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- Quantum Machine Learning – MĂĄria KieferovĂĄ
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- R. Patron (University of Edinburgh): Limitations of optimization algorithms on noisy quantum
- AI IN QUANTUM COMPUTING – HOLISTIC INTEGRATION OF AI IN MULTIDISCIPLINARY
- IAIFI Colloquium Series: Neural-Network Quantum States

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## projUNN: efficient method for training deep networks with unitary matrices

Bobak Kiani,Â Randall Balestriero,Â Yann Lecun,Â Seth Lloyd

Mar 11 2022Â cs.LGÂ cs.AIÂ quant-phÂ arXiv:2203.05483v1

In learning with recurrent or very deep feed-forward networks, employing unitary matrices in each layer can be very effective at maintaining long-range stability. However, restricting network parameters to be unitary typically comes at the cost of expensive parameterizations or increased training runtime. We propose instead an efficient method based on rank-kkÂ updates — or their rank-kkÂ approximation — that maintains performance at a nearly optimal training runtime. We introduce two variants of this method, named Direct (projUNN-D) and Tangent (projUNN-T) projected Unitary Neural Networks, that can parameterize fullÂ NN-dimensional unitary or orthogonal matrices with a training runtime scaling asÂ O(kN2)O(kN2). Our method either projects low-rank gradients onto the closest unitary matrix (projUNN-T) or transports unitary matrices in the direction of the low-rank gradient (projUNN-D). Even in the fastest setting (k=1k=1), projUNN is able to train a model’s unitary parameters to reach comparable performances against baseline implementations. By integrating our projUNN algorithm into both recurrent and convolutional neural networks, our models can closely match or exceed benchmarked results from state-of-the-art algorithms.

## A highly efficient tensor network algorithm for multi-asset Fourier options pricing

Michael Kastoryano,Â Nicola Pancotti

Mar 08 2022Â quant-phÂ q-fin.CPÂ q-fin.RMÂ arXiv:2203.02804v1

Risk assessment and in particular derivatives pricing is one of the core areas in computational finance and accounts for a sizeable fraction of the global computing resources of the financial industry. We outline a quantum-inspired algorithm for multi-asset options pricing. The algorithm is based on tensor networks, which have allowed for major conceptual and numerical breakthroughs in quantum many body physics and quantum computation. In the proof-of-concept example explored, the tensor network approach yields several orders of magnitude speedup over vanilla Monte Carlo simulations. We take this as good evidence that the use of tensor network methods holds great promise for alleviating the computation burden of risk evaluation in the financial and other industries, thus potentially lowering the carbon footprint these simulations incur today.

## Surviving The Barren Plateau in Variational Quantum Circuits with Bayesian Learning Initialization

Ali Rad,Â Alireza Seif,Â Norbert M. Linke

Mar 07 2022Â quant-phÂ arXiv:2203.02464v1

Variational quantum-classical hybrid algorithms are seen as a promising strategy for solving practical problems on quantum computers in the near term. While this approach reduces the number of qubits and operations required from the quantum machine, it places a heavy load on a classical optimizer. While often under-appreciated, the latter is a computationally hard task due to the barren plateau phenomenon in parameterized quantum circuits. The absence of guiding features like gradients renders conventional optimization strategies ineffective as the number of qubits increases. Here, we introduce the fast-and-slow algorithm, which uses Bayesian Learning to identify a promising region in parameter space. This is used to initialize a fast local optimizer to find the global optimum point efficiently. We illustrate the effectiveness of this method on the Bars-and-Stripes (BAS) quantum generative model, which has been studied on several quantum hardware platforms. Our results move variational quantum algorithms closer to their envisioned applications in quantum chemistry, combinatorial optimization, and quantum simulation problems.

## Symmetry enhanced variational quantum eigensolver

Chufan Lyu,Â Xusheng Xu,Â Manhong Yung,Â Abolfazl Bayat

Mar 07 2022Â quant-phÂ arXiv:2203.02444v1

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.

## Quantum neural networks force fields generation

Oriel Kiss,Â Francesco Tacchino,Â Sofia Vallecorsa,Â Ivano Tavernelli

Mar 10 2022Â quant-phÂ cs.LGÂ physics.chem-phÂ physics.comp-phÂ arXiv:2203.04666v1

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum machine learning is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network potentials. To this end, we design a quantum neural network architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum machine learning.

