arXiv subjects

Aleksey K. Fedorov

Publications and source records attributed to Aleksey K. Fedorov.

At least 19 recordsLinked to original sources

arXiv2026

Quantum-optical reset with classical memory

Dynamic quantum circuits generate states that depend on the measurement results obtained during circuit execution. To date such a quantum computing model has mainly been implemented with qubit-based superconducting hardware utilizing reset operations and classical logic. Here we develop a model of optical reset by using time-bin self-looped interferometers demonstrated in recent experiments. Synchronizing the optical reset with a simple classical device storing history of measurement results allows one to decrease uncertainty of future measurements, which suggests new possibilities for constructing dynamical circuits on optical platforms. Information flow with significant multi-time correlations and memory depth is identified through distinct information-theoretic measures. We discuss potential applications of the proposed reset model, including the realization of boson sampling and experimental tests of the quantum-mechanical formulation of Landauer's principle.

quant-ph↗

arXiv2026

Evidence for effectively constant shot complexity in the quantum approximate optimization algorithm without per-instance optimization

We study a modified fixed-point version of the Quantum Approximate Optimization Algorithm (fpQAOA), where parameters are trained classically on small instances and then transferred to larger problems. Our scheme combines three ingredients: (i) targeting approximate solutions via a prescribed approximation ratio (AR), (ii) scaling the circuit depth linearly with the problem size using a two-parameter sin-cos angle encoding, and (iii) normalizing QUBO Hamiltonians by their Frobenius norm. Noiseless numerical simulations (for system sizes up to 30 qubits) across a variety of random QUBO ensembles show that with these modifications the median number of quantum circuit runs ("shots") required to achieve AR=0.95 counterintuitively decreases towards a nearly constant value as the problem size increases, while the per-shot time remains polynomial. Extrapolation of this finite-size behavior is consistent with an effectively constant sampling complexity. Moreover, removing any single component of the scheme restores rapid growth of the required number of shots, highlighting the synergistic nature of the three modifications. These empirical findings suggest that fpQAOA, equipped with the proposed protocol, may achieve scalable approximate performance with polynomial-depth circuits for the considered problem classes.

quant-ph↗

arXiv2026

Transition-aware decomposition of single-qudit gates

Quantum computation with $d$-level quantum systems, also known as qudits, benefits from the possibility to use a richer computational space compared to qubits. However, for an arbitrary qudit-based hardware platform, the issue is that a generic qudit operation has to be decomposed into the sequence of native operations $-$ pulses that are adjusted to the transitions between two levels in a qudit. Typically, not all levels in a qudit are simply connected to each other due to specific selection rules. Moreover, the number of pulses plays a significant role, since each pulse takes a certain execution time and may introduce error. In this paper, we propose a resource-efficient algorithm to decompose single-qudit operations into the sequence of pulses that are allowed by qudit selection rules. Using the developed algorithm, the number of pulses is at most $d(d{-}1)/2$ for an arbitrary single-qudit operation. For specific operations, the algorithm could produce even fewer pulses. We provide a comparison of qudit decompositions for several types of trapped ions, specifically $^{171}\text{Yb}^+$, $^{137}\text{Ba}^+$ and $^{40}\text{Ca}^+$ with different selection rules, and also decomposition for superconducting qudits. Although our approach deals with single-qudit operations, the proposed approach is important for realizing two-qudit operations since they can be implemented as a standard two-qubit gate that is surrounded by efficiently implemented single-qudit gates.

quant-ph↗

arXiv2026

Applying Grover-mixer quantum alternating operator ansatz algorithm to higher-order unconstrained binary optimization problems

The quantum approximate optimization algorithm (QAOA) is among the leading candidates for achieving quantum advantage on near-term processors. While typically implemented with a transverse-field mixer (XM-QAOA), the Grover-mixer variant (GM-QAOA) offers a compelling alternative due to its global search capabilities. This work investigates the application of GM-QAOA to higher-order unconstrained binary optimization (HUBO) problems, also known as polynomial unconstrained binary optimization (PUBO), which form a general class of combinatorial optimization problems involving multivariable interactions. We present a comprehensive numerical study demonstrating that GM-QAOA, unlike XM-QAOA, exhibits monotonic improvement in performance with circuit depth and achieves superior results for HUBO problems within a layerwise optimization framework. An important component of our approach is an analytical framework for modeling GM-QAOA dynamics, which enables a classical approximation of the optimal parameters and helps reduce the optimization overhead. Our resource-efficient parametrized version of GM-QAOA nearly matches the performance of the version optimized using the layerwise approach while being significantly less demanding, making it a highly effective approach for complex optimization tasks. These findings highlight the potential of GM-QAOA and provide a practical pathway for its implementation on current quantum hardware.

