Learning quantum graph states with product measurements

Yingkai Ouyang, Marco Tomamichel

May 16 2022 quant-ph arXiv:2205.06432v1

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We consider the problem of learning NN identical copies of an unknown nn-qubit quantum graph state with product measurements. These graph states have corresponding graphs where every vertex has exactly dd neighboring vertices. Here, we detail an explicit algorithm that uses product measurements on multiple identical copies of such graph states to learn them. When n≫dn≫d and N=O(dlog(1/ϵ)+d2logn),N=O(dlog⁡(1/ϵ)+d2log⁡n), this algorithm correctly learns the graph state with probability at least 1−ϵ1−ϵ. From channel coding theory, we find that for arbitrary joint measurements on graph states, any learning algorithm achieving this accuracy requires at least Ω(log(1/ϵ)+dlogn)Ω(log⁡(1/ϵ)+dlog⁡n) copies when d=o(n−−√)d=o(n). We also supply bounds on NN when every graph state encounters identical and independent depolarizing errors on each qubit.

The QAOA with Slow Measurements

Anthony Polloreno, Graeme Smith

May 17 2022 quant-ph arXiv:2205.06845v2

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The Quantum Approximate Optimization Algorithm (QAOA) was originally developed to solve combinatorial optimization problems, but has become a standard for assessing the performance of quantum computers. Fully descriptive benchmarking techniques are often prohibitively expensive for large numbers of qubits (n≳10n≳10), so the QAOA often serves in practice as a computational benchmark. The QAOA involves a classical optimization subroutine that attempts to find optimal parameters for a quantum subroutine. Unfortunately, many optimizers used for the QAOA require many shots (N≳1000N≳1000) per point in parameter space to get a reliable estimate of the energy being minimized. However, some experimental quantum computing platforms such as neutral atom quantum computers have slow repetition rates, placing unique requirements on the classical optimization subroutine used in the QAOA in these systems. In this paper we investigate the performance of a gradient free classical optimizer for the QAOA – dual annealing – and demonstrate that optimization is possible even with N=1N=1 and n=16n=16.

Say NO to Optimization: A Non-Orthogonal Quantum Eigensolver

Unpil Baek, Diptarka Hait, James Shee, Oskar Leimkuhler, William J. Huggins, Torin F. Stetina, Martin Head-Gordon, K. Birgitta Whaley

May 19 2022 quant-ph cond-mat.str-el physics.chem-ph arXiv:2205.09039v1

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A balanced description of both static and dynamic correlations in electronic systems with nearly degenerate low-lying states presents a challenge for multi-configurational methods on classical computers. We present here a quantum algorithm utilizing the action of correlating cluster operators to provide high-quality wavefunction ansätze employing a non-orthogonal multireference basis that captures a significant portion of the exact wavefunction in a highly compact manner, and that allows computation of the resulting energies and wavefunctions at polynomial cost with a quantum computer. This enables a significant improvement over the corresponding classical non-orthogonal solver, which incurs an exponential cost when evaluating off-diagonal matrix elements between the ansatz states, and is therefore intractable. We implement the non-orthogonal quantum eigensolver (NOQE) here with an efficient ansatz parameterization inspired by classical quantum chemistry methods that succeed in capturing significant amounts of electronic correlation accurately. By taking advantage of classical methods for chemistry, NOQE provides a flexible, compact, and rigorous description of both static and dynamic electronic correlation, making it an attractive method for the calculation of electronic states of a wide range of molecular systems.

