Product State Research Articles

Renewable energy economics in the European part of Russia

Subject of research: methods for assessing the economic efficiency of renewable energy sources Purpose of research: describe the state of electricity production based on renewable energy sources in the world and in Russia, and provide calculations of efficiency indicators. Object of research: electrical power systems with renewable energy sources. Main results of research: an overview of the performance of power plants based on renewable energy sources around the world and an analysis of the economics of promising projects based on the use of renewable energy sources in Russia are provided. An analysis of statistical deviations over the past eight years was carried out. Object: to describe the state of electricity production based on renewable energy sources in the world and in Russia, to calculate the efficiency indicators of renewable energy sources.

Scaling whole-chip QAOA for higher-order ising spin glass models on heavy-hex graphs

We show that the quantum approximate optimization algorithm (QAOA) for higher-order, random coefficient, heavy-hex compatible spin glass Ising models has strong parameter concentration across problem sizes from 16 up to 127 qubits for p = 1 up to p = 5, which allows for computationally efficient parameter transfer of QAOA angles. Matrix product state (MPS) simulation is used to compute noise-free QAOA performance. Hardware-compatible short-depth QAOA circuits are executed on ensembles of 100 higher-order Ising models on noisy IBM quantum superconducting processors with 16, 27, and 127 qubits using QAOA angles learned from a single 16-qubit instance using the JuliQAOA tool. We show that the best quantum processors find lower energy solutions up to p = 2 or p = 3, and find mean energies that are about a factor of two off from the noise-free distribution. We show that p = 1 QAOA energy landscapes remain very similar as the problem size increases using NISQ hardware gridsearches with up to a 414 qubit processor.

Efficient Simulation of Inhomogeneously Correlated Systems Using Block Interaction Product States.

The strength of the density matrix renormalization group (DMRG) in handling strongly correlated systems lies in its unbiased and simultaneous treatment of identical sites that are both energetically degenerate and spatially similar, as typically encountered in physical models. However, this very feature becomes a drawback when DMRG is applied to quantum chemistry calculations for large, realistic correlated systems. This is because entangled orbitals often span broad ranges in both energy and space, with their interactions being notably inhomogeneous. In this study, we suggest addressing the strong intrafragment correlations and weak interfragment correlations separately, utilizing a large-scale multiconfigurational calculation framework grounded in the block interaction product state formulation. The strong intrafragment correlation can be encapsulated in several electronic states located on fragments, which are obtained by considering the entanglement between fragments and their environments. Moreover, we incorporate non-Abelian spin-SU(2) symmetry in our work to target the desired states we interested with well-defined particle number and spin, providing deeper insights into the corresponding chemical processes. The described method has been examined in various chemical systems and demonstrates high efficiency in addressing the inhomogeneous effects in strong correlation quantum chemistry.

Soybean cultivation in Russia under modern conditions

The article presents an analysis of the current state of soybean production in the Russian Federation. It is shown that the production of this valuable high-protein oilseed crop over the previous years has made a huge breakthrough in conquering the market and increasing its share in the country’s total agricultural production. In Russia, in 2023, a record was set for the gross soybean production in history, with a total grain of 6.8 million tons. At the same time, the production leader also changed: from the traditional Far East, where soybeans have been cultivated for more than 100 years, to the Central Federal District, which has achieved the largest gross soybean yields in the country – about 3.0 million tons. Production growth is realized not only through extensive development paths, but also through increasing crop productivity. In 2023, the average yield in the country was 1.92 t/ha, which is also a historical maximum. It should be noted that in increasing productivity, the direction has been taken, according to the Food Security Doctrine, to increase to 75% the share of seeds of domestic varieties in the total volume by 2030, and for this there are all the necessary resources.

Nuclear norm regularized loop optimization for tensor network

We propose a loop optimization algorithm based on nuclear norm regularization for the tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to the standard variational periodic matrix product states method, this algorithm can circumvent the local minima related to short-ranged correlation in a simpler fashion. We demonstrate its performance when used as a part of the tensor network renormalization algorithms [S. Yang, Z.-C. Gu, and X.-G. Wen, ] for the critical two-dimensional Ising model. The scale invariance of the renormalized tensors is attained with higher accuracy while the higher parts of the scaling dimension spectrum are obtained in a more stable fashion. Published by the American Physical Society 2024

