Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session Z38: Quantum Machine Learning IVRecordings Available

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Sponsoring Units: DQI GDS Chair: Gerry Angelatos, Princeton Room: McCormick Place W195 
Friday, March 18, 2022 11:30AM  11:42AM 
Z38.00001: NonBoolean Quantum Amplitude Amplification and Machine Learning applications Prasanth Shyamsundar, Evan Peters Amplitude amplification involving boolean oracles provides a quadratic speedup over naive measurementbased techniques and is an essential subroutine for many quantum algorithms. This work generalizes the quantum amplitude amplification and amplitude estimation algorithms to work with nonboolean oracles. It also introduces a new, fully quantum technique for training quantum neural networks, based on nonboolean amplitude amplification. 
Friday, March 18, 2022 11:42AM  11:54AM 
Z38.00002: Quantum State Tomography with Modeassisted Training YuanHang Zhang As a tool to model manybody systems, restricted Boltzmann machines (RBMs) have achieved some success when applied to the task of quantum state tomography. However, RBMs are notoriously hard to train, as the computation of the exact gradient is intractable, and estimation with Gibbs sampling is expensive and inefficient. Here, we show that, with the introduction of an offgradient training step constructed from the mode of the RBM distribution (which we call ``modeassisted training"), we can improve the quality of quantum state tomography significantly, while reducing the number of required measurements. We employ a novel computing paradigm, MemComputing, to sample the mode efficiently. 
Friday, March 18, 2022 11:54AM  12:06PM 
Z38.00003: Quantum Cross Entropy in Quantum Machine Learning Shangnan Zhou Quantum machine learning is an emerging field at the intersection of machine learning and quantum computing. Classical cross entropy plays a central role in machine learning. We define its quantum generalization, the quantum cross entropy, prove its lower bounds, and investigate its relation to quantum fidelity. We also develop a protocol in doing faithful quantum data compression with incorrect prior information of the quantum source. Moreover, We prove that the compression rate is the quantum cross entropy. 
Friday, March 18, 2022 12:06PM  12:18PM 
Z38.00004: Quantum constraint learning for quantum approximate optimization algorithm Santosh Radha The quantum approximate optimization algorithm (QAOA) is a hybrid quantumclassical variational algorithm which offers the potential to handle combinatorial optimization problems. Introducing constraints in such combinatorial optimization problems poses a major challenge in the extensions of QAOA to support relevant larger scale problems. In this paper, we introduce a quantum machine learning approach to learn the mixer Hamiltonian that is required to hard constrain the search subspace. We show that this method can be used for encoding any general form of constraints. By using a form of an adaptable ansatz, one can directly plug the learnt unitary into the QAOA framework. This procedure gives the flexibility to control the depth of the circuit at the cost of accuracy of enforcing the constraint, thus having immediate application in the Noisy Intermediate Scale Quantum (NISQ) era. We also develop an intuitive metric that uses Wasserstein distance to assess the performance of general approximate optimization algorithms with/without constrains. Finally using this metric, we evaluate the performance of the proposed algorithm. 
Friday, March 18, 2022 12:18PM  12:30PM 
Z38.00005: Approximating Entanglement Measures Using VQA Ryan T McGaha, George Androulakis Many common measures of entanglement are defined using the convex roof construction, which requires one to minimize a certain quantity over the set of all pure state ensembles of a given density matrix. This minimization is often difficult to compute directly for a given state and is usually approximated via classical optimization techniques. We supply a quantum algorithm to access the various pure state ensembles of a density matrix using parametrized quantum circuits, made possible by the SchrodingerHJW theorem. Using standard optimization techniques, one can find an approximate optimal pure state ensemble for a given density matrix and entanglement measure. We also attempted to analyze the landscapes of the cost functions induced by both the Von Neumann entanglement entropy and the Tsallis entanglement entropy for barren plateaus, but were unsuccessful in doing so. We instead supply an entanglement witness derived from the Tsallis entropy, whose landscape exhibits barren plateaus. This entanglement witness illustrates that highly nonlinear cost functions can still have barren plateaus even if they involve exponentially many terms in their definition. 