Machine learning applications for noisy intermediate-scale quantum computers

Brian Coyle

May 20 2022 quant-ph cs.LG arXiv:2205.09414v1

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Quantum machine learning has proven to be a fruitful area in which to search for potential applications of quantum computers. This is particularly true for those available in the near term, so called noisy intermediate-scale quantum (NISQ) devices. In this Thesis, we develop and study three quantum machine learning applications suitable for NISQ computers, ordered in terms of increasing complexity of data presented to them. These algorithms are variational in nature and use parameterised quantum circuits (PQCs) as the underlying quantum machine learning model. The first application area is quantum classification using PQCs, where the data is classical feature vectors and their corresponding labels. Here, we study the robustness of certain data encoding strategies in such models against noise present in a quantum computer. The second area is generative modelling using quantum computers, where we use quantum circuit Born machines to learn and sample from complex probability distributions. We discuss and present a framework for quantum advantage for such models, propose gradient-based training methods and demonstrate these both numerically and on the Rigetti quantum computer up to 28 qubits. For our final application, we propose a variational algorithm in the area of approximate quantum cloning, where the data becomes quantum in nature. For the algorithm, we derive differentiable cost functions, prove theoretical guarantees such as faithfulness, and incorporate state of the art methods such as quantum architecture search. Furthermore, we demonstrate how this algorithm is useful in discovering novel implementable attacks on quantum cryptographic protocols, focusing on quantum coin flipping and key distribution as examples.

Quantum neural networks

Kerstin Beer

May 18 2022 quant-ph arXiv:2205.08154v1

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This PhD thesis combines two of the most exciting research areas of the last decades: quantum computing and machine learning. We introduce dissipative quantum neural networks (DQNNs), which are designed for fully quantum learning tasks, are capable of universal quantum computation and have low memory requirements while training. These networks are optimised with training data pairs in form of input and desired output states and therefore can be used for characterising unknown or untrusted quantum devices. We not only demonstrate the generalisation behaviour of DQNNs using classical simulations, but also implement them successfully on actual quantum computers. To understand the ultimate limits for such quantum machine learning methods, we discuss the quantum no free lunch theorem, which describes a bound on the probability that a quantum device, which can be modelled as a unitary process and is optimised with quantum examples, gives an incorrect output for a random input. Moreover we expand the area of applications of DQNNs in two directions. In the first case, we include additional information beyond just the training data pairs: since quantum devices are always structured, the resulting data is always structured as well. We modify the DQNN’s training algorithm such that knowledge about the graph-structure of the training data pairs is included in the training process and show that this can lead to better generalisation behaviour. Both the original DQNN and the DQNN including graph structure are trained with data pairs in order to characterise an underlying relation. However, in the second extension of the algorithm we aim to learn characteristics of a set of quantum states in order to extend it to quantum states which have similar properties. Therefore we build a generative adversarial model where two DQNNs, called the generator and discriminator, are trained in a competitive way.

Variational learning algorithms for quantum query complexity

Zipeng Wu, Shi-Yao Hou, Chao Zhang, Lvzhou Li, Bei Zeng

May 17 2022 quant-ph arXiv:2205.07449v1

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Quantum query complexity plays an important role in studying quantum algorithms, which captures the most known quantum algorithms, such as search and period finding. A query algorithm applies UtOx⋯U1OxU0UtOx⋯U1OxU0 to some input state, where OxOx is the oracle dependent on some input variable xx, and UiUis are unitary operations that are independent of xx, followed by some measurements for readout. In this work, we develop variational learning algorithms to study quantum query complexity, by formulating UiUis as parameterized quantum circuits and introducing a loss function that is directly given by the error probability of the query algorithm. We apply our method to analyze various cases of quantum query complexity, including a new algorithm solving the Hamming modulo problem with 44 queries for the case of 55-bit modulo 55, answering an open question raised in arXiv:2112.14682, and the result is further confirmed by a Semidefinite Programming (SDP) algorithm. Compared with the SDP algorithm, our method can be readily implemented on the near-term Noisy Intermediate-Scale Quantum (NISQ) devices and is more flexible to be adapted to other cases such as the fractional query models.

Barren plateaus from learning scramblers with local cost functions

Roy J. Garcia, Chen Zhao, Kaifeng Bu, Arthur Jaffe

May 16 2022 quant-ph arXiv:2205.06679v1

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The existence of barren plateaus has recently revealed new training challenges in quantum machine learning (QML). Uncovering the mechanisms behind barren plateaus is essential in understanding the scope of problems that QML can efficiently tackle. Barren plateaus have recently been shown to exist when learning global properties of random unitaries. Establishing whether local cost functions can circumvent these barren plateaus is pertinent if we hope to apply QML to quantum many-body systems. We prove a no-go theorem showing that local cost functions encounter barren plateaus in learning random unitary properties.