Boosted imaginary time evolution of matrix product states

In this work, we consider the imaginary time evolution of matrix product states. We present a quantum-inspired classical method that, when combined with time evolving block decimation (TEBD), is able to potentially speed up the convergence to a ground state compared to TEBD alone. Our method, referred to as boosted imaginary time evolution, relies on the use of reflections to boost to lower energy states. Interleaving TEBD steps with boosts reduces the total number of TEBD steps and potentially the computational cost required to imaginary time evolve a matrix product state to a ground state. We give the mathematical details of the method followed by an algorithmic implementation and finally some results for a simple test case. Published by the American Physical Society 2024

Local certification of unitary operations

In this work, we analyze the local certification of unitary quantum channels, which is a natural extension of quantum hypothesis testing. A particular case of a quantum channel operating on two systems corresponding to product states at the input, is considered. The goal is to minimize the probability of the type II error, given a specified maximum probability of the type I error, considering assistance through entanglement with auxiliary systems. Our result indicates connection of the local certification problem with a product numerical range of unitary matrices. We show that the optimal local strategy does not need usage of auxiliary systems and requires only single round of one-way classical communication. Moreover, we compare local and global certification strategies and show that typically local strategies are optimal, yet in some extremal cases, where global strategies make no errors, local ones may fail miserably. Finally, some application for local certification of von Neumann measurements are discussed as well.

Emphasizing the innovation of urological robotic-assisted surgical instruments and technology driven by new quality productivity forces

New quality productivity force is an advanced form of productive force that is innovation-driven, characterized by high technology, high efficiency, and high quality. It aligns with the new development philosophy and represents an advanced state of productivity. Within the medical sphere, this concept is epitomized by the progressive evolution of surgical instruments and techniques. In recent years, the rapid development of new quality productivity forces in the medical field has generated significant anticipation for innovations in urological robotic surgery instruments and techniques. Advancements in domestically produced robotic surgery systems, remote robotic surgery, single-port robotic surgery, and pediatric-specific robotic surgery exemplify the critical application of new quality productivity forces in urology. The integration of artificial intelligence, haptic feedback technology, and sensory enhancement technologies has further enhanced the safety and precision of surgeries. Driven by these new quality productivity forces, the development of urological robotic surgery instruments and techniques has reached a new milestone, potentially setting a new gold standard for urological surgeries and providing patients with safer, more efficient, and personalized medical care. However, certain emerging technologies still face challenges in their application, necessitating further research and clinical validation.

AN INNOVATIVE APPROACH TO THE SOCIAL MANAGEMENT OF FILM PRODUCTION: THE ROLE INSTALLATION METHOD

The article analyzes the current state of film production in Russia. It considers changes in the domestic film market, including government support, increased production volumes, and the development of online platforms. It notes problems associated with increased production costs and lack of time to prepare for a role. The paper presents an innovative approach called “role installation” for managing the preparation of actors for filming and shows its possibilities in the context of modern mass film production. The method is aimed at quickly and effectively immersing the actor in the role, taking into account time constraints and directors’ requirements. The author emphasizes the importance of a sociological approach in film production, which helps producers, actors, and directors understand the context and social atom of the images they create. The article touches upon the issues of transforming acting education and the position of cinematography in shaping public consciousness. The “role installation” method can become an effective tool in solving modern problems of film production, motivation, and joint project management, contributing to the creation of high-quality and socially significant content.

Tensor product random matrix theory

The evolution of complex correlated quantum systems such as random circuit networks is governed by the dynamical buildup of both entanglement and entropy. We here introduce a real-time field theory approach—essentially a fusion of the GΣ functional of the SYK model and the field theory of disordered systems—engineered to microscopically describe the full range of such crossover dynamics: from initial product states to a maximum entropy ergodic state. To showcase this approach in the simplest nontrivial setting, we consider a tensor product of coupled random matrices, and compare to exact diagonalization. Published by the American Physical Society 2024

Nonthermal eigenstates and slow relaxation in quantum Fredkin spin chains

We study the dynamics and thermalization of the Fredkin spin chain, a system with local three-body interactions, particle conservation, and explicit kinetic constraints. We consider deformations away from its stochastic point in order to tune between regimes where kinetic energy dominates and those where potential energy does. By means of exact diagonalization, perturbation theory, and variational matrix product states, we show there is a sudden change of behavior in the dynamics that occurs, from one of fast thermalization to one of slow metastable (prethermal) dynamics near the stochastic point. This change in relaxation is connected to the emergence of additional kinetic constraints, which lead to the fragmentation of Hilbert space in the limit of a large potential energy. We also show that this change can lead to thermalization being evaded for special initial conditions because of nonthermal eigenstates (akin to quantum many-body scars). We provide clear evidence for the existence of these nonthermal states for large system sizes even when far from the large-potential-energy limit, and explain their connection to the emergent kinetic constraints. Published by the American Physical Society 2024

Dynamics of a small quantum system open to a bath with thermostat.

