We are entering a time in which quantum channel capacity is becoming increasingly dependent on having high-dimensional entangled systems. However, existing methods of detecting high-dimensional entanglement are hindered by their need for an unwieldy amount of measurements and computational power. Indeed, the use of entanglement witnesses circumvents this problem by only considering a small subset of the entangled states in Hilbert Space. Although efficient witnesses for 2-qubit Bell States and 3-Qubit GHZ states are well-known, the predominant “fidelity method" witnesses used for detecting multipartite W states remain relatively complex in the amount of measurements that they require. The work outlined in this thesis aims to improve on existing entanglement witnesses by drawing their correspondence with supervised learning techniques, specifically Support Vector Machines. In doing so, one can derive entanglement witnesses whose features (observables obtained via local operations and classical communications) can be ranked according to their impact on the classification of entangled and separable states. This method allows us to derive W state witnesses that require fewer measurements than those derived via the fidelity method. The process of Recursive Feature Elimination is also presented, by which we can define witnesses that can be decomposed into fewer Pauli observables at the cost of inferior tolerance to noise. Finally, we present the practical utility of our derived witnesses through physical experiments performed on the superconducting qubit devices provided by IBM.
We are entering a time in which quantum channel capacity is becoming increasingly dependent on having high-dimensional entangled systems. However, existing methods of detecting high-dimensional entanglement are hindered by their need for an unwieldy amount of measurements and computational power. Indeed, the use of entanglement witnesses circumvents this problem by only considering a small subset of the entangled states in Hilbert Space. Although efficient witnesses for 2-qubit Bell States and 3-Qubit GHZ states are well-known, the predominant “fidelity method" witnesses used for detecting multipartite W states remain relatively complex in the amount of measurements that they require. The work outlined in this thesis aims to improve on existing entanglement witnesses by drawing their correspondence with supervised learning techniques, specifically Support Vector Machines. In doing so, one can derive entanglement witnesses whose features (observables obtained via local operations and classical communications) can be ranked according to their impact on the classification of entangled and separable states. This method allows us to derive W state witnesses that require fewer measurements than those derived via the fidelity method. The process of Recursive Feature Elimination is also presented, by which we can define witnesses that can be decomposed into fewer Pauli observables at the cost of inferior tolerance to noise. Finally, we present the practical utility of our derived witnesses through physical experiments performed on the superconducting qubit devices provided by IBM.
In this work, we show a correspondence between linear support vector machines (SVMs) and entanglement witnesses, and use this correspondence to generate entanglement witnesses for bipartite and tripartite qubit (and qudit) target entangled states. An SVM allows for the construction of a hyperplane that clearly delineates between separable states and the target entangled state; this hyperplane is a weighted sum of observables (``features'') whose coefficients are optimized during the training of the SVM. We demonstrate with this method the ability to obtain witnesses that require only local measurements even when the target state is a nonstabilizer state. Furthermore, we show that SVMs are flexible enough to allow us to rank features, and to reduce the number of features systematically while bounding the inference error. This allows us to derive W-state witnesses capable of detecting entanglement with fewer measurement terms than the fidelity method dominant in today's literature. The utility of this approach is demonstrated on quantum hardware furnished through the IBM Quantum Experience.
Entanglement witnesses are essential for certifying entanglement, yet constructing ones that are both noise-robust and economical in measurement settings remains challenging - particularly beyond qubits and for non-stabilizer ("magic") states. We present a machine-learning method that, given a target state and a user-specified number of measurement settings, generates an entanglement witness optimized for noise tolerance in the neighborhood of that state, requiring only local measurements. The approach is fully general, applying to multipartite qubit and qudit systems alike, including non-stabilizer states. For N qudits of dimension d, we train on the fully-separable eigenstates of each qudit's SU(d) generators to find a prototype witness, then tune the witness's bias term via gradient descent to maximize noise tolerance. Adversarial training further strengthens the witnesses, delivering greater noise tolerance with even fewer settings; critically, under this scheme the required training-set size becomes independent of system size. We package the entire pipeline as an automated script that, in every case we tested, produces witnesses surpassing all existing methods in noise tolerance and/or number of measurement settings. We demonstrate the method on Bell, GHZ, W, and hypergraph states, along with a range of qudit states, spanning 2-6 qubits, bipartite qudits up to d=10, and tripartite qutrits. Our witnesses achieve perfect accuracy across both physical experimental test states and large numerical sets of separable mixed states-including 30 million test states for a 3-qubit W-state witness and 10 million for a 4-qubit hypergraph-state witness-and we experimentally confirm the noise tolerance of Bell- and hypergraph state witnesses on both photonic and superconducting platforms, respectively.