Entanglement distillation towards minimal bond cut surface in tensor networks

Takato Mori, Hidetaka Manabe, Hiroaki Matsueda

May 16 2022 hep-th cond-mat.stat-mech quant-ph arXiv:2205.06633v1

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We propose that a minimal bond cut surface is characterized by entanglement distillation in tensor networks. Our proposal is not only consistent with the holographic models of perfect or tree tensor networks, but also can be applied for several different classes of tensor networks including matrix product states and multi-scale entanglement renormalization ansatz. We confirmed our proposal by a numerical simulation based on the random tensor network. The result sheds new light on a deeper understanding of the Ryu-Takayanagi formula for entanglement entropy in holography.

Quantum Receiver Enhanced by Adaptive Learning

Chaohan Cui, William Horrocks, Shuhong Hao, Saikat Guha, N. Peyghambarian, Quntao Zhuang, Zheshen Zhang

May 17 2022 quant-ph physics.optics arXiv:2205.07755v1Scite!5  PDF

Quantum receivers aim to effectively navigate the vast quantum-state space to endow quantum information processing capabilities unmatched by classical receivers. To date, only a handful of quantum receivers have been constructed to tackle the problem of discriminating coherent states. Quantum receivers designed by analytical approaches, however, are incapable of effectively adapting to diverse environment conditions, resulting in their quickly diminishing performance as the operational complexities increase. Here, we present a general architecture, dubbed the quantum receiver enhanced by adaptive learning (QREAL), to adapt quantum receiver structures to diverse operational conditions. QREAL is experimentally implemented in a hardware platform with record-high efficiency. Combining the QREAL architecture and the experimental advances, the error rate is reduced up to 40% over the standard quantum limit in two coherent-state encoding schemes.

Algorithmic Phases in Variational Quantum Ground-State Preparation

Nikita Astrakhantsev, Guglielmo Mazzola, Ivano Tavernelli, Giuseppe Carleo

May 16 2022 quant-ph cond-mat.stat-mech cond-mat.str-el arXiv:2205.06278v2

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The fidelity of a variational quantum circuit state prepared within stochastic gradient descent depends on, in addition to the circuit architecture, the number NsNs of measurements performed to estimate the gradient components. Simulating the variational quantum eigensolver (VQE) approach applied to two-dimensional frustrated quantum magnets, we observe that this dependence has systematic features. First, the algorithm manifests pronouncedly separated regimes on the NsNs axis with state fidelity FF vanishing at Ns<NcsNs<Nsc and rapidly growing at Ns>NcsNs>Nsc. The point of transition NcsNsc is marked by a peak of energy variance, resembling the behaviour of specific heat in second-order phase transitions. The extrapolation of the system-dependent threshold value NcsNsc to the thermodynamic limit suggests the possibility of obtaining sizable state fidelities with an affordable shots budget, even for large-scale spin clusters. Second, above NcsNsc, the state infidelity I=1−FI=1−F satisfies I−I0∝1/(Δ2Ns)I−I0∝1/(Δ2Ns), with I0I0 representing the circuit’s inability to express the exact state, FF is the achieved state fidelity, and ΔΔ represents the system energy gap. This 1/Δ21/Δ2 empirical law implies optimization resources increase inversely proportional to the squared gap of the system. We provide a symmetry-enhanced simulation protocol, which, in case of a closing gap, can significantly reduce the frustrated magnets simulation costs in quantum computers.

