arXiv subjects

A. K. Fedorov

Publications and source records attributed to A. K. Fedorov.

At least 19 recordsLinked to original sources

arXiv2025

Simulating quantum circuits using the multi-scale entanglement renormalization ansatz

Understanding the limiting capabilities of classical methods in simulating complex quantum systems is of paramount importance for quantum technologies. Although many advanced approaches have been proposed and recently used to challenge quantum advantage experiments, novel efficient methods for the approximate simulation of complex quantum systems are still in high demand. Here we propose a scalable technique for approximate simulations of intermediate-size quantum circuits on the basis of the multi-scale entanglement renormalization ansatz (MERA) and Riemannian optimization. The MERA is a tensor network, whose geometry together with orthogonality constraints imposed on its tensors allow approximating many-body quantum states lying beyond the area-law scaling of the entanglement entropy. We benchmark the proposed technique for brick-wall quantum circuits of up to 243 qubits with various depths up to 20 layers. Our approach paves a way to exploring efficient simulation techniques for quantum many-body systems.

quant-ph↗

arXiv2024

Reliable confidence regions for quantum tomography using distribution moments

Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum states with reliable confidence intervals. In this work we suggest a computationally efficient and reliable scheme for determining well-justified error bars for quantum tomography. We approximate the probability distribution of the Hilbert-Schmidt distance between the target state and the estimation, which is given by the linear inversion, by calculating its two moments. We also present a generalization of this approach for quantum process tomography and deriving confidence intervals for affine functions. We benchmark our approach for a number of quantum tomography protocols using both simulation and demonstration with the use of a cloud-accessible quantum processor. The obtained results pave the way for the use of the suggested scheme for the complete characterization of quantum systems of various natures.

quant-ph↗

arXiv2023

Density-wave-type supersolid of two-dimensional tilted dipolar bosons

We predict a stable density-waves-type supersolid phase of a dilute gas of tilted dipolar bosons in a two-dimensional (2D) geometry. This many-body phase is manifested by the formation of the stripe pattern and elasticity coexisting together with the Bose-Einstein condensation and superfluidity at zero temperature. With the increasing the tilting angle the type of the gas-supersolid transition changes from the first order to the second one despite the 2D character of the system, whereas the anisotropy and many-body stabilizing interactions play crucial role. Our approach is based on the numerical analysis of the phase diagram using the simulated annealing method for a free-energy functional. The predicted supersolid effect can be realized in a variety of experimental setups ranging from excitons in heterostructures to cold atoms and polar molecules in optical potentials.

cond-mat.quant-gas↗

arXiv2023

Hybrid quantum-classical machine learning for generative chemistry and drug design

Deep generative chemistry models emerge as powerful tools to expedite drug discovery. However, the immense size and complexity of the structural space of all possible drug-like molecules pose significant obstacles, which could be overcome with hybrid architectures combining quantum computers with deep classical networks. As the first step toward this goal, we built a compact discrete variational autoencoder (DVAE) with a Restricted Boltzmann Machine (RBM) of reduced size in its latent layer. The size of the proposed model was small enough to fit on a state-of-the-art D-Wave quantum annealer and allowed training on a subset of the ChEMBL dataset of biologically active compounds. Finally, we generated 2331 novel chemical structures with medicinal chemistry and synthetic accessibility properties in the ranges typical for molecules from ChEMBL. The presented results demonstrate the feasibility of using already existing or soon-to-be-available quantum computing devices as testbeds for future drug discovery applications.

quant-ph↗

arXiv2023

Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits

The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. Here we present a proof-of-principle realization of a quantum processor register that uses optically-addressed $^{171}$Yb$^{+}$ ion qudits in a linear trap. The rich level structure of $^{171}$Yb$^{+}$ ions allows using the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and a two-qudit Molmer-Sorensen operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way towards further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors and, specifically, exploring properties of $^{171}$Yb$^{+}$ ion qudits.