## Novel Architecture of Parameterized Quantum Circuit for Graph Convolutional Network

Yanhu Chen,Â Cen Wang,Â Hongxiang Guo,Â Jianwu

Mar 08 2022Â quant-phÂ arXiv:2203.03251v1

Recently, the implementation of quantum neural networks is based on noisy intermediate-scale quantum (NISQ) devices. Parameterized quantum circuit (PQC) is such the method, and its current design just can handle linear data classification. However, data in the real world often shows a topological structure. In the machine learning field, the classical graph convolutional layer (GCL)-based graph convolutional network (GCN) can well handle the topological data. Inspired by the architecture of a classical GCN, in this paper, to expand the function of the PQC, we design a novel PQC architecture to realize a quantum GCN (QGCN). More specifically, we first implement an adjacent matrix based on linear combination unitary and a weight matrix in a quantum GCL, and then by stacking multiple GCLs, we obtain the QGCN. In addition, we first achieve gradients decent on quantum circuit following the parameter-shift rule for a GCL and then for the QGCN. We evaluate the performance of the QGCN by conducting a node classification task on Cora dataset with topological data. The numerical simulation result shows that QGCN has the same performance as its classical counterpart, the GCN, in contrast, requires less tunable parameters. Compared to a traditional PQC, we also verify that deploying an extra adjacent matrix can significantly improve the classification performance for quantum topological data.

## Quantum spectral clustering algorithm for unsupervised learning

Qingyu Li,Â Yuhan Huang,Â Shan Jin,Â Xiaokai Hou,Â Xiaoting Wang

Mar 08 2022Â quant-phÂ arXiv:2203.03132v1

Clustering is one of the most crucial problems in unsupervised learning, and the well-knownÂ kk-means clustering algorithm has been shown to be implementable on a quantum computer with a significant speedup. However, many clustering problems cannot be solved byÂ kk-means, and a powerful method called spectral clustering is introduced to solve these problems. In this work, we propose a circuit design to implement spectral clustering on a quantum processor with a substantial speedup, by initializing the processor into a maximally entangled state and encoding the data information into an efficiently-simulatable Hamiltonian. Compared with the established quantumÂ kk-means algorithms, our method does not require a quantum random access memory or a quantum adiabatic process. It relies on an appropriate embedding of quantum phase estimation into Grover’s search to gain the quantum speedup. Simulations demonstrate that our method is effective in solving clustering problems and will serve as an important supplement to quantumÂ kk-means for unsupervised learning.

## Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learning

Fergus Barratt,Â James Dborin,Â Lewis Wright

Mar 08 2022Â cs.LGÂ cond-mat.str-elÂ quant-phÂ arXiv:2203.03366v1

Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks suffer from initialization problems resulting in exploding or vanishing gradients and require extensive hyperparameter tuning. Efforts to overcome these problems usually depend on specific network architectures, or ad hoc prescriptions. In this paper we address the problems of initialization and hyperparameter tuning, making it possible to train tensor networks using established machine learning techniques. We introduce a `copy node’ method that successfully initializes arbitrary tensor networks, in addition to a gradient based regularization technique for bond dimensions. We present numerical results that show that the combination of techniques presented here produces quantum inspired tensor network models with far fewer parameters, while improving generalization performance.

- Unsupervised Quantum Circuit Learning in High Energy PhysicsAndrea Delgado,Â Kathleen E. HamiltonMar 08 2022Â quant-phÂ hep-exÂ arXiv:2203.03578v1Scite!2Â Â PDFUnsupervised training of generative models is a machine learning task that has many applications in scientific computing. In this work we evaluate the efficacy of using quantum circuit-based gener- ative models to generate synthetic data of high energy physics processes. We use non-adversarial, gradient-based training of quantum circuit Born machines to generate joint distributions over 2 and 3 variables.

