#42: Oct 9th – 15th

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Learnability of the output distributions of local quantum circuits

Marcel Hinsche,Marios Ioannou,Alexander Nietner,Jonas Haferkamp,Yihui Quek,Dominik Hangleiter,Jean-Pierre Seifert,Jens Eisert,Ryan SwekeOct 13 2021 quant-phcs.CCcs.LGstat.ML arXiv:2110.05517v1

There is currently a large interest in understanding the potential advantages quantum devices can offer for probabilistic modelling. In this work we investigate, within two different oracle models, the probably approximately correct (PAC) learnability of quantum circuit Born machines, i.e., the output distributions of local quantum circuits. We first show a negative result, namely, that the output distributions of super-logarithmic depth Clifford circuits are not sample-efficiently learnable in the statistical query model, i.e., when given query access to empirical expectation values of bounded functions over the sample space. This immediately implies the hardness, for both quantum and classical algorithms, of learning from statistical queries the output distributions of local quantum circuits using any gate set which includes the Clifford group. As many practical generative modelling algorithms use statistical queries — including those for training quantum circuit Born machines — our result is broadly applicable and strongly limits the possibility of a meaningful quantum advantage for learning the output distributions of local quantum circuits. As a positive result, we show that in a more powerful oracle model, namely when directly given access to samples, the output distributions of local Clifford circuits are computationally efficiently PAC learnable by a classical learner. Our results are equally applicable to the problems of learning an algorithm for generating samples from the target distribution (generative modelling) and learning an algorithm for evaluating its probabilities (density modelling). They provide the first rigorous insights into the learnability of output distributions of local quantum circuits from the probabilistic modelling perspective.

A scalable and fast artificial neural network syndrome decoder for surface codes

Spiro Gicev,Lloyd C. L. Hollenberg,Muhammad UsmanOct 13 2021 quant-phcs.ETcs.LG arXiv:2110.05854v1

Surface code error correction offers a highly promising pathway to achieve scalable fault-tolerant quantum computing. When operated as stabilizer codes, surface code computations consist of a syndrome decoding step where measured stabilizer operators are used to determine appropriate corrections for errors in physical qubits. Decoding algorithms have undergone substantial development, with recent work incorporating machine learning (ML) techniques. Despite promising initial results, the ML-based syndrome decoders are still limited to small scale demonstrations with low latency and are incapable of handling surface codes with boundary conditions and various shapes needed for lattice surgery and braiding. Here, we report the development of an artificial neural network (ANN) based scalable and fast syndrome decoder capable of decoding surface codes of arbitrary shape and size with data qubits suffering from the depolarizing error model. Based on rigorous training over 50 million random quantum error instances, our ANN decoder is shown to work with code distances exceeding 1000 (more than 4 million physical qubits), which is the largest ML-based decoder demonstration to-date. The established ANN decoder demonstrates an execution time in principle independent of code distance, implying that its implementation on dedicated hardware could potentially offer surface code decoding times of O(μμsec), commensurate with the experimentally realisable qubit coherence times. With the anticipated scale-up of quantum processors within the next decade, their augmentation with a fast and scalable syndrome decoder such as developed in our work is expected to play a decisive role towards experimental implementation of fault-tolerant quantum information processing.

QAOAKit: A Toolkit for Reproducible Study, Application, and Verification of the QAOA

Ruslan Shaydulin,Kunal Marwaha,Jonathan Wurtz,Phillip C. LotshawOct 13 2021 quant-phcs.ET arXiv:2110.05555v1

Understanding the best known parameters, performance, and systematic behavior of the Quantum Approximate Optimization Algorithm (QAOA) remain open research questions, even as the algorithm gains popularity. We introduce QAOAKit, a Python toolkit for the QAOA built for exploratory research. QAOAKit is a unified repository of preoptimized QAOA parameters and circuit generators for common quantum simulation frameworks. We combine, standardize, and cross-validate previously known parameters for the MaxCut problem, and incorporate this into QAOAKit. We also build conversion tools to use these parameters as inputs in several quantum simulation frameworks that can be used to reproduce, compare, and extend known results from various sources in the literature. We describe QAOAKit and provide examples of how it can be used to reproduce research results and tackle open problems in quantum optimization.