Qubit-efficient simulation of thermal states with quantum tensor networks

Yuxuan Zhang, Shahin Jahanbani, Daoheng Niu, Reza Haghshenas, Andrew C. Potter

May 16 2022 quant-ph cond-mat.quant-gas cond-mat.str-el arXiv:2205.06299v1

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We present a holographic quantum simulation algorithm to approximately prepare thermal states of dd-dimensional interacting quantum many-body systems, using only enough hardware qubits to represent a (dd-1)-dimensional cross-section. This technique implements the thermal state by approximately unraveling the quantum matrix-product density operator (qMPDO) into a stochastic mixture of quantum matrix product states (sto-qMPS), and variationally optimizing the quantum circuits that generate the sto-qMPS tensors, and parameters of the probability distribution generating the stochastic mixture. We demonstrate this technique on Quantinuum’s trapped-ion quantum processor to simulate thermal properties of correlated spin-chains over a wide temperature range using only a single pair of hardware qubits. We then explore the representational power of two versions of sto-qMPS ansatzes for larger and deeper circuits through classical simulations and establish empirical relationships between the circuit resources and the accuracy of the variational free-energy.

AutoQML: Automated Quantum Machine Learning for Wi-Fi Integrated Sensing and Communications

Toshiaki Koike-Akino, Pu Wang, Ye Wang

May 20 2022 cs.LG eess.SP quant-ph arXiv:2205.09115v1

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Commercial Wi-Fi devices can be used for integrated sensing and communications (ISAC) to jointly exchange data and monitor indoor environment. In this paper, we investigate a proof-of-concept approach using automated quantum machine learning (AutoQML) framework called AutoAnsatz to recognize human gesture. We address how to efficiently design quantum circuits to configure quantum neural networks (QNN). The effectiveness of AutoQML is validated by an in-house experiment for human pose recognition, achieving state-of-the-art performance greater than 80% accuracy for a limited data size with a significantly small number of trainable parameters.

An Introduction to Quantum Machine Learning for Engineers

Osvaldo Simeone

May 20 2022 quant-ph cs.ET cs.LG arXiv:2205.09510v1

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In the current noisy intermediate-scale quantum (NISQ) era, quantum machine learning is emerging as a dominant paradigm to program gate-based quantum computers. In quantum machine learning, the gates of a quantum circuit are parametrized, and the parameters are tuned via classical optimization based on data and on measurements of the outputs of the circuit. Parametrized quantum circuits (PQCs) can efficiently address combinatorial optimization problems, implement probabilistic generative models, and carry out inference (classification and regression). This monograph provides a self-contained introduction to quantum machine learning for an audience of engineers with a background in probability and linear algebra. It first describes the necessary background, concepts, and tools necessary to describe quantum operations and measurements. Then, it covers parametrized quantum circuits, the variational quantum eigensolver, as well as unsupervised and supervised quantum machine learning formulations.

Quantum Transfer Learning for Wi-Fi Sensing

Toshiaki Koike-Akino, Pu Wang, Ye Wang

May 19 2022 cs.LG cs.NI eess.SP quant-ph arXiv:2205.08590v1

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Beyond data communications, commercial-off-the-shelf Wi-Fi devices can be used to monitor human activities, track device locomotion, and sense the ambient environment. In particular, spatial beam attributes that are inherently available in the 60-GHz IEEE 802.11ad/ay standards have shown to be effective in terms of overhead and channel measurement granularity for these indoor sensing tasks. In this paper, we investigate transfer learning to mitigate domain shift in human monitoring tasks when Wi-Fi settings and environments change over time. As a proof-of-concept study, we consider quantum neural networks (QNN) as well as classical deep neural networks (DNN) for the future quantum-ready society. The effectiveness of both DNN and QNN is validated by an in-house experiment for human pose recognition, achieving greater than 90% accuracy with a limited data size.

A hybrid classical-quantum approach to speed-up Q-learning

A. Sannia, A. Giordano, N. Lo Gullo, C. Mastroianni, F. Plastina

May 17 2022 quant-ph arXiv:2205.07730v1

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We introduce a classical-quantum hybrid approach to computation, allowing for a quadratic performance improvement in the decision process of a learning agent. In particular, a quantum routine is described, which encodes on a quantum register the probability distributions that drive action choices in a reinforcement learning set-up. This routine can be employed by itself in several other contexts where decisions are driven by probabilities. After introducing the algorithm and formally evaluating its performance, in terms of computational complexity and maximum approximation error, we discuss in detail how to exploit it in the Q-learning context.