## Quantum Approximate Optimization Algorithm for Bayesian network structure learning

Vicente P. Soloviev,Â Concha Bielza,Â Pedro LarraĂąaga

Mar 07 2022Â quant-phÂ cs.LGÂ arXiv:2203.02400v1

Bayesian network structure learning is an NP-hard problem that has been faced by a number of traditional approaches in recent decades. Currently, quantum technologies offer a wide range of advantages that can be exploited to solve optimization tasks that cannot be addressed in an efficient way when utilizing classic computing approaches. In this work, a specific type of variational quantum algorithm, the quantum approximate optimization algorithm, was used to solve the Bayesian network structure learning problem, by employingÂ 3n(nâ1)/23n(nâ1)/2Â qubits, whereÂ nnÂ is the number of nodes in the Bayesian network to be learned. Our results showed that the quantum approximate optimization algorithm approach offers competitive results with state-of-the-art methods and quantitative resilience to quantum noise. The approach was applied to a cancer benchmark problem, and the results justified the use of variational quantum algorithms for solving the Bayesian network structure learning problem.

## Boosting the Performance of Quantum Annealers using Machine Learning

Jure Brence,Â Dragan MihailoviÄ,Â Viktor Kabanov,Â LjupÄo Todorovski,Â SaĹĄo DĹžeroski,Â Jaka Vodeb

Mar 07 2022Â quant-phÂ cs.LGÂ arXiv:2203.02360v2

Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of problems that can be solved by quantum annealers is limited mainly by errors caused by environmental noise and intrinsic imperfections of the processor. We address the issue of intrinsic imperfections with a novel error correction approach, based on machine learning methods. Our approach adjusts the input Hamiltonian to maximize the probability of finding the solution. In our experiments, the proposed error correction method improved the performance of annealing by up to three orders of magnitude and enabled the solving of a previously intractable, maximally complex problem.

## The Existence of Barren Plateaus in Detection of Quantum Entanglement

George Androulakis,Ryan McGaha

Mar 07 2022Â quant-phÂ arXiv:2203.02099v1

Many entanglement measures are first defined for pure states of a bipartite Hilbert space, and then extended to mixed states via the convex roof extension. In this article we alter the convex roof extension of an entanglement measure, to produce a sequence of extensions that we callÂ ff-ddÂ extensions, forÂ dâNdâN, whereÂ f:[0,1]â[0,â)f:[0,1]â[0,â)Â is a fixed continuous function which vanishes only at zero. We prove that for any such functionÂ ff, and any continuous, faithful, non-negative function, (such as an entanglement measure),Â ÎźÎźÂ on the set of pure states of a finite dimensional bipartite Hilbert space, the collection ofÂ ff-ddÂ extensions ofÂ ÎźÎźÂ detects entanglement, i.e. a mixed stateÂ ĎĎÂ on a finite dimensional bipartite Hilbert space is separable, if and only if there existsÂ dâNdâNÂ such that theÂ ff-ddÂ extension ofÂ ÎźÎźÂ applied toÂ ĎĎÂ is equal to zero. We introduce a quantum variational algorithm which aims to approximate theÂ ff-ddÂ extensions of entanglement measures defined on pure states. However, the algorithm does have its drawbacks. We show that this algorithm exhibits barren plateaus when used to approximate the family ofÂ ff-ddÂ extensions of the Tsalis entanglement entropy for a certain functionÂ f

## Parameterized Two-Qubit Gates for Enhanced Variational Quantum Eigensolver

S. E. Rasmussen,Â N. T. Zinner

Mar 11 2022Â quant-phÂ arXiv:2203.04978v1

The variational quantum eigensolver is a prominent hybrid quantum-classical algorithm expected to impact near-term quantum devices. They are usually based on a circuit ansatz consisting of parameterized single-qubit gates and fixed two-qubit gates. We study the effect of parameterized two-qubit gates in the variational quantum eigensolver. We simulate a variational quantum eigensolver algorithm using fixed and parameterized two-qubit gates in the circuit ansatz and show that the parameterized versions outperform the fixed versions for a range of Hamiltonians with applications in quantum chemistry and materials science.

## Modular Parity Quantum Approximate Optimization

Kilian Ender,Â Anette Messinger,Â Michael Fellner,Â Clemens Dlaska,Â Wolfgang Lechner

Mar 10 2022Â quant-phÂ arXiv:2203.04340v1

The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert-space with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, the implicit approach shows better QAOA performance. Here we combine the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. In particular, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.