quant-ph↗

arXiv2026

Analog Circuit-QED Simulator of Quantum Spin Dynamics Through the Extended Bose-Hubbard Model

We propose and validate a framework for analog simulation of the Heisenberg spin model using a circuit quantum electrodynamics (circuit-QED) platform. To this end, we develop a continuous family of deformed boson representations of the SU(2) algebra, which includes the Holstein-Primakoff and Dyson-Maleev transformations as special cases. For spin-1/2 systems, we introduce a procedure to circumvent the inherent non-Hermiticity of the representation, showing that this entire family yields the extended Bose-Hubbard (EBH) Hamiltonian. For the experimental realization of this EBH model, we design a scalable circuit-QED architecture based on an engineered Josephson junction array. Numerical simulations confirm that the microwave photon dynamics in this simulator accurately reproduces the original spin dynamics. Our work establishes an experimentally accessible method for investigating complex quantum spin dynamics in a highly controllable bosonic setting.

quant-ph↗

arXiv2026

Scalable platform for qudit-based quantum computing using polar molecules

We propose a scalable qudit-based quantum processor using rotational states of polar molecules. Previously, molecular internal states were used to enlarge Hilbert space, whereas our approach uses optical tweezer arrays to achieve scalable architectures with exponential state-space growth without increasing qudit dimensionality $d$. Entangling gates are implemented by adiabatically bringing traps together to activate dipole-dipole interactions. We develop encoding schemes mapping single qubits into qudits with $2\leq d\leq5$ and pairs of qubits into $d=4,5$ qudits, enabling universal set of quantum gates. Additional levels in $d=3$ and $d=5$ qudits simplify multiqubit gate decompositions. We analyze experimental parameters for SrF and NaCs molecules. This approach provides a promising route to scalable quantum information processing with multilevel systems using existing experimental platforms.

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arXiv2026

Further improvements to stabilizer simulation theory: classical rewriting of CSS-preserving stabilizer circuits, quadratic form expansions of stabilizer operations, and framed hidden variable models

Simulation of stabilizer circuits is a well-studied problem in quantum information processing, with a number of highly optimized algorithms available. Yet, we argue that further improvements can arise from the theoretical structure of stabilizer operations themselves. We focus on the subclass of stabilizer circuits composed of Calderbank-Shor-Steane (CSS)-preserving stabilizer operations, which naturally appear in fault-tolerant computations over CSS stabilizer codes. Using elementary circuit transformation techniques, we show that such circuits can be exactly rewritten as classical probabilistic circuits that reproduce measurement statistics. This rewriting introduces no computational overhead, in contrast to the general case of stabilizer circuits. To clarify the origin of this simplification, we introduce the standard quadratic form representation of general stabilizer operations (Clifford channels). It provides an efficient way to describe compositions of stabilizer operations and thus to simulate stabilizer circuits. CSS-preserving operations correspond to purely linear forms, which under a Walsh-Hadamard-Fourier transform yield a noncontextual hidden variable model, providing an alternative proof of the introduced rewriting. Finally, we develop a theory of reference frames for multiqubit systems, where frames are encoded by quadratic forms. This allows us to express stabilizer operations as probabilistic maps for proper reference frames. Non-CSS-preserving stabilizer circuits require dynamical modifications of reference frames, embodying a contextuality resource that leads to the computational overhead. This framework provides a new perspective on simulating stabilizer and near-stabilizer circuits within dynamically evolving quasiprobability models.

quant-ph↗

arXiv2025

Qudit-native simulation of the Potts model

Simulating entangled, many-body quantum systems is notoriously hard, especially in the case of high-dimensional nature of physical underlying objects. In this work, we propose an approach for simulating the Potts model based on the Suzuki-Trotter decomposition that we construct for qudit systems. Specifically, we introduce two qudit-native decomposition schemes: (i) the first utilizes Molmer-Sorensen gate and additional local levels to encode the Potts interactions, while (ii) the second employs an light-shift gate that naturally fits qudit architectures. These decompositions enable a direct and efficient mapping of the Potts model dynamics into hardware-efficient qudit gate sequences for trapped-ion platform. Furthermore, we demonstrate the use of a Suzuki-Trotter approximation with our evolution-into-gates framework, for detecting the dynamical quantum phase transition. Our results establish a pathway toward qudit-based digital quantum simulation of many-body models and provide a new perspective on probing nonanalytic behavior in high-dimensional quantum many-body models.

quant-ph↗

arXiv2025

All-to-all connectivity of Rydberg-atom-based quantum processors with messenger qubits

Rydberg atom arrays are a front-running platform for quantum processors. A major challenge threatening the scalability of this platform is the limited qubit connectivity due to the finite range of interatomic interactions. We explore an approach to realize dynamical all-to-all connectivity with the use of moving "messenger" atomic qubits that couple distant "computational" qubits held in a static tweezer array. We detail and compare four specific architectures based on this concept, each presenting distinct advantages and challenges tied to the efficacy of techniques used to couple, move and measure atomic qubits. We demonstrate that, though technologically demanding, the messenger-qubit paradigm opens a promising avenue to a truly scalable quantum processor based on Rydberg atoms.