Design and Implementation of a Quantum Kernel for Natural Language Processing

Matt Wright

May 16 2022 cs.CL cs.LG quant-ph arXiv:2205.06409v1

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Natural language processing (NLP) is the field that attempts to make human language accessible to computers, and it relies on applying a mathematical model to express the meaning of symbolic language. One such model, DisCoCat, defines how to express both the meaning of individual words as well as their compositional nature. This model can be naturally implemented on quantum computers, leading to the field quantum NLP (QNLP). Recent experimental work used quantum machine learning techniques to map from text to class label using the expectation value of the quantum encoded sentence. Theoretical work has been done on computing the similarity of sentences but relies on an unrealized quantum memory store. The main goal of this thesis is to leverage the DisCoCat model to design a quantum-based kernel function that can be used by a support vector machine (SVM) for NLP tasks. Two similarity measures were studied: (i) the transition amplitude approach and (ii) the SWAP test. A simple NLP meaning classification task from previous work was used to train the word embeddings and evaluate the performance of both models. The Python module lambeq and its related software stack was used for implementation. The explicit model from previous work was used to train word embeddings and achieved a testing accuracy of 93.09±0.0193.09±0.01%. It was shown that both the SVM variants achieved a higher testing accuracy of 95.72±0.0195.72±0.01% for approach (i) and 97.14±0.0197.14±0.01% for (ii). The SWAP test was then simulated under a noise model defined by the real quantum device, ibmq_guadalupe. The explicit model achieved an accuracy of 91.94±0.0191.94±0.01% while the SWAP test SVM achieved 96.7% on the testing dataset, suggesting that the kernelized classifiers are resilient to noise. These are encouraging results and motivate further investigations of our proposed kernelized QNLP paradigm.

Natural evolutionary strategies applied to quantum-classical hybrid neural networks

Lucas Friedrich, Jonas Maziero

May 18 2022 quant-ph cs.AI arXiv:2205.08059v1

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With the rapid development of quantum computers, several applications are being proposed for them. Quantum simulations, simulation of chemical reactions, solution of optimization problems and quantum neural networks are some examples. However, problems such as noise, limited number of qubits and circuit depth, and gradient vanishing must be resolved before we can use them to their full potential. In the field of quantum machine learning, several models have been proposed. In general, in order to train these different models, we use the gradient of a cost function with respect to the model parameters. In order to obtain this gradient, we must compute the derivative of this function with respect to the model parameters. For this we can use the method called parameter-shift rule. This method consists of evaluating the cost function twice for each parameter of the quantum network. A problem with this method is that the number of evaluations grows linearly with the number of parameters. In this work we study an alternative method, called Natural Evolutionary Strategies (NES), which are a family of black box optimization algorithms. An advantage of the NES method is that in using it one can control the number of times the cost function will be evaluated. We apply the NES method to the binary classification task, showing that this method is a viable alternative for training quantum neural networks.

Machine learning via relativity-inspired quantum dynamics

Zejian Li, Valentin Heyraud, Kaelan Donatella, Zakari Denis, Cristiano Ciuti

May 18 2022 quant-ph cond-mat.other arXiv:2205.07925v1

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We present a machine-learning scheme based on the relativistic dynamics of a quantum system, namely a quantum detector inside a cavity resonator. An equivalent analog model can be realized for example in a circuit QED platform subject to properly modulated driving fields. We consider a reservoir-computing scheme where the input data are embedded in the modulation of the system (equivalent to the acceleration of the relativistic object) and the output data are obtained by linear combinations of measured observables. As an illustrative example, we have simulated such a relativistic quantum machine for a challenging classification task, showing a very large enhancement of the accuracy in the relativistic regime. Using kernel-machine theory, we show that in the relativistic regime the task-independent expressivity is dramatically magnified with respect to the Newtonian regime.

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