We investigate dynamics of a small quantum system open to a bath with thermostat. We introduce another bath, called a superbath, weakly coupled with the bath to provide it with a thermostat, which has either the Lindblad or Redfield type. We treat the interaction between the system and bath via a rigorous perturbation theory. Due to the thermostat, the bath behaves dissipative and stochastic, for which the usual Born-Markov assumption is not needed. We consider a specific example of a harmonic oscillator system of interest and a photonic bath in a large container, and a superbath of the Caldeira-Legget oscillators distributed on the inner surface of the container. After taking the trace over the superbath states, we use the P representation for the total harmonic system of the system and bath. We derive the reduced time-evolution equationfor the system by explicitly finding the correlation between the system and bath beyond the product state that was not obtainable in the previous theory for the system and bath isolated from environment, and marginalizing bath degrees of freedom. Remarkably, the associated dynamic equationfor the system density matrix is of the same form as the Redfield master equationwith different coefficients depending on thermostat used. We find the steady state does not depend on the thermostat but the time-dependent state does, which agrees with common expectation. We expect to apply our theory to general systems. Unlike the usual quantum master equations, our reduced dynamics allows investigation for time-dependent protocols, and nonequilibrium quantum stochastic dynamics will be investigated in the future.

Operator product states on tensor powers of $$C^*$$-algebras

Operator product states on tensor powers of $$C^*$$-algebras

A universal formula for the entanglement asymmetry of matrix product states

Abstract Symmetry breaking is a fundamental concept in understanding quantum phases of matter, studied
so far mostly through the lens of local order parameters. Recently, a new entanglement-based probe
of symmetry breaking has been introduced under the name of entanglement asymmetry, which has
been employed to investigate the mechanism of dynamical symmetry restoration. Here, we provide
a universal formula for the entanglement asymmetry of matrix product states with finite bond
dimension, valid in the large volume limit. We show that the entanglement asymmetry of any
compact – discrete or continuous – group depends only on the symmetry breaking pattern, and is
not related to any other microscopic features.

Tangent Space Generators of Matrix Product States and Exact Floquet Quantum Scars

The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator that exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with an error that decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is not only useful for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars—periodically driven models with quasilocal generators of dynamics that have exact MPS eigenstates in their spectrum. Published by the American Physical Society 2024

Extending Non-Perturbative Simulation Techniques for Open-Quantum Systems to Excited-State Proton Transfer and Ultrafast Non-Adiabatic Dynamics.

Excited state proton transfer is an ubiquitous phenomenon in biology and chemistry, spanning from the ultrafast reactions of photobases and acids to light-driven, enzymatic catalysis and photosynthesis. However, the simulation of such dynamics involves multiple challenges, since high-dimensional, out-of-equilibrium vibronic states play a crucial role, while a fully quantum description of the proton's dissipative, real-space dynamics is also required. In this work, we extend the powerful matrix product state approach to open quantum systems (TEDOPA) to study these demanding dynamics, and also more general nonadiabatic processes that can appear in complex photochemistry subject to strong laser driving. As an illustration, we initially consider an open model of a four-level electronic system interacting with hundreds of intramolecular vibrations that drive ultrafast excited state proton transfer, as well as an explicit photonic environment that allows us to directly monitor the resulting dual fluorescence in this system. We then demonstrate how to include a continuous "reaction coordinate" of the proton transfer that allows numerically exact simulations that can be understood, visualized and interpreted in the familiar language of diabatic and adiabatic dynamics on potential surfaces, while also retaining an exact quantum treatment of dissipation and driving effects that could be used to study diverse problems in ultrafast photochemistry.

Comparison of Matrix Product State and Multiconfiguration Time-Dependent Hartree Methods for Nonadiabatic Dynamics of Exciton Dissociation.