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arXiv2025

Detection states of ions in a Paul trap via conventional and quantum machine learning algorithms

Trapped ions are among the leading platforms for quantum technologies, particularly in the field of quantum computing. Detecting states of trapped ions is essential for ensuring high-fidelity readouts of quantum states. In this work, we develop and benchmark a set of methods for ion quantum state detection using images obtained by a highly sensitive camera. By transforming the images from the camera and applying conventional and quantum machine learning methods, including convolution, support vector machine (classical and quantum), and quantum annealing, we demonstrate a possibility to detect the positions and quantum states of ytterbium ions in a Paul trap. Quantum state detection is performed with an electron shelving technique: depending on the quantum state of the ion its fluorescence under the influence of a 369.5 nm laser beam is either suppressed or not. We estimate fidelities for conventional and quantum detection techniques. In particular, conventional algorithms for detecting $^{171}$Yb$^{+}$, such as the support vector machine and photon statistics-based method,as well as our quantum annealing-based approach, have achieved perfect fidelity, which is beneficial compared to standard techniques. This result may pave the way for ultrahigh-fidelity detection of trapped ions via conventional and quantum machine learning techniques.

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arXiv2025

Quantum-inspired algorithm for simulating viral response

Understanding the properties of biological systems is an exciting avenue for applying advanced approaches to solving corresponding computational tasks. A specific class of problems that arises in the resolution of biological challenges is optimization. In this work, we present the results of a proof-of-concept study that applies a quantum-inspired optimization algorithm to simulate a viral response. We formulate an Ising-type model to describe the patterns of gene activity in host responses. Reducing the problem to the Ising form allows the use of available quantum and quantum-inspired optimization tools. We demonstrate the application of a quantum-inspired optimization algorithm to this problem. Our study paves the way for exploring the full potential of quantum and quantum-inspired optimization tools in biological applications.

q-bio.GN↗

arXiv2025

Emergence of global receptive fields capturing multipartite quantum correlations

In quantum physics, even simple data with a well-defined structure at the wave function level can be characterized by extremely complex correlations between its constituent elements. The inherent non-locality of the quantum correlations generally prevents one from providing their simple and transparent interpretation, which also remains a challenging problem for advanced classical techniques that approximate quantum states with neural networks. Here we show that monitoring the neural network weight space while learning quantum statistics from measurements allows to develop physical intuition about complex multipartite patterns and thus helps to construct more effective classical representations of the wave functions. Particularly, we observe the formation of distinct global convolutional structures, receptive fields in the hidden layer of the Restricted Boltzmann Machine (RBM) within the neural quantum tomography of the highly-entangled Dicke states. On this basis we propose an exact two-parameter classical representation not only for a specific quantum wave function, but for the whole family of the N-qubit Dicke states of different entanglement. Our findings suggest a fresh look at constructing convolutional neural networks for processing data with non-local patterns and pave the way for developing exact learning-based representations of entangled quantum states.

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arXiv2025

Qudits for decomposing multiqubit gates and realizing quantum algorithms

The paradigm behind digital quantum computing inherits the idea of using binary information processing. Nature in fact gives much more rich structures of physical objects that can be used for encoding information, which is especially interesting in the quantum-mechanical domain. In this Colloquium several ideas are reviewed that indicate how multilevel quantum systems, also known as qudits, can be used for efficient realization of quantum algorithms, which are represented via standard qubit circuits. The focus in the Colloquium is on techniques for leveraging qudits for simplifying decomposition of multiqubit gates and for compressing quantum information by encoding multiple qubits in a single qudit. As discussed in the Colloquium, these approaches can be efficiently combined. This allows a reduction in the number of entangling (two-body) operations and the number of quantum information carriers used compared to straightforward qubit realizations. These theoretical schemes can be implemented with quantum computing platforms of various natures, such as trapped ions, neutral atoms, superconducting junctions, quantum light, spin systems, and molecules. The Colloquium concludes by summarizing a set of open problems whose resolution will be an important further step toward employing universal qudit-based processors for running qubit algorithms.