## Quantum algorithm for neural network enhanced multi-class parallel classification

Anqi Zhang,Â Xiaoyun He,Â Shengmei Zhao

Mar 09 2022Â quant-phÂ arXiv:2203.04097v1

Using the properties of quantum superposition, we propose a quantum classification algorithm to efficiently perform multi-class classification tasks, where the training data are loaded into parameterized operators which are applied to the basis of the quantum state in quantum circuit composed by \emphsample register and \emphlabel register, and the parameters of quantum gates are optimized by a hybrid quantum-classical method, which is composed of a trainable quantum circuit and a gradient-based classical optimizer. After several quantum-to-class repetitions, the quantum state is optimal that the state in \emphsample register is the same as that in \emphlabel register. %A structure of loading data many times is performed as a quantum version of neural network to improve the expression ability of quantum circuit. For a classification task ofÂ LL-class, the analysis shows that the space and time complexity of the quantum circuit areÂ O(LâlogL)O(LâlogL)Â andÂ O(logL)O(logL), respectively. The numerical simulation results of 2-class task and 5-class task show that the proposed algorithm has a higher classification accuracy, faster convergence and higher expression ability. The classification accuracy and the speed of converging can also be improved by increasing the number times of applying multi-qubit controlled operators on the quantum circuit, especially for multiple classes classification.

## Quantum Deep Learning for Mutant COVID-19 Strain Prediction

Yu-Xin Jin,Â Jun-Jie Hu,Â Qi Li,Â Zhi-Cheng Luo,Â Fang-Yan Zhang,Â Hao Tang,Â Kun Qian,Â Xian-Min Jin

Mar 08 2022Â cs.LGÂ quant-phÂ arXiv:2203.03556v1

New COVID-19 epidemic strains like Delta and Omicron with increased transmissibility and pathogenicity emerge and spread across the whole world rapidly while causing high mortality during the pandemic period. Early prediction of possible variants (especially spike protein) of COVID-19 epidemic strains based on available mutated SARS-CoV-2 RNA sequences may lead to early prevention and treatment. Here, combining the advantage of quantum and quantum-inspired algorithms with the wide application of deep learning, we propose a development tool named DeepQuantum, and use this software to realize the goal of predicting spike protein variation structure of COVID-19 epidemic strains. In addition, this hybrid quantum-classical model for the first time achieves quantum-inspired blur convolution similar to classical depthwise convolution and also successfully applies quantum progressive training with quantum circuits, both of which guarantee that our model is the quantum counterpart of the famous style-based GAN. The results state that the fidelities of random generating spike protein variation structure are always beyond 96% for Delta, 94% for Omicron. The training loss curve is more stable and converges better with multiple loss functions compared with the corresponding classical algorithm. At last, evidences that quantum-inspired algorithms promote the classical deep learning and hybrid models effectively predict the mutant strains are strong.

## Post-Error Correction for Quantum Annealing Processor using Reinforcement Learning

Tomasz Ĺmierzchalski,Â Lukasz Pawela,Â Zbigniew PuchaĹa,Â Tomasz TrzciĹski,Â BartĹomiej Gardas

Mar 07 2022Â quant-phÂ arXiv:2203.02030v1

Finding the ground state of the Ising spin-glass is an important and challenging problem (NP-hard, in fact) in condensed matter physics. However, its applications spread far beyond physic due to its deep relation to various combinatorial optimization problems, such as travelling salesman or protein folding. Sophisticated and promising new methods for solving Ising instances rely on quantum resources. In particular, quantum annealing is a quantum computation paradigm, that is especially well suited for Quadratic Unconstrained Binary Optimization (QUBO). Nevertheless, commercially available quantum annealers (i.e., D-Wave) are prone to various errors, and their ability to find low energetic states (corresponding to solutions of superior quality) is limited. This naturally calls for a post-processing procedure to correct errors (capable of lowering the energy found by the annealer). As a proof-of-concept, this work combines the recent ideas revolving around the DIRAC architecture with the Chimera topology and applies them in a real-world setting as an error-correcting scheme for quantum annealers. Our preliminary results show how to correct states output by quantum annealers using reinforcement learning. Such an approach exhibits excellent scalability, as it can be trained on small instances and deployed for large ones. However, its performance on the chimera graph is still inferior to a typical algorithm one could incorporate in this context, e.g., simulated annealing.

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