Friday, March 18, 2022 12:30PM  12:42PM 
Z38.00006: Topological and geometric patterns in optimal bangbang protocols for variational quantum algorithms: application to the XXZ model on the square lattice Armin Rahmani, Matthew T Scoggins Uncovering patterns in variational optimal protocols for taking a quantum system to ground states of manybody Hamiltonians is a significant challenge. Here, we develop highly efficient algorithms to find the optimal protocols for transformations between the ground states of the squarelattice XXZ model, which obtain optimal bangbang protocols, as predicted by Pontryagin's minimum principle. We identify the minimum time needed for reaching an acceptable error for different system sizes for various initial and target states and reveal correlations between the total time and the wavefunction overlap. We determine a dynamical phase diagram for the optimal protocols, with different phases characterized by a topological number, namely the number of onpulses. Bifurcation transitions as a function of initial and final states, associated with new jumps in the optimal protocols, demarcate these different phases. The number of pulses furthermore correlates with the total evolution time. In addition to the topological characteristic above, we introduce a correlation function to characterize bangbang protocols' quantitative geometric similarities. We find that protocols within one phase are indeed geometrically correlated. Identifying and extrapolating patterns in these protocols may inform efficient largescale simulations on noisy intermediatescale quantum devices. 
Friday, March 18, 2022 12:42PM  12:54PM 
Z38.00007: Quantum Algorithm for Topological Data Analysis Bernardo Ameneyro, George Siopsis, Vasileios Maroulas Physiological signals are typically nonstationary, noisy, and nonlinear, and current signal processing methods may fail due to underlying assumptions. Persistent homology is a powerful mathematical tool that can be used to extract useful information from large datasets, including topological features and how these features persist or change at different scales. However, the computation is often a rather formidable task. I present a quantum algorithm which yields a summary of topological features by computing the eigenvectors and eigenvalues of the persistent combinatorial Laplacian and the persistent Betti numbers of a point cloud. In particular, the algorithm tracks how topological features of a point cloud, such as the number of connected components, holes, and voids, change across different resolutions or scales. 
Friday, March 18, 2022 12:54PM  1:06PM 
Z38.00008: Shapes of quantum entanglement with persistent homology Bart Olsthoorn, Alexander V Balatsky Persistent homology is a modern computational technique that can identify shapes in discrete data. We convert quantum states into barcodes using quantum mutual information as a distance metric [1]. This general approach has three applications. Firstly, it functions as a kind of order parameter, where abrupt changes in the barcode indicate phase transitions. Secondly, it describes the shapes of entanglement present in the quantum state. Thirdly, it is a numerical framework that could prove to be a useful step towards the construction of spacetime. We demonstrate its computational power on two commonly used quantum spin models. 
Friday, March 18, 2022 1:06PM  1:18PM 
Z38.00009: Quantum Supervised Learning Method for Outlier Detection Anna Hughes, Santosh Radha, Jack S Baker

Friday, March 18, 2022 1:18PM  1:30PM 
Z38.00010: Quantum continual learning overcoming catastrophic forgetting Wenjie Jiang, Zhide Lu, DongLing Deng Catastrophic forgetting describes the fact that machine learning models will likely forget the knowledge of previously learned tasks after the learning process of a new one. It is a vital problem in the continual learning scenario and recently has attracted tremendous concern across different communities. In this paper, we explore the catastrophic forgetting phenomena in the context of quantum machine learning. We find that, similar to those classical learning models based on neural networks, quantum learning systems likewise suffer from such forgetting problem in classification tasks emerging from various application scenes. We show that based on the local geometrical information in the loss function landscape of the trained model, a uniform strategy can be adapted to overcome the forgetting problem in the incremental learning setting. Our results uncover the catastrophic forgetting phenomena in quantum machine learning and offer a practical method to overcome this problem, which opens a new avenue for exploring potential quantum advantages towards continual learning. 
Friday, March 18, 2022 1:30PM  1:42PM 
Z38.00011: Subtleties in the trainability of quantum machine learning models Supanut Thanasilp, Samson Wang, Nhat Anh Nghiem Vu, Patrick J Coles, Marco Cerezo Quantum Machine Learning (QML) aims to achieve a speedup over traditional machine learning for data analysis. However, its success hinges on efficiently training the parameters in models like quantum neural networks, and the field is still lacking theoretical scaling results for trainability. Some trainability results have been proven for a closely related field called Variational Quantum Algorithms (VQAs). While both fields involve training a parametrized quantum circuit, there are crucial differences that make the results for one setting not readily applicable to the other. In this work we bridge the two frameworks and show that gradient scaling results for VQAs can also be applied to study the gradient scaling of QML models, indicating that detrimental features for VQA trainability can lead to issues such as barren plateaus in QML. Consequently, our work has implications for several QML proposals in the literature. In addition, we provide evidence that QML models exhibit further trainability issues, arising from a dataset  referred here as datasetinduced barren plateaus. These results are most relevant when dealing with classical data, as the choice of embedding scheme can greatly affect the gradient scaling. 