quant-ph↗

arXiv2023

Disordered impenetrable two-component fermions in one dimension

We study the one-dimensional Hubbard model for two-component fermions with infinitely strong on-site repulsion (t-0 model) in the presence of disorder. Our analytical treatment demonstrates that the type of disorder drastically changes the nature of the emerging phases. The case of spin-independent disorder can be treated as a single-particle problem with Anderson localization. On the contrary, recent numerical findings show that spin-dependent disorder, which can be realized as a random magnetic field, leads to the many-body localization-delocalization transition. We find an explicit analytic expression for the matrix elements of the random magnetic field between the eigenstates of the t-0 model with potential disorder on a finite lattice. Analysis of the matrix elements supports the existence of the many-body localization-delocalization transition in this system and provides an extended physical picture of the random magnetic field.

cond-mat.dis-nn↗

arXiv2023

Fractal states of the Schwinger model

The lattice Schwinger model (SM), the discrete version of QED in 1+1 dimensions, is a well-studied test bench for lattice gauge theories. Here we study the fractal properties of the SM. We reveal the self-similarity of the ground state, which allows one to develop a recurrent procedure for finding the ground-state wave functions and predicting ground-state energies. We provide the results of recurrently calculating ground-state wave functions using the fractal ansatz and automized software package for fractal image processing. In certain parameter regimes, just a few terms are enough for our recurrent procedure to predict ground state energies close to the exact ones for several hundreds of sites. Our findings pave the way to understanding the complexity of calculating many-body wave functions in terms of their fractal properties as well as finding new links between condensed matter and high-energy lattice models.

quant-ph↗

arXiv2023

Realizing a class of stabilizer quantum error correction codes using a single ancilla and circular connectivity

We describe a class of "neighboring-blocks" stabilizer quantum error correction codes and demonstrate that such class of codes can be implemented in a resource-efficient manner using a single ancilla and circular near-neighbor qubit connectivity. We propose an implementation for syndrome-measurement circuits for codes from the class and illustrate its workings for cases of 3-qubit repetition code, Laflamme's 5-qubit code, and Shor's 9-qubit code. For 3-qubit repetition code and Laflamme's 5-qubit code suggested scheme has the property that it uses only native two-qubit CNS gates, which potentially reduces the amount of non-correctable errors due to the shorter gate time. Elements of the scheme can be used to implement surface code with near-neighbour connectivity using single ancilla, as demonstrated in an example. We developed efficient decoding procedures for repetition codes and the Laflamme's 5-qubit code using a minimum weight-perfect matching approach to account for the specific order of measurements in our scheme. The analysis of noise levels for which the scheme could show improvements in the fidelity of a stored logical qubit in the 3-qubit repetition code and Laflamme's 5-qubit code cases is provided. We complement our results by realizing the developed scheme for a 3-qubit code using an IBM quantum processor and the Laflamme's 5-qubit code using the state-vector simulator.

quant-ph↗

arXiv2023

Quantum and quantum-inspired optimization for solving the minimum bin packing problem

Quantum computing devices are believed to be powerful in solving hard computational tasks, in particular, combinatorial optimization problems. In the present work, we consider a particular type of the minimum bin packing problem, which can be used for solving the problem of filling spent nuclear fuel in deep-repository canisters that is relevant for atomic energy industry. We first redefine the aforementioned problem it in terms of quadratic unconstrained binary optimization. Such a representation is natively compatible with existing quantum annealing devices as well as quantum-inspired algorithms. We then present the results of the numerical comparison of quantum and quantum-inspired methods. Results of our study indicate on the possibility to solve industry-relevant problems of atomic energy industry using quantum and quantum-inspired optimization.

quant-ph↗

arXiv2023

Continuous monitoring for noisy intermediate-scale quantum processors

We present a continuous monitoring system for intermediate-scale quantum processors that allows extracting estimates of noisy native gate and read-out measurements based on the set of executed quantum circuits and resulting measurement outcomes. In contrast to standard approaches for calibration and benchmarking quantum processors, the executed circuits, which are input to the monitoring system, are assumed to be out of any control. We provide the results of applying our system to the synthetically generated data obtained from a quantum emulator, as well as to the experimental data collected from a publicly accessible cloud-based quantum processor. In the both cases, we demonstrate that the developed approach provides valuable results about inherent noises of emulators/processors. Considering that our approach uses only already accessible data from implemented circuits without the need to run additional algorithms, the monitoring system can complement existing approaches. We expect that our monitoring system can become a useful tool for various quantum computers in the near-term horizon, including publicly accessible cloud-based platforms, and reduce resources that are required for their benchmarking and calibration.

