Юрий Кругляк_Квантовое моделирование в квантовой химии на квантовых компьютерах_399_стр

real world problems is a subject of active investigation. Analysis of many-body quantum system is particularly challenging for classical computers due to the exponential scaling of Hilbert space dimension with the number of particles. Hence, solving problems relevant to chemistry and condensed matter physics are expected to be the first successful applications of quantum computers. In this paper, we propose another class of problems from the quantum realm that can be solved efficiently on quantum computers: model inference for nuclear magnetic resonance (NMR) spectroscopy, which is important for biological and medical research. Our results are based on the cumulation of three interconnected studies. Firstly, we use methods from classical machine learning to analyze a dataset of NMR spectra of small molecules. Secondly, we propose a simple and efficient method, aided by a quantum simulator, to extract the NMR spectrum of any hypothetical molecule described by a parametric Heisenberg model. Thirdly, we propose an efficient variational Bayesian inference procedure for extracting Hamiltonian parameters of experimentally relevant NMR spectra.

PR-10

Anders S. Christensen, O. Anatole von Lilienfeld

Operator quantum machine learning: Navigating the chemical space of response properties

https://arxiv.org/abs/1910.14418 31.10.2019

The identification and use of structure property relationships lies at the heart of the chemical sciences. Quantum mechanics forms the basis for the unbiased virtual exploration of chemical compound space (CCS), imposing substantial compute needs if chemical accuracy is to be reached. In order to accelerate predictions of quantum properties without compromising accuracy, our lab has been developing quantum machine learning (QML) based models which can be applied throughout CCS. Here, we briefly explain, review, and discuss the recently introduced operator formalism which substantially improves the data efficiency for QML models of common response properties.

PR-11

Andrew Patterson, Hongxiang Chen, Leonard Wossnig et al

Quantum State Discrimination Using Noisy Quantum Neural Networks https://arxiv.org/abs/1911.00352

01.11.2019

Near-term quantum computers are noisy, and therefore must run algorithms with a low circuit depth and qubit count. Here we investigate how noise affects a quantum neural network (QNN) for state discrimination, applicable on near-term quantum devices as it fulfils the above criteria. We find that when simulating gradient 390

calculation on a noisy device, a large number of parameters is disadvantageous. By introducing a new smaller circuit ansatz we overcome this limitation, and find that the QNN performs well at noise levels of current quantum hardware. We also show that networks trained at higher noise levels can still converge to useful parameters. Our findings show that noisy quantum computers can be used in applications for state discrimination and for classifiers of the output of quantum generative adversarial networks.

PR-12

Trevor Keen, Pavel Lougovski, Steven Johnston, Thomas Maier

Quantum-classical implementation of two-site dynamical mean-field theory using quantum computers

http://meetings.aps.org/Meeting/SES19/Session/A01.5 01.11.2019

We report on a quantum-classical simulation of a two-site dynamical mean-field theory (DMFT) calculation of a Hubbard model. We employ IBM's superconducting qubit chip to compute the zero-temperature impurity Green's function in the time domain and utilize a classical computer to fit the measured Green's function and determine its frequency dependence. We find that Trotter errors lead to erroneous impurity parameters, which, along with noise from the quantum chip, prevent the DMFT algorithm from converging to the correct solution. To reduce this sensitivity to Trotter errors, we determine the impurity parameters by integrating the quasiparticle peaks in the spectral function. This allows us to iterate the DMFT loop to self-consistency for a strongly Mott insulating system at halffilling.

PR-13

Andrew D. King, Jack Raymond, Trevor Lanting at al

Scaling advantage in quantum simulation of geometrically frustrated magnets https://arxiv.org/abs/1911.03446

08.11.2019

The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of relaxation in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) relaxation timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation over the classical approach of path-integral Monte Carlo (PIMC) fixed-

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Hamiltonian relaxation with multiqubit cluster updates. The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over a CPU. This is an important piece of experimental evidence that in general, PIMC does not mimic QA dynamics for stoquastic Hamiltonians. The observed scaling advantage, for simulation of frustrated magnetism in quantum condensed matter, demonstrates that near-term quantum devices can be used to accelerate computational tasks of practical relevance.

