements. The statistical methods have a long- Such a class of problems can be addressed via various ML- 22 23 standing focus on inference via creation and fitting problem- based regression algorithms (linear, logistic, Bayesian 24 21 specific probability models. Such approaches allow for regression models support vector machine regression )or computing a quantitative measure of confidence of the CNN-based regression models. The choice of the most developed mathematical model based on the acquired noisy suitable ML algorithm for different problems depends on data. In contrast, ML frameworks aim at predicting the many factors, such as the physics involved, final measurement outcome of the experiment by using general-purpose learning value/outcome, type of available data sets (complexity, algorithms, which allows one to find correlations between the variance, and size), and available computational resources. features of the data sets and the results of the measurement. The common requirement for most of the ML techniques is to Such data-driven formalism makes ML frameworks applicable gather a sufficient amount of data to get reliable predictions. to the quantum photonics problems, where conventional However, for quantum measurements, this may be excessively statistical methods fail due to the sparsity of the collected data. time-consuming, which leads to the constraints of the acquired This makes ML techniques a unique enabler for the realization data set, such as reduced variance and the number of the of the next-generation, rapid, precise, quantum measurement available training sets. Thus, if the