Friday, March 18, 2022 1:42PM  1:54PM 
Z38.00012: Closing in on Practical Quantum Advantage for Combinatorial Optimization with Quantum Generative Models (Part 1) Alejandro PerdomoOrtiz, Francisco J Fernandez Alcazar Practical quantum advantage, the demonstration of a quantum or quantumassisted model solving a valuable academic or industry interest problem faster, better, or more costefficient than any classical algorithm, is the most soughtafter milestone after the recent results on quantum computational advantage with random quantum circuits. Besides quantum chemistry, where a more explicit path is laid out for achieving quantum advantage, machine learning (ML) and combinatorial optimization problems (COP) stand out as key candidates. Despite all the efforts, there is still no demonstration of quantum advantage for practical and industrial applications in ML and COP. 
Friday, March 18, 2022 1:54PM  2:06PM 
Z38.00013: Closing in on Practical Quantum Advantage for Combinatorial Optimization with Quantum Generative Models (Part 2) Alejandro PerdomoOrtiz, Francisco J Fernandez Alcazar Practical quantum advantage, the demonstration of a quantum or quantumassisted model solving a valuable academic or industry interest problem faster, better, or more costefficient than any classical algorithm, is the most soughtafter milestone after the recent results on quantum computational advantage with random quantum circuits. Besides quantum chemistry, where a more explicit path is laid out for achieving quantum advantage, machine learning (ML) and combinatorial optimization problems (COP) stand out as key candidates. Despite all the efforts, there is still no demonstration of quantum advantage for practical and industrial applications in ML and COP. 
Friday, March 18, 2022 2:06PM  2:18PM 
Z38.00014: Differentiable Quantum Circuits for Solving Differential Equations and Generating Time Series Annie E Paine, Oleksandr Kyriienko, Vincent E Elfving I will discuss a quantum algorithm to solve nonlinear differential equations which is suited to near term quantum devices. For this method a function is defined via expectation values of a parametrised quantum circuit which makes use of feature map encoding and variational ansatz. This parametrised circuit can be considered as a quantum neural network and can be differentiated to represent the function derivative analytically by using the parameter shift rule. The circuit is trained using a hybrid classicalquantum workflow and quantum machine learning techniques to provide a representation of the solution to a given differential equation. I will introduce different strategies for imposing boundary conditions. Furthermore, a Chebyshev feature map which offers high expressivity will also be introduced. I will show the results of simulating this method to solve various systems of differential equations cumulating in solving an instance of the NavierStoke equations for a convergentdivergent nozzle and applying similar strategies for achieving trainable generative modelling in the form of Quantum Quantile Mechanics. 
Friday, March 18, 2022 2:18PM  2:30PM 
Z38.00015: Quantum algorithm for the spectral analysis of a random walk operator with the application in manifold learning Apimuk Sornsaeng, Ninnat Dangniam, Pantita Palittapongarnpim, Thiparat Chotibut Inspired by random walks on graphs, the diffusion map (DM) is a ubiquitous unsupervised machine learning algorithm that offers automatic identification of lowdimensional data structure hidden in a highdimensional data set. In recent years, among its many applications, the DM has been successfully applied to discover relevant order parameters in manybody systems, enabling automatic classification of quantum phases of matter. However, a classical DM algorithm is computationally prohibitive for a large data set, and any reduction of the time complexity would be desirable. With a quantum computational speedup in mind, we propose a quantum algorithm for the DM, termed the quantum diffusion map (qDM). Our qDM takes as an input N classical data vectors, performs an eigendecomposition of the Markov transition matrix in time O(log^3 N), and classically constructs the diffusion map via the readout (tomography) of the eigenvectors, giving a total expected runtime proportional to N^2 polylog N . Importantly, quantum subroutines in the qDM for constructing a Markov transition matrix and for analyzing its spectral properties provide an exponential speedup, which can also be useful for other randomwalkbased algorithms. 
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