PR-14

Raffaele Miceli, Michael McGuigan

Thermo field dynamics on a quantum computer https://arxiv.org/abs/1911.03335

08.11.2019

In this paper we develop a quantum algorithm to realize finite temperature simulation on a quantum computer. As quantum computers use real-time evolution we did not use the imaginary time methods popular on classical algorithms. Instead, we implemented a real-time thermo field dynamics formalism, which has the added benefit of being able to compute quantities that are both timeand temperaturedependent. To implement thermo field dynamics we apply a unitary transformation to discrete quantum mechanical operators to make new Hamiltonians with encoded temperature dependence. The method works normally for fermions, which have a finite representation, but needs some modification to work with bosons. These Hamiltonians are then processed into a Pauli matrix representation in order to be used as input for IBM's Qiskit package. We then use IBM's quantum simulator to calculate an approximation to the Hamiltonaian's ground state energy via the variational quantum eigensolver (VQE) algorithm. This approximation is then compared to a classically calculated value for the exact energy. The thermo field dynamics quantum algorithm has general applications to material science, highenergy physics and nuclear physics, particularly in those situations involving realtime evolution at high temperature.

PR-15

Prashant S. Emani, Jonathan Warrell, Alan Anticevic at al

Quantum Computing at the Frontiers of Biological Sciences https://arxiv.org/abs/1911.07127

17.11.2019

The search for meaningful structure in biological data has relied on cutting-edge advances in computational technology and data science methods. However, challenges arise as we push the limits of scale and complexity in biological problems. Innovation in massively parallel, classical computing hardware and algorithms continues to address many of these challenges, but there is a need to simultaneously

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consider new paradigms to circumvent current barriers to processing speed. Accordingly, we articulate a view towards quantum computation and quantum information science, where algorithms have demonstrated potential polynomial and exponential computational speedups in certain applications, such as machine learning. The maturation of the field of quantum computing, in hardware and algorithm development, also coincides with the growth of several collaborative efforts to address questions across length and time scales, and scientific disciplines. We use this coincidence to explore the potential for quantum computing to aid in one such endeavor: the merging of insights from genetics, genomics, neuroimaging and behavioral phenotyping. By examining joint opportunities for computational innovation across fields, we highlight the need for a common language between biological data analysis and quantum computing. Ultimately, we consider current and future prospects for the employment of quantum computing algorithms in the biological sciences.

PR-16

Dario Gil, William M. J. Green

The Future of Computing: Bits + Neurons + Qubits https://arxiv.org/abs/1911.08446: LiH

15.11.2019

The laptops, cell phones, and internet applications commonplace in our daily lives are all rooted in the idea of zeros and ones - in bits. This foundational element originated from the combination of mathematics and Claude Shannon's Theory of Information. Coupled with the 50-year legacy of Moore's Law, the bit has propelled the digitization of our world. In recent years, artificial intelligence systems, merging neuron-inspired biology with information, have achieved superhuman accuracy in a range of narrow classification tasks by learning from labelled data. Advancing from Narrow AI to Broad AI will encompass the unification of learning and reasoning through neuro-symbolic systems, resulting in a form of AI which will perform multiple tasks, operate across multiple domains, and learn from small quantities of multi-modal input data. Finally, the union of physics and information led to the emergence of Quantum Information Theory and the development of the quantum bit - the qubit - forming the basis of quantum computers. We have built the first programmable quantum computers, and although the technology is still in its early days, these systems offer the potential to solve problems which even the most powerful classical computers cannot. The future of computing will look fundamentally different than it has in the past. It will not be based on more and cheaper bits alone, but rather, it will be built upon bits + neurons + qubits. This future will enable the next generation of intelligent mission-critical systems and accelerate the rate of science-driven discovery.

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PR-17

Andrei Alexandru, Paulo F. Bedaque, Scott Lawrence

Quantum Algorithms For Disordered Physics https://arxiv.org/abs/1911.11117

25.11.2019

We show how a quantum computer may efficiently simulate a disordered Hamiltonian, by incorporating a pseudo-random number generator directly into the time evolution circuit. This technique is applied to quantum simulation of few-body disordered systems in the large volume limit; in particular, Anderson localization. The method requires a number of (error corrected) qubits proportional to the logarithm of the volume of the system, and each time evolution step requires a number of gates polylogarithmic in the volume. We simulate the method to observe the metal-insulator transition on a three-dimensional lattice. Additionally, we demonstrate the algorithm on a one-dimensional lattice, using physical quantum processors.

PR-18

K Jansen, T Hartung

Zeta-regularized vacuum expectation values from quantum computing simulations

https://arxiv.org/pdf/1912.01276.pdf: H 03.12.2019

The zeta-regularization allows to establish a connection between Feynman’s path integral and Fourier integral operator zeta-functions. This fact can be utilized to perform the regularization of the vacuum expectation values in quantum field theories. In this proceeding, we will describe the concept of the zeta-regularization, give a simple example and demonstrate that quantum computing can be employed to numerically evaluate zeta-regulated vacuum expectation values on a quantum computer.

