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Tensor Network States with Low-Rank Tensors

Hao Chen, Thomas Barthel

May 31 2022 cond-mat.str-el quant-ph arXiv:2205.15296v1

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Tensor networks are used to efficiently approximate states of strongly-correlated quantum many-body systems. More generally, tensor network approximations may allow to reduce the costs for operating on an order-NN tensor from exponential to polynomial in NN, and this has become a popular approach for machine learning. We introduce the idea of imposing low-rank constraints on the tensors that compose the tensor network. With this modification, the time and space complexities for the network optimization can be substantially reduced while maintaining high accuracy. We detail this idea for tree tensor network states (TTNS) and projected entangled-pair states. Simulations of spin models on Cayley trees with low-rank TTNS exemplify the effect of rank constraints on the expressive power. We find that choosing the tensor rank rr to be on the order of the bond dimension mm, is sufficient to obtain high-accuracy groundstate approximations and to substantially outperform standard TTNS computations. Thus low-rank tensor networks are a promising route for the simulation of quantum matter and machine learning on large data sets.

Introducing Non-Linearity into Quantum Generative Models

Kaitlin Gili, Mykolas Sveistrys, Chris Ballance

May 31 2022 quant-ph cs.LG arXiv:2205.14506v1

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The evolution of an isolated quantum system is linear, and hence quantum algorithms are reversible, including those that utilize quantum circuits as generative machine learning models. However, some of the most successful classical generative models, such as those based on neural networks, involve highly non-linear and thus non-reversible dynamics. In this paper, we explore the effect of these dynamics in quantum generative modeling by introducing a model that adds non-linear activations via a neural network structure onto the standard Born Machine framework – the Quantum Neuron Born Machine (QNBM). To achieve this, we utilize a previously introduced Quantum Neuron subroutine, which is a repeat-until-success circuit with mid-circuit measurements and classical control. After introducing the QNBM, we investigate how its performance depends on network size, by training a 3-layer QNBM with 4 output neurons and various input and hidden layer sizes. We then compare our non-linear QNBM to the linear Quantum Circuit Born Machine (QCBM). We allocate similar time and memory resources to each model, such that the only major difference is the qubit overhead required by the QNBM. With gradient-based training, we show that while both models can easily learn a trivial uniform probability distribution, on a more challenging class of distributions, the QNBM achieves an almost 3x smaller error rate than a QCBM with a similar number of tunable parameters. We therefore show that non-linearity is a useful resource in quantum generative models, and we put forth the QNBM as a new model with good generative performance and potential for quantum advantage.

Simulating quantum circuits using tree tensor networks

Philipp Seitz, Ismael Medina, Esther Cruz, Qunsheng Huang, Christian B. Mendl

Jun 03 2022 quant-ph physics.comp-ph arXiv:2206.01000v1

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We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected entanglement generated by the quantum circuit. The gates are sequentially applied to the tree by absorbing single-qubit gates into leaf nodes, and splitting two-qubit gates via singular value decomposition and threading the resulting virtual bond through the tree. We theoretically analyze the applicability of the method as well as its computational cost and memory requirements, and identify advantageous scenarios in terms of required bond dimensions as compared to a matrix product state representation. The study is complemented by numerical experiments for different quantum circuit layouts up to 37 qubits.

Optimize cooling-by-measurement by reinforcement learning

Jia-shun Yan, Jun Jing

Jun 02 2022 quant-ph arXiv:2206.00246v1

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Cooling by the conditional measurement demonstrates a transparent advantage over that by the unconditional counterpart on the average-population-reduction rate. This advantage, however, is blemished by few percentage of the successful probability of finding the detector system in the measured state. In this work, we propose an optimized architecture to cool down a target resonator, which is initialized as a thermal state, using an interpolation of the conditional and unconditional measurement strategies. Analogous to the conditional measurement, an optimal measurement-interval τuoptτoptu for the unconditional (nonselective) measurement is analytically found for the first time, which is inversely proportional to the collective dominant Rabi frequency ΩdΩd as a function of the resonator’s population at the end of the last round. A cooling algorithm under the global optimization by the reinforcement learning results in the maximum value for the cooperative cooling performance, an indicator function to quantify the comprehensive cooling efficiency for arbitrary cooling-by-measurement architecture. In particular, the average population of the target resonator under only 1616 rounds of measurements can be reduced by over four orders in magnitude with a successful probability about 30%30%.