quant-ph↗

arXiv2022

Controlling quantum many-body systems using reduced-order modelling

Quantum many-body control is among most challenging problems in quantum science, due to computational complexity of related underlying problems. We propose an efficient approach for solving a class of control problems for many-body quantum systems, where time-dependent controls are applied to a sufficiently small subsystem. The approach is based on a tensor-networks-based scheme to build a low-dimensional reduced-order model of the subsystem's non-Markovian dynamics. Simulating dynamics of such a reduced-order model, viewed as a ``digital twin" of the original subsystem, is significantly more efficient, which enables the use of gradient-based optimization toolbox in the control parameter space. We validate the proposed method by solving control problems for quantum spin chains. In particular, the approach automatically identifies sequences for exciting the quasiparticles and guiding their dynamics to recover and transmit information. Additionally, when disorder is induced and the system is in the many body localized phase, we find generalized spin-echo sequences for dynamics inversion, which show improved performance compared to standard ones. Our approach by design takes advantage of non-Markovian dynamics of a subsystem to make control protocols more efficient, and, under certain conditions can store information in the rest of the many-body system and subsequently retrieve it at a desired moment of time. We expect that our results will find direct applications in the study of many-body systems, in probing non-trivial quasiparticle properties, as well as in development control tools for quantum computing devices.

quant-ph↗

arXiv2022

Learning entanglement breakdown as a phase transition by confusion

Quantum technologies require methods for preparing and manipulating entangled multiparticle states. However, the problem of determining whether a given quantum state is entangled or separable is known to be an NP-hard problem in general, and even the task of detecting entanglement breakdown for a given class of quantum states is difficult. In this work, we develop an approach for revealing entanglement breakdown using a machine learning technique, which is known as 'learning by confusion'. We consider a family of quantum states, which is parameterized such that there is a single critical value dividing states within this family into separate and entangled. We demonstrate the 'learning by confusion' scheme allows us to determine the critical value. Specifically, we study the performance of the method for the two-qubit, two-qutrit, and two-ququart entangled state. In addition, we investigate the properties of the local depolarization and the generalized amplitude damping channel in the framework of the confusion scheme. Within our approach and setting the parameterization of special trajectories, we obtain an entanglement-breakdown 'phase diagram' of a quantum channel, which indicates regions of entangled (separable) states and the entanglement-breakdown region. Then we extend the way of using the 'learning by confusion' scheme for recognizing whether an arbitrary given state is entangled or separable. We show that the developed method provides correct answers for a variety of states, including entangled states with positive partial transpose. We also present a more practical version of the method, which is suitable for studying entanglement breakdown in noisy intermediate-scale quantum devices. We demonstrate its performance using an available cloud-based IBM quantum processor.

quant-ph↗

arXiv2022

Probing non-Markovian quantum dynamics with data-driven analysis: Beyond "black-box" machine learning models

A precise understanding of the influence of a quantum system's environment on its dynamics, which is at the heart of the theory of open quantum systems, is crucial for further progress in the development of controllable large-scale quantum systems. However, existing approaches to account for complex system-environment interaction in the presence of memory effects are either based on heuristic and oversimplified principles or give rise to computational difficulties. In practice, one can leverage on available experimental data and replace first-principles simulations with a data-driven analysis that is often much simpler. Inspired by recent advances in data analysis and machine learning, we propose a data-driven approach to the analysis of the non-Markovian dynamics of open quantum systems. Our method allows, on the one hand, capturing the most important characteristics of open quantum systems such as the effective dimension of the environment and the spectrum of the joint system-environment quantum dynamics, and, on the other hand, reconstructing a predictive model of non-Markovian quantum dynamics, and denoising the measured quantum trajectories. We demonstrate the performance of the proposed approach with various models of open quantum systems, including a qubit coupled with a finite environment, a spin-boson model, and the damped Jaynes-Cummings model.

quant-ph↗

arXiv2022

Efficient realization of quantum primitives for Shor's algorithm using PennyLane library

Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package containing implementations of various quantum gates and well-known quantum algorithms using PennyLane library. Additoinally, we used a simplified technique for decomposition of algorithms into a set of gates which are native for trapped-ion quantum processor and realized this technique using PennyLane library. The decomposition is used to analyze resources required for an execution of Shor's algorithm on the level of native operations of trapped-ion quantum computer. Our original contribution is the derivation of coefficients needed for implementation of the decomposition. Templates within the package include all required elements from the quantum part of Shor's algorithm, specifically, efficient modular exponentiation and quantum Fourier transform that can be realized for an arbitrary number of qubits specified by a user. All the qubit operations are decomposed into elementary gates realized in PennyLane library. Templates from the developed package can be used as qubit-operations when defining a QNode.

quant-ph↗

arXiv2022

Variational quantum eigensolver techniques for simulating carbon monoxide oxidation

A family of Variational Quantum Eigensolver (VQE) methods is designed to maximize the resource of existing noisy intermediate-scale quantum (NISQ) devices. However, VQE approaches encounter various difficulties in simulating molecules of industrially relevant sizes, among which the choice of the ansatz for the molecular wavefunction plays a crucial role. In this work, we push forward the capabilities of adaptive variational algorithms (ADAPT-VQE) by demonstrating that the measurement overhead can be significantly reduced via adding multiple operators at each step while keeping the ansatz compact. Within the proposed approach, we simulate a set of molecules, O$_2$, CO, and CO$_2$, participating in the carbon monoxide oxidation processes using the statevector simulator and compare our findings with the results obtained using VQE-UCCSD and classical methods. Based on these results, we estimate the energy characteristics of the chemical reaction. Our results pave the way to the use of variational approaches for solving practically relevant chemical problems.

physics.chem-ph↗

arXiv2022

Floquet integrability and long-range entanglement generation in the one-dimensional quantum Potts model

We develop a Floquet protocol for long-range entanglement generation in the one-dimensional quantum Potts model, which generalizes the transverse-filed Ising model by allowing each spin to have $n>2$ states. We focus on the case of $n=3$, so that the model describes a chain of qutrits. The suggested protocol creates qutrit Bell-like pairs with non-local long-range entanglement that spans over the entire chain. We then conjecture that the proposed Floquet protocol is integrable and explicitly construct a few first non-trivial conserved quantities that commute with the stroboscopic evolution operator. Our analysis of the Floquet integrability relies on the deep connection between the quantum Potts model and a much broader class of models described by the Temperley-Lieb algebra. We work at the purely algebraic level and our results on Floquet integrability are valid for any representation of the Temperley-Lieb algebra. We expect that our findings can be probed with present experimental facilities using Rydberg programmable quantum simulators and can find various applications in quantum technologies.

cond-mat.quant-gas↗

arXiv2022

Decomposing the generalized Toffoli gate with qutrits

The problem of finding efficient decompositions of multi-qubit gates is of importance for quantum computing, especially, in application to existing noisy intermediate-scale quantum devices, whose resources are substantially limited. Here we propose a decomposition scheme for a generalized $N$-qubit Toffoli gate with the use of $2N-3$ two-qutrit gates for arbitrary connectivity. The fixed number of the required additional levels (the choice of qutrits is optimal) and the use of the iSWAP gate as a native operation make our approach directly applicable for ongoing experiments with superconducting quantum processors. Specifically, we present a blueprint of the realization of the proposed scheme for the Aspen-9 processor supporting quantum operations with qutrits.

quant-ph↗

arXiv2022

Quantum computing at the quantum advantage threshold: a down-to-business review

It is expected that quantum computers would enable solving various problems that are beyond the capabilities of the most powerful current supercomputers, which are based on classical technologies. In the last three decades, advances in quantum computing stimulated significant interest in this field from industry, investors, media, executives, and general public. However, the understanding of this technology, its current capabilities and its potential impact in these communities is still lacking. Closing this gap requires a complete picture of how to assess quantum computing devices' performance and estimate their potential, a task made harder by the variety of quantum computing models and physical platforms. Here we review the state of the art in quantum computing, promising computational models and the most developed physical platforms. We also discuss potential applications, the requirements posed by these applications and technological pathways towards addressing these requirements. Finally, we summarize and analyze the arguments for the quantum computing market's further exponential growth. The review is written in a simple language without equations, and should be accessible to readers with no advanced background in mathematics and physics.

quant-ph↗