PR-19

Anirban Ganguly, Bikash K. Behera, Prasanta K. Panigrahi

Demonstration of Minisuperspace Quantum Cosmology Using Quantum Computational Algorithms on IBM Quantum Computer https://arxiv.org/abs/1912.00298

01.12.2019

Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. Quantum computational algorithms have the potential to be an exciting new way of studying quantum cosmology. In quantum cosmology, we learn about the dynamics of the universe without constructing a 394

complete theory of quantum gravity. Since the universal wavefunction exists in an infinite-dimensional superspace over all possible 3D metrics and modes of matter configurations, we take minisuperspaces for our work by constraining the degrees of freedom to particular 3D metrics and uniform scalar field configurations. Here, we consider a wide variety of cosmological models. We begin by analyzing an anisotropic universe with cosmological constant and classical radiation. We then study the results for higher derivatives, Kaluza-Klein theories and string dilaton in quantum cosmology. We use IBM's Quantum Information Science Kit (QISKit) python library and the Variational Quantum Eigensolver (VQE) algorithm for studying these systems. The VQE algorithm is a hybrid algorithm that uses the variational approach and interleaves quantum and classical computations in order to find the minimum eigenvalue of the Hamiltonian for a given system.

PR-20

Jordan Burns, David Maughan, Yih Sung

A Data Driven Approach to Learning The Hamiltonian Matrix in Quantum Mechanics

https://arxiv.org/abs/1911.12548 28.11.2019

We present a new machine learning technique which calculates a real-valued, time independent, finite dimensional Hamiltonian matrix from only experimental data. A novel cost function is given along with a proof that the cost function has the theoretically correct Hamiltonian as a global minimum. We present results based on data simulated on a classical computer and results based on simulations of quantum systems on IBM's ibmqx2 quantum computer. We conclude with a discussion on the limitations of this data driven framework, as well as several possible extensions of this work. We also note that algorithm presented in this article not only serves as an example of using domain knowledge to design a machine learning framework, but also as an example of using domain knowledge to improve the speed of such algorithm.

PR-21

A. K. Fedorov, A. V. Akimov, J. D. Biamonte et al

Quantum Technologies in Russia

Quantum Sci. Technol., 4, 040501 (2019) 16.10.2019

Remarkable advancements in the ability to create, manipulate, and measure quantum systems are paving the way to build next generations of devices based on quantum physics. Quantum technologies in Russia are on the list of strategically important cross-cutting directions in the framework of the National Technology Initiative programs and the Digital Economy National Program. The broad focus includes

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quantum computing and simulation, quantum communications, quantum metrology and sensing. This paper reviews existing research on quantum science and technologies in Russia and summarizes the main goals for the next few years that form the basis of an upcoming major national initiative.

PR-22

Bipasha Chakraborty, Masazumi Honda, Taku Izubuchi, Yuta Kikuchi, Akio Tomiya

Digital Quantum Simulation of the Schwinger Model with Topological Term via Adiabatic State Preparation

https://arxiv.org/abs/2001.00485 02.01.2020

We perform a digital quantum simulation of a gauge theory with a topological term in Minkowski spacetime, which is practically inaccessible by standard lattice Monte Carlo simulations. We focus on 1+1 dimensional quantum electrodynamics with the θ-term known as the Schwinger model. We construct the true vacuum state of a lattice Schwinger model using adiabatic state preparation which, in turn, allows us to compute an expectation value of the fermion mass operator with respect to the vacuum. Upon taking a continuum limit we find that our result in massless case agrees with the known exact result. In massive case, we find an agreement with mass perturbation theory in small mass regime and deviations in large mass regime. We estimate computational costs required to take a reasonable continuum limit. Our results imply that digital quantum simulation is already useful tool to explore non-perturbative aspects of gauge theories with real time and topological terms.

PR-23

Dmitri E. Kharzeev, Yuta Kikuchi

Real-time chiral dynamics from a digital quantum simulation https://arxiv.org/abs/2001.00698

03.01.2020

The chiral magnetic effect in a strong magnetic field can be described using the chiral anomaly in (1+1)-dimensional massive Schwinger model with a time-dependent θ- term. We perform a digital quantum simulation of the model using an IBM-Q digital quantum simulator, and observe the corresponding vector current induced in a system of relativistic fermions by a global "chiral quench" – a sudden change in the chiral chemical potential or θ-angle. At finite fermion mass, there appears an additional contribution to this current that stems from the non-anomalous relaxation of chirality. Our results are relevant for the real-time dynamics of chiral magnetic effect in heavy ion collisions and in chiral materials, as well as for modeling high-energy processes at hadron colliders.