Abstract An entanglement witness (EW) is a Hermitian operator that can distinguish an entangled state from all separable states. We developed and implemented a numerical method based on machine learning to create multipartite EW. Using a Support Vector Machine (SVM) algorithm, we construct EW's based on local orthogonal observables in the form of a hyperplane that separates the separable region from the entangled state for two, three, and four qubits Bell-diagonal mixed states which can be generalized to a multipartite mixed state. One of the important features of this method is that the EW s are optimal and are completely tangent to the separable region. Also, we generate non-decomposable EW's that can detect positive partial transpose entangled states (PPTES).
Detection of entanglement is an indispensable step to practical quantum computation and communication. Compared with the conventional entanglement witness method based on fidelity, we propose a flexible, machine learning assisted entanglement detection protocol that is robust to different types of noises and sample efficient. In this protocol, an entanglement classifier for a generic entangled state is obtained by training a classical machine learning model with a synthetic dataset. The dataset contains classical features of two types of states and their labels (either entangled or separable). The classical features of a state, which are expectation values of a set of k-local Pauli observables, are estimated sample-efficiently by the classical shadow method. In the numerical simulation, our classifier can detect the entanglement of 4-qubit GHZ states with coherent noise and W states mixed with large white noise, with high accuracy.
Abstract We propose a support vector machine (SVM) based approach for generating an entanglement witness that requires exponentially less training data than previously proposed methods. SVMs generate hyperplanes represented by a weighted sum of expectation values of local observables whose coefficients are optimized to sum to a positive number for all separable states and a negative number for as many entangled states as possible near a specific target state. Previous SVM-based approaches for entanglement witness generation used large amounts of randomly generated separable states to perform training, a task with considerable computational overhead. Here, we propose a method for orienting the witness hyperplane using only the significantly smaller set of states consisting of the eigenstates of the generalized Pauli matrices and a set of entangled states near the target entangled states. With the orientation of the witness hyperplane set by the SVM, we tune the plane’s placement using a differential program that ensures perfect classification accuracy on a limited test set as well as maximal noise tolerance. For N qubits, the SVM portion of this approach requires only O ( 6 N ) training states, whereas an existing method needs O ( 2 4 N ) . We use this method to construct witnesses of 4 and 5 qubit GHZ states with coefficients agreeing with stabilizer formalism witnesses to within 3.7 percent and 1 percent, respectively. We also use the same training states to generate novel 4 and 5 qubit W state witnesses. Finally, we computationally verify these witnesses on small test sets and propose methods for further verification.
Quantum entanglement is a fundamental resource in quantum information, but its characterization becomes increasingly challenging as the size of multipartite systems grows. This thesis investigates machine learning methods to detect and quantify entanglement in pure multiqubit states using only single qubit Pauli expectation values. Two complementary tasks are considered: the distinction between fully separable and entangled states, with particular attention to weakly entangled states close to the separability boundary, and the regression of normalized multipartite classical squashed entanglement. Several machine learning models are evaluated for detection, while multilayer perceptrons are employed for quantification. The low entanglement regime is investigated through dedicated datasets and targeted data augmentation strategies. The proposed approaches are studied for systems of 5, 10, 15, and 20 qubits and are further evaluated under realistic measurement conditions, including finite shot noise, asymmetric readout errors, calibration drift, and data acquired from real quantum processors. The study assesses the scalability, robustness, and practical limitations of data-driven entanglement characterization based on a linearly scaling set of local observables.