Learning ground states of quantum Hamiltonians with graph networks

Dmitrii Kochkov,Tobias Pfaff,Alvaro Sanchez-Gonzalez,Peter Battaglia,Bryan K. ClarkOct 14 2021 quant-phcond-mat.str-elcs.LG arXiv:2110.06390v1

Solving for the lowest energy eigenstate of the many-body Schrodinger equation is a cornerstone problem that hinders understanding of a variety of quantum phenomena. The difficulty arises from the exponential nature of the Hilbert space which casts the governing equations as an eigenvalue problem of exponentially large, structured matrices. Variational methods approach this problem by searching for the best approximation within a lower-dimensional variational manifold. In this work we use graph neural networks to define a structured variational manifold and optimize its parameters to find high quality approximations of the lowest energy solutions on a diverse set of Heisenberg Hamiltonians. Using graph networks we learn distributed representations that by construction respect underlying physical symmetries of the problem and generalize to problems of larger size. Our approach achieves state-of-the-art results on a set of quantum many-body benchmark problems and works well on problems whose solutions are not positive-definite. The discussed techniques hold promise of being a useful tool for studying quantum many-body systems and providing insights into optimization and implicit modeling of exponentially-sized objects.

F-Divergences and Cost Function Locality in Generative Modelling with Quantum Circuits

Chiara Leadbeater,Louis Sharrock,Brian Coyle,Marcello BenedettiOct 11 2021 quant-phcs.LG arXiv:2110.04253v1

Generative modelling is an important unsupervised task in machine learning. In this work, we study a hybrid quantum-classical approach to this task, based on the use of a quantum circuit Born machine. In particular, we consider training a quantum circuit Born machine using ff-divergences. We first discuss the adversarial framework for generative modelling, which enables the estimation of any ff-divergence in the near term. Based on this capability, we introduce two heuristics which demonstrably improve the training of the Born machine. The first is based on ff-divergence switching during training. The second introduces locality to the divergence, a strategy which has proved important in similar applications in terms of mitigating barren plateaus. Finally, we discuss the long-term implications of quantum devices for computing ff-divergences, including algorithms which provide quadratic speedups to their estimation. In particular, we generalise existing algorithms for estimating the Kullback-Leibler divergence and the total variation distance to obtain a fault-tolerant quantum algorithm for estimating another ff-divergence, namely, the Pearson divergence.

Optimizing quantum control pulses with complex constraints and few variables through Tensorflow

Yao Song,Junning Li,Yong-Ju Hai,Qihao Guo,Xiu-Hao DengOct 12 2021 quant-phphysics.comp-ph arXiv:2110.05334v2

Applying optimal control algorithms on realistic quantum systems confronts two key challenges: to efficiently adopt physical constraints in the optimization and to minimize the variables for the convenience of experimental tune-ups. In order to resolve these issues, we propose a novel algorithm by incorporating multiple constraints into the gradient optimization over piece-wise pulse constant values, which are transformed to contained numbers of the finite Fourier basis for bandwidth control. Such complex constraints and variable transformation involved in the optimization introduce extreme difficulty in calculating gradients. We resolve this issue efficiently utilizing auto-differentiation on Tensorflow. We test our algorithm by finding smooth control pulses to implement single-qubit and two-qubit gates for superconducting transmon qubits with always-on interaction, which remains a challenge of quantum control in various qubit systems. Our algorithm provides a promising optimal quantum control approach that is friendly to complex and optional physical constraints.

QuOp_MPI: a framework for parallel simulation of quantum variational algorithms

Edric Matwiejew,Jingbo B. WangOct 11 2021 quant-phphysics.comp-ph arXiv:2110.03963v1

QuOp_MPI is a Python package designed for parallel simulation of quantum variational algorithms. It presents an object-orientated approach to quantum variational algorithm design and utilises MPI-parallelised sparse-matrix exponentiation, the fast Fourier transform and parallel gradient evaluation to achieve the highly efficient simulation of the fundamental unitary dynamics on massively parallel systems. In this article, we introduce QuOp_MPI and explore its application to the simulation of quantum algorithms designed to solve combinatorial optimisation algorithms including the Quantum Approximation Optimisation Algorithm, the Quantum Alternating Operator Ansatz, and the Quantum Walk-assisted Optimisation Algorithm.