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PR-24

Brian Rost, Barbara Jones, Mariya Vyushkova, Aaila Ali at al

Noisy Simulation of Quantum Beats in Radical Pairs on a Quantum Computer https://arxiv.org/abs/2001.00794

03.01.2020

Current and near term quantum computers (i.e. NISQ devices) are limited in their computational power in part due to imperfect gate operations and imperfect qubits. This naturally constrains the computations run on these devices to be low-depth and short lived, lest the output turn to random noise. Here we seek to take advantage of the imperfect qubit as a means of simulating thermal relaxation in physical systems with no additional computational overhead. As a first step toward this goal we simulate the thermal relaxation of quantum beats in radical pairs on a quantum computer. Our approach is to classically compute a dynamic quantity of interest, construct a parameterized quantum circuit which returns this quantity as a function of the parameters (e.g. magnetic field, time), then simulate the system undergoing thermal relaxation. We simulate the thermal relaxation by 1) explicitly constructing an ancillary circuit to implement Kraus operators associated with the thermal decay channels. 2) Adding wait cycles into the quantum circuit to allow the natural thermal decay of the qubits to effectively simulate the thermal decay of the system of interest. Time dependence of radical pairs in a magnetic field as the dynamical quantity of interest was chosen because it is amenable to analytic solutions classically and also has readily available experimental data, allowing for easy and robust comparison of the results. We find the Kraus operator method gives very accurate results, agreeing with the experiment across its entire range of validity and having a mean squared error of 0.015% compared to the theoretical calculations. We also demonstrate a proof of concept for using the thermal relaxation of the qubits to model the thermal relaxation of the physical system.

PR-25

Junxu Li and Sabre Kais

Entanglement classifier in chemical reactions

Sci. Adv., 5: 8, eaax5283 (2019); https://arxiv.org/abs/1904.01141v1

01.04.2019

The Einstein, Podolsky, and Rosen (EPR) entanglement, which features the essential difference between classical and quantum physics, has received wide theoretical and experimental attentions. Recently, the desire to understand and create quantum entanglement between particles such as spins, photons, atoms, and molecules is fueled by the development of quantum teleportation, quantum communication, quantum cryptography, and quantum computation. Although most of the work has focused on showing that entanglement violates the famous Bell’s inequality and its

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generalization for discrete measurements, few recent attempts focus on continuous measurement results. Here, we have developed a general practical inequality to test entanglement for continuous measurement results, particularly scattering of chemical reactions. After we explain how to implement this inequality to classify entanglement in scattering experiments, we propose a specific chemical reaction to test the violation of this inequality. The method is general and could be used to classify entanglement for continuous measurement results.

Квантовые вычисления в целом

QG-1

F. J. Duarte

Fundamentals of Quantum Entanglement

https://iopscience.iop.org/book/978-0-7503-2228-7.pdf 10.2019

Quantum entanglement (QE) is undoubtedly one of the most, if not the most, mysterious and yet most promising subjects of current physics. With applications in cryptographic space-to-space, space-to-earth, and fibre communications, in addition to teleportation and quantum computing, QE goes beyond fascination and into the pragmatic spheres of commerce and the military. This book is written by Professor Duarte, an expert in the field of quantum optics. He provides the first side-by-side description of the philosophical path and the physical path to quantum entanglement, and does so in a clear and cohesive manner. This is also the first book to describe and explain, in a transparent exposition, the interferometric derivation, à la Dirac, of the ubiquitous probability amplitude for quantum entanglement. The book will be useful for optical engineers working in the field of quantum entanglement and quantum communications as well as graduate students. The book includes 29 succinct, to the point, chapters and utilizes 10 useful appendices to further detail QE.

QG-2

Leonardo Novo, Juani Bermejo-Vega, Raúl García-Patrón

Quantum advantage from energy measurements of many-body quantum systems

https://arxiv.org/abs/1912.06608 13.12.2019

The problem of sampling outputs of quantum circuits has been proposed as a candidate for demonstrating a quantum computational advantage (sometimes referred to as quantum "supremacy"). An open question is whether quantum advantage demonstrations backed by complexity-theoretic evidence can be achieved for physically motivated problems. In this work, we show quantum advantage for the natural problem of measuring the energy of a many-body quantum system. In particular, we describe a family of Hamiltonians with nearest-neighbour interactions

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on a 2D lattice that can be measured with high resolution by sampling from a quantum device, which can conceivably be implemented in the near-term. At the same time, we provide strong complexity theoretic evidence that an efficient classical simulation of this problem is impossible. Our proof exploits the ability to build a simple quantum circuit which efficiently diagonalizes these Hamiltonians. Furthermore, we highlight limitations of current theoretical tools to develop quantum advantage proposals involving Hamiltonians where such diagonalization is not known or, more generally, for Hamiltonians whose time-evolution cannot be exponentially fast-forwarded. We believe our work brings a new perspective to the problem of demonstrating quantum advantage and leads to interesting new questions in Hamiltonian complexity.

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