The excited-state dynamics of organic molecules, molecular aggregates, and donor-acceptor clusters is typically governed by the interplay of electronic excitations and, due to their flexibility and soft bonding, by the interaction with their vibrations. This interaction in these systems can be characterized by a few relevant electronic states that are coupled to numerous vibrational normal modes, encompassing a vast configurational space of the molecules. The full quantum simulation of these type of systems has been long dominated by the multiconfiguration time-dependent Hartree (MCTDH) approach and its multilayer variants, which are considered the gold standard in the presence of electron-vibration coupling with a large number of modes. Recently, also the matrix product state ansatz (MPS) with appropriate time-evolution schemes has been applied to these types of Hamiltonians. In this article, we provide a numerical comparison of excited-state dynamics between the MCTDH and MPS approaches for two electron-vibration coupled systems. Notably, we consider two models for exciton dissociation at a P3HT:PCBM heterojunction, comprising two electronic states and 100 vibrational modes, and 26 electronic states and 113 vibrational modes, respectively. While both methods agree very well for the first model, more pronounced deviations are found for the second model. We trace back the divergence between the methods to the different way entanglement is treated.

Grassmann time-evolving matrix product operators: An efficient numerical approach for fermionic path integral simulations.

Developing numerical exact solvers for open quantum systems is a challenging task due to the non-perturbative and non-Markovian nature when coupling to structured environments. The Feynman-Vernon influence functional approach is a powerful analytical tool to study the dynamics of open quantum systems. Numerical treatments of the influence functional including the quasi-adiabatic propagator technique and the tensor-network-based time-evolving matrix product operator method have proven to be efficient in studying open quantum systems with bosonic environments. However, the numerical implementation of the fermionic path integral suffers from the Grassmann algebra involved. In this work, we present a detailed introduction to the Grassmann time-evolving matrix product operator method for fermionic open quantum systems. In particular, we introduce the concepts of Grassmann tensor, signed matrix product operator, and Grassmann matrix product state to handle the Grassmann path integral. Using the single-orbital Anderson impurity model as an example, we review the numerical benchmarks for structured fermionic environments for real-time nonequilibrium dynamics, real-time and imaginary-time equilibration dynamics, and its application as an impurity solver. These benchmarks show that our method is a robust and promising numerical approach to study strong coupling physics and non-Markovian dynamics. It can also serve as an alternative impurity solver to study strongly correlated quantum matter with dynamical mean-field theory.

Elucidating Dynamical Behaviors in Kinetically Constrained Models via Energy-Activity Double-Biased Matrix Product State Analysis.

We investigate dynamical phase transitions in two representative kinetically constrained models: the 1D Fredrickson-Andersen and East Models. A recently developed energy-activity double-bias approach utilizing both s and g fields, conjugated with dynamical activity and trajectory energy, is combined with matrix product state (MPS) methods. It is demonstrated that MPS methods facilitate the numerical approximation of large-deviation statistics of dynamics by determining the eigenvalues of tilted dynamical generators under the influence of double-biasing fields. Specifically, by focusing on the g-field, a nearly "half-filled" state at moderate negative g values is identified, indicating the potential existence of an anomalous phase. Additionally, dynamical quantities under various s, g, and T conditions are obtained via tensor networks, showing good qualitative consistency with mean-field results and our previous extensive numerical simulation results obtained by the path sampling method. Our study introduces novel methodologies for examining decoupled dynamical behaviors that, although energetically active, remain dynamically inactive within the system. This approach offers a fresh perspective on the theoretical framework and computational strategies for studying dynamical phase transitions in kinetically constrained systems.

Catalytic enhancement in the performance of the microscopic two-stroke heat engine.

We consider a model of heat engine operating in the microscopic regime: the two-stroke engine. It produces work and exchanges heat in two discrete strokes that are separated in time. The working body of the engine consists of two d-level systems initialized in thermal states at two distinct temperatures. Additionally, an auxiliary nonequilibrium system called catalyst may be incorporated with the working body of the engine, provided the state of the catalyst remains unchanged after the completion of a thermodynamic cycle. This ensures that the work produced by the engine arises solely from the temperature difference. Upon establishing the rigorous thermodynamic framework, we characterize twofold improvement stemming from the inclusion of a catalyst. Firstly, we prove that in the noncatalytic scenario, the optimal efficiency of the two-stroke heat engine with a working body composed of two-level systems is given by the Otto efficiency, which can be surpassed by incorporating a catalyst with the working body. Secondly, we show that incorporating a catalyst allows the engine to operate in frequency and temperature regimes that are not accessible for noncatalytic two-stroke engines. We conclude with a general conjecture about the advantage brought by a catalyst: including the catalyst with the working body always allows to improve efficiency over the noncatalytic scenario for any microscopic two-stroke heat engines. We prove this conjecture for two-stroke engines where the working body is composed of two d-level systems initialized in thermal states at two distinct temperatures, as long as the final joint state leading to optimal efficiency in the noncatalytic scenario is not a product state, or at least one of the d-level system is not thermal.