Style-based quantum generative adversarial networks for Monte Carlo events

Carlos Bravo-Prieto,Julien Baglio,Marco Cè,Anthony Francis,Dorota M. Grabowska,Stefano CarrazzaOct 15 2021 quant-phcs.LGhep-ph arXiv:2110.06933v1

We propose and assess an alternative quantum generator architecture in the context of generative adversarial learning for Monte Carlo event generation, used to simulate particle physics processes at the Large Hadron Collider (LHC). We validate this methodology by implementing the quantum network on artificial data generated from known underlying distributions. The network is then applied to Monte Carlo-generated datasets of specific LHC scattering processes. The new quantum generator architecture leads to an improvement in state-of-the-art implementations while maintaining shallow-depth networks. Moreover, the quantum generator successfully learns the underlying distribution functions even if trained with small training sample sets; this is particularly interesting for data augmentation applications. We deploy this novel methodology on two different quantum hardware architectures, trapped-ion and superconducting technologies, to test its hardware-independent viability

Evaluation on Genetic Algorithms as an optimizer of Variational Quantum Eigensolver(VQE) method

Hikaru Wakaura,Takao Tomono,Shoya YasudaOct 15 2021 quant-ph arXiv:2110.07441v1

Variational-Quantum-Eigensolver(VQE) method on a quantum computer is a well-known hybrid algorithm to solve the eigenstates and eigenvalues that uses both quantum and classical computers. This method has the potential to solve quantum chemical simulation including polymer and complex optimization problems that are never able to be solved in a realistic time. Though they are many papers on VQE, there are many hurdles before practical application. Therefore, we tried to evaluate VQE methods with Genetic Algorithms(GA). In this paper, we propose the VQE method with GA. We selected ground and excited-state energy on hydrogen molecules as the target because there are many local minimum values on excited states though the molecular structure is extremely simple. Therefore it is not easy to find the energy of states. We compared the GA method with other methods from the viewpoint of log error of the ground, triplet, singlet, and doubly excited state energy value. As a result, we denoted that the BFGS method has the highest accuracy. We thought that rcGA used as an optimization for the VQE method was proved disappointing. The rcGA does not show an advantage compared to other methods. we suggest that the cause is due to initial convergence. In the future, we want to try to introduce Genetic Algorithms then local search.

Applying quantum approximate optimization to the heterogeneous vehicle routing problem

David Fitzek,Toheed Ghandriz,Leo Laine,Mats Granath,Anton Frisk KockumOct 14 2021 quant-ph arXiv:2110.06799v1

Quantum computing offers new heuristics for combinatorial problems. With small- and intermediate-scale quantum devices becoming available, it is possible to implement and test these heuristics on small-size problems. A candidate for such combinatorial problems is the heterogeneous vehicle routing problem (HVRP): the problem of finding the optimal set of routes, given a heterogeneous fleet of vehicles with varying loading capacities, to deliver goods to a given set of customers. In this work, we investigate the potential use of a quantum computer to find approximate solutions to the HVRP using the quantum approximate optimization algorithm (QAOA). For this purpose we formulate a mapping of the HVRP to an Ising Hamiltonian and simulate the algorithm on problem instances of up to 21 qubits. We find that the number of qubits needed for this mapping scales quadratically with the number of customers. We compare the performance of different classical optimizers in the QAOA for varying problem size of the HVRP, finding a trade-off between optimizer performance and runtime.