Design and Simulation of an Autonomous Quantum Flying Robot Vehicle: An IBM Quantum Experience

Sudev Pradhan, Anshuman Padhi, Bikash Kumar Behera

Jun 02 2022 quant-ph cs.RO arXiv:2206.00157v1

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The application of quantum computation and information in robotics has caught the attention of researchers off late. The field of robotics has always put its effort on the minimization of the space occupied by the robot, and on making the robot `smarter. `The smartness of a robot is its sensitivity to its surroundings and the user input and its ability to react upon them desirably. Quantum phenomena in robotics make sure that the robots occupy less space and the ability of quantum computation to process the huge amount of information effectively, consequently making the robot smarter. Braitenberg vehicle is a simple circuited robot that moves according to the input that its sensors receive. Building upon that, we propose a quantum robot vehicle that is `smart’ enough to understand the complex situations more than that of a simple Braitenberg vehicle and navigate itself as per the obstacles present. It can detect an obstacle-free path and can navigate itself accordingly. It also takes input from the user when there is more than one free path available. When left with no option on the ground, it can airlift itself off the ground. As these vehicles sort of `react to the surrounding conditions, this idea can be used to build artificial life and genetic algorithms, space exploration and deep-earth exploration probes, and a handy tool in defense and intelligence services.

Are classical neural networks quantum?

Andrei T. Patrascu

Jun 02 2022 cs.LG cond-mat.dis-nn hep-th quant-ph arXiv:2206.00005v1

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Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual classical neural networks have some actual hidden quantum properties that make them such suitable tools for a highly coupled quantum problem. I discuss here what makes a system quantum and to what extent we can interpret a neural network as having quantum remnants.

A digital quantum simulation of an extended Agassi model assisted by machine learning

Álvaro Sáiz, José-Enrique García-Ramos, José Miguel Arias, Lucas Lamata, Pedro Pérez-Fernández

May 31 2022 quant-ph nucl-th arXiv:2205.15122v1

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A digital quantum simulation for the extended Agassi model is proposed using a quantum platform with eight trapped ions. The extended Agassi model is an analytically solvable model including both short range pairing and long range monopole-monopole interactions with applications in nuclear physics and in other many-body systems. In addition, it owns a rich phase diagram with different phases and the corresponding phase transition surfaces. The aim of this work is twofold: on one hand, to propose a quantum simulation of the model at the present limits of the trapped ions facilities and, on the other hand, to show how to use a machine learning algorithm on top of the quantum simulation to accurately determine the phase of the system. Concerning the quantum simulation, this proposal is scalable with polynomial resources to larger Agassi systems. Digital quantum simulations of nuclear physics models assisted by machine learning may enable one to outperform the fastest classical computers in determining fundamental aspects of nuclear matter.

Geometric measure of entanglement from Wehrl Moments using Artificial Neural Networks

Jérôme Denis, François Damanet, John Martin

May 31 2022 quant-ph physics.comp-ph arXiv:2205.15095v1

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In recent years, artificial neural networks (ANNs) have become an increasingly popular tool for studying problems in quantum theory, and in particular entanglement theory. In this work, we analyse to what extent ANNs can provide us with an accurate estimate of the geometric measure of entanglement of symmetric multiqubit states on the basis of a few Wehrl moments (moments of the Husimi function of the state). We compare the results we obtain by training ANNs with the informed use of convergence acceleration methods. We find that even some of the most powerful convergence acceleration algorithms do not compete with ANNs when given the same input data, provided that enough data is available to train these ANNs. More generally, this work opens up perspectives for the estimation of entanglement measures and other SU(2) invariant quantities, such as Wehrl entropy, on the basis of a few Wehrl moments that should be more easily accessible in experiments than full state tomography.

Characterizing quantum pseudorandomness by machine learning

Masahiro Fujii, Ryosuke Kutsuzawa, Yasunari Suzuki, Yoshihumi Nakata, Masaki Owari

May 31 2022 quant-ph arXiv:2205.14667v1

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Random dynamics in isolated quantum systems is of practical use in quantum information and is of theoretical interest in fundamental physics. Despite a large number of theoretical studies, it has not been addressed how random dynamics can be verified from experimental data. In this paper, based on an information-theoretic formulation of random dynamics, i.e., unitary tt-designs, we propose a method for verifying random dynamics from the data that is experimentally easy-to-access. More specifically, we use measurement probabilities of quantum states generated by a given random dynamics. Based on a supervised learning method, we construct classifiers of random dynamics and show that the classifiers succeed to characterize random dynamics. We then apply the classifiers to the data set generated by local random circuits (LRCs), which are canonical quantum circuits exhibiting transitions of randomness by increasing the circuit depth, and show that the classifiers successfully detect the transition. We further apply the classifiers to noisy LRCs, showing the possibility of using them for verifying noisy quantum devices, and to monitored LRCs, indicating that the measurement-induced phase transition may possibly not be a transition of randomness.

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