It is well known that correlations predicted by quantum mechanics cannot be explained by any classical (local-realistic) theory. The relative strength of quantum and classical correlations is usually studied in the context of Bell inequalities, but this tells us little about the geometry of the quantum set of correlations. In other words, we do not have good intuition about what the quantum set actually looks like. In this paper we study the geometry of the quantum set using standard tools from convex geometry. We find explicit examples of rather counter-intuitive features in the simplest non-trivial Bell scenario (two parties, two inputs and two outputs) and illustrate them using 2-dimensional slice plots. We also show that even more complex features appear in Bell scenarios with more inputs or more parties. Finally, we discuss the limitations that the geometry of the quantum set imposes on the task of self-testing.

Device-independent self-testing is the possibility of certifying the quantum state and the measurements, up to local isometries, using only the statistics observed by querying uncharacterized local devices. In this paper, we study parallel self-testing of two maximally entangled pairs of qubits: in particular, the local tensor product structure is not assumed but derived. We prove two criteria that achieve the desired result: a double use of the Clauser-Horne-Shimony-Holt inequality and the 3 × 3 Magic Square game. This demonstrate that the magic square game can only be perfectly won by measureing a two-singlets state. The tolerance to noise is well within reach of state-of-the-art experiments.

Recent progress in building large-scale quantum devices for exploring quantum computing and simulation paradigms has relied upon effective tools for achieving and maintaining good experimental parameters, i.e., tuning up devices. In many cases, including in quantum-dot based architectures, the parameter space grows substantially with the number of qubits, and may become a limit to scalability. Fortunately, machine learning techniques for pattern recognition and image classification using so-called deep neural networks have shown surprising successes for computer-aided understanding of complex systems. In this work, we use deep and convolutional neural networks to characterize states and charge configurations of semiconductor quantum dot arrays when one can only measure a current-voltage characteristic of transport through such a device. For simplicity, we model a semiconductor nanowire connected to leads and capacitively coupled to depletion gates using the Thomas-Fermi approximation and Coulomb blockade physics. We then generate labeled training data for the neural networks, and find at least 90 % accuracy for charge and state identification for single and double dots purely from the dependence of the nanowire's conductance upon gate voltages. Using these characterization networks, we can then optimize the parameter space to achieve a desired configuration of the array, a technique we call 'auto-tuning'. Finally, we show how such techniques can be implemented in an experimental setting by applying our approach to an experimental data set, and outline further problems in this domain, from using charge sensing data to extensions to full one and two-dimensional arrays, that can be tackled with machine learning.

Self-testing refers to the possibility of characterizing uniquely (up to local isometries) the state and measurements contained in quantum devices, based only on the observed input-output statistics. Already in the basic case of the two-qubit singlet, self-testing is not unique: the two known criteria (the maximal violation of the CHSH inequality and the Mayers-Yao correlations) are not equivalent. It is unknown how many criteria there are. In this paper, we find the whole set of criteria for the ideal selftesting of a singlet with two measurements and two outcomes on each side; it coincides with all the extremal points of the quantum set that can be obtained by measuring the singlet. Definition of self-testingWe consider 2 parties, Alice and Bob, each having a device with 2 inputs ('measurements'), and each measurement has 2 outcomes [(2,2,2) scenario]. Alice's inputs and outputs are denoted respectively by x and a,

Self-testing is a device independent method which can be used to determine the nature of a physical system or device, without knowing any detail of the inner mechanism or the physical dimension of Hilbert space of the system. The only information required are the number of measurements, number of outputs of each measurement and the statistics of each measurement. Earlier works on self testing restricted either to two parties scenario or multipartite graph states. Here, we construct a method to self-test the three-qubit W state, and show how to extend it to other pure three-qubit states. Our bounds are robust against the inevitable experimental errors.

BackgroundOver the past decade, machine learning techniques have revolutionized how research and science are done, from designing new materials and predicting their properties to data mining and analysis to assisting drug discovery to advancing cybersecurity. Recently, we added to this list by showing how a machine learning algorithm (a so-called learner) combined with an optimization routine can assist experimental efforts in the realm of tuning semiconductor quantum dot (QD) devices. Among other applications, semiconductor quantum dots are a candidate system for building quantum computers. In order to employ QDs, one needs to tune the devices into a desirable configuration suitable for quantum computing. While current experiments adjust the control parameters heuristically, such an approach does not scale with the increasing size of the quantum dot arrays required for even near-term quantum computing demonstrations. Establishing a reliable protocol for tuning QD devices that does not rely on the gross-scale heuristics developed by experimentalists is thus of great importance.Materials and methodsTo implement the machine learning-based approach, we constructed a dataset of simulated QD device characteristics, such as the conductance and the charge sensor response versus the applied electrostatic gate voltages. The gate voltages are the experimental ‘knobs’ for tuning the device into useful regimes. Here, we describe the methodology for generating the dataset, as well as its validation in training convolutional neural networks.Results and discussionFrom 200 training sets sampled randomly from the full dataset, we show that the learner’s accuracy in recognizing the state of a device is ≈ 96.5% when using either current-based or charge-sensor-based training. The spread in accuracy over our 200 training sets is 0.5% and 1.8% for current- and charge-sensor-based data, respectively. In addition, we also introduce a tool that enables other researchers to use this approach for further research: QFlow lite—a Python-based mini-software suite that uses the dataset to train neural networks to recognize the state of a device and differentiate between states in experimental data. This work gives the definitive reference for the new dataset that will help enable researchers to use it in their experiments or to develop new machine learning approaches and concepts.

The core of quantum machine learning is to devise quantum models with good trainability and low generalization error bound than their classical counterparts to ensure better reliability and interpretability. Recent studies confirmed that quantum neural networks (QNNs) have the ability to achieve this goal on specific datasets. With this regard, it is of great importance to understand whether these advantages are still preserved on real-world tasks. Through systematic numerical experiments, we empirically observe that current QNNs fail to provide any benefit over classical learning models. Concretely, our results deliver two key messages. First, QNNs suffer from the severely limited effective model capacity, which incurs poor generalization on real-world datasets. Second, the trainability of QNNs is insensitive to regularization techniques, which sharply contrasts with the classical scenario. These empirical results force us to rethink the role of current QNNs and to design novel protocols for solving real-world problems with quantum advantages.

The boundary between classical and quantum correlations is well characterised by linear constraints called Bell inequalities. It is much harder to characterise the boundary of the quantum set itself in the space of no-signaling correlations. For the points on the quantum boundary that violate maximally some Bell inequalities, Oppenheim and Wehner [Science 330, 1072 (2010)] pointed out a complex property: the optimal measurements of Alice steer Bob's local state to the eigenstate of an effective operator corresponding to its maximal eigenvalue. This effective operator is the linear combination of Bob's local operators induced by the coefficients of the Bell inequality, and it can be interpreted as defining a fine-grained uncertainty relation. It is natural to ask whether the same property holds for other points on the quantum boundary, using the Bell expression that defines the tangent hyperplane at each point. We prove that this is indeed the case for a large set of points, including some that were believed to provide counterexamples. The price to pay is to acknowledge that the Oppenheim-Wehner criterion does not respect equivalence under the no-signaling constraint: for each point, one has to look for specific forms of writing the Bell expressions.