QTN-VQC: An End-to-End Learning framework for Quantum Neural Networks

Jun Qi,Chao-Han Huck Yang,Pin-Yu ChenOct 11 2021 quant-phcs.AIcs.CLcs.CVcs.LGcs.NE arXiv:2110.03861v2

The advent of noisy intermediate-scale quantum (NISQ) computers raises a crucial challenge to design quantum neural networks for fully quantum learning tasks. To bridge the gap, this work proposes an end-to-end learning framework named QTN-VQC, by introducing a trainable quantum tensor network (QTN) for quantum embedding on a variational quantum circuit (VQC). The architecture of QTN is composed of a parametric tensor-train network for feature extraction and a tensor product encoding for quantum encoding. We highlight the QTN for quantum embedding in terms of two perspectives: (1) we theoretically characterize QTN by analyzing its representation power of input features; (2) QTN enables an end-to-end parametric model pipeline, namely QTN-VQC, from the generation of quantum embedding to the output measurement. Our experiments on the MNIST dataset demonstrate the advantages of QTN for quantum embedding over other quantum embedding approaches.

Image Compression and Classification Using Qubits and Quantum Deep Learning

Ali Mohsen,Mo TiwariOct 13 2021 quant-phcs.LGeess.IV arXiv:2110.05476v1

Recent work suggests that quantum machine learning techniques can be used for classical image classification by encoding the images in quantum states and using a quantum neural network for inference. However, such work has been restricted to very small input images, at most 4 x 4, that are unrealistic and cannot even be accurately labeled by humans. The primary difficulties in using larger input images is that hitherto-proposed encoding schemes necessitate more qubits than are physically realizable. We propose a framework to classify larger, realistic images using quantum systems. Our approach relies on a novel encoding mechanism that embeds images in quantum states while necessitating fewer qubits than prior work. Our framework is able to classify images that are larger than previously possible, up to 16 x 16 for the MNIST dataset on a personal laptop, and obtains accuracy comparable to classical neural networks with the same number of learnable parameters. We also propose a technique for further reducing the number of qubits needed to represent images that may result in an easier physical implementation at the expense of final performance. Our work enables quantum machine learning and classification on classical datasets of dimensions that were previously intractable by physically realizable quantum computers or classical simulation

Tunable Realizations of Correlated Quantum Walks using an Unsupervised Generative Model

Miri Kenig,Yoav LahiniOct 14 2021 quant-phcond-mat.dis-nnphysics.comp-ph arXiv:2110.06911v1

Quantum particles co-propagating on a lattice develop complex correlations due to an interplay between quantum statistics, interactions, and lattice disorder. Here we present a novel algorithm capable of learning these correlations and identifying the physical control parameters in a completely unsupervised manner. After training on a limited data set, the algorithm can generate a much larger number of new, unbiased, adjustable, yet physically correct instances. The knowledge encapsulated in the algorithm’s latent space allows tuning physical parameters to values the algorithm was not explicitly trained on and accelerate the learning of new, more complex problems. Our results demonstrate the ability of neural networks to learn quantum dynamics in an unsupervised manner and offer a route to their use in quantum simulations and computation.

Improving the Accuracy of the Variational Quantum Eigensolver for Molecular Systems by the Explicitly-Correlated Perturbative [2]R12R12-Correction

Philipp Schleich,Jakob S. Kottmann,Alán Aspuru-GuzikOct 14 2021 quant-phphysics.chem-phphysics.comp-ph arXiv:2110.06812v1

We provide an integration of the universal, perturbative explicitly correlated [2]R12R12-correction in the context of the Variational Quantum Eigensolver (VQE). This approach is able to increase the accuracy of the underlying reference method significantly while requiring no additional quantum resources. Our proposed approach only requires knowledge of the one- and two-particle reduced density matrices (RDMs) of the reference wavefunction; these can be measured after having reached convergence in VQE. The RDMs are then combined with a set of molecular integrals. This computation comes at a cost that scales as the sixth power of the number of electrons. We explore the performance of the VQE+[2]R12R12 approach using both conventional Gaussian basis sets and our recently proposed directly determined pair-natural orbitals obtained by multiresolution analysis (MRA-PNOs). Both Gaussian orbital and PNOs are investigated as a potential set of complementary basis functions in the computation of [2]R12R12. In particular the combination of MRA-PNOs with [2]R12R12 has turned out to be very promising — persistently throughout our data, this allowed very accurate simulations at a quantum cost of a minimal basis set. Additionally, we found that the deployment of PNOs as complementary basis can greatly reduce the number of complementary basis functions that enter the computation of the correction at a cubic complexity.

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