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arXiv2025

Supervised binary classification of small-scale digit images and weighted graphs with a trapped-ion quantum processor

Here we present the results of benchmarking a quantum processor based on trapped $^{171}$Yb$^{+}$ ions by performing basic quantum machine learning algorithms. Using a quantum-enhanced support vector machine algorithm with up to five qubits we perform a supervised binary classification on two types of datasets: small binary digit images and weighted graphs with a ring topology. For the first dataset, images are intentionally selected so that they could be classified with 100% accuracy. This allows us to specifically examine different types of quantum encodings of the digit dataset and study the impact of experimental noise. In the second dataset, graphs are divided into two categories based on the spectral structure of their Ising Hamiltonian models, which is related to the NP-hard problem. For this problem we consider an embedding of an exponentially large Hamiltonian spectrum into an entangled state of a linear number of qubits. For both problems, we study various levels of circuit optimization and found that, for all experiments conducted, we achieve classifiers with 100% accuracy on both training and testing datasets. This demonstrates that the quantum processor has the ability to correctly solve the basic classification task under consideration. As we expect, with the increase in the capabilities of quantum processors, they can be utilized for solving machine learning tasks.

quant-ph↗

arXiv2025

Regularizing quantum loss landscapes by noise injection

The difficulty of training variational quantum algorithms and quantum machine learning models is well established. In particular, quantum loss landscapes are often highly non-convex and dominated by poor local minima. While this renders their training NP-hard in general, efficient heuristics that work well for typical instances may still exist. Here, we propose a protocol that uses a targeted noise injection to smooth and regularize quantum loss landscapes. It works by exponentially suppressing the high-frequency components in the Fourier expansion of the quantum loss function. The protocol can be efficiently implemented both in hardware and in simulations. We observe significant and robust improvements of solution quality across various problem types. Our method can be combined with existing techniques mitigating the local minima, such as the quantum natural gradient optimizer, and adds to the toolbox of methods for optimizing quantum loss functions.

quant-ph↗

arXiv2025

Progress in the development of quantum algorithms and software

A quantum processor, like any computing device, requires the development of both hardware and the necessary set of software solutions, starting with quantum algorithms and ending with means of accessing quantum devices. As part of the roadmap for the development of the high-tech field of quantum computing in the period from 2020 to 2024, a set of software solutions for quantum computing devices was developed. This software package includes a set of quantum algorithms for solving prototypes of applied tasks, monitoring and benchmarking tools for quantum processors, error suppression and correction methods, tools for compiling and optimizing quantum circuits, as well as interfaces for remote cloud access. This review presents the key results achieved, among which it is necessary to mention the execution of quantum algorithms using a cloud-based quantum computing platform.

quant-ph↗

arXiv2025

Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits

An efficient implementation of the Toffoli gate is of conceptual importance for running various quantum algorithms, including Grover's search and Shor's integer factorization. However, direct implementation of the Toffoli gate either entails a prohibitive increase in the number of two-qubit gates or requires ancilla qubits, whereas both of these resources are limited in the current generation of noisy intermediate-scale quantum devices. Here, we experimentally demonstrate a scalable $N$-qubit Toffoli gate improvement using $^{171}$Yb$^{+}$ trapped-ion-based optical-metastable-ground encoded qutrits for the cases of up to $N$=10. With the use of the Molmer-Sorensen gate as a basic entangling operation, we compare the standard qubit decomposition with the qutrit approach, where upper levels are used as ancillas.The presented decomposition requires only global control of the ancilla levels, which simplifies experimental implementation of the proposed approach. Using the example of a three-qubit Grover's search, we also demonstrate an increase in the algorithm's accuracy by monitoring the leakage from the qubit subspace during a qutrit-based Toffoli gate implementation.

quant-ph↗

arXiv2025

Simulating methylamine using symmetry adapted qubit-excitation-based variational quantum eigensolver

In this work, we propose and analyze optimization strategies for the VQE algorithm that combine various methods, including molecular point group symmetries (symmetry adaptation), compact excitation circuits (qubit-excitation-based), different types of excitation sets, and qubit tapering. These strategies allow for a significant reduction in computational requirements while ensuring convergence to the correct energies. First, we apply these combinations to small molecules, such as LiH and BeH2, to evaluate their compatibility, accuracy, and potential applicability to larger problems. We then simulate the methylamine molecule within its restricted active space using the best-performing optimization strategies. Finally, we complete our analysis by estimating the resources required for full active-space simulations of the methylamine and formic acid molecules. Our best-performing optimization strategy reduces the number of two-qubit operations for simulating the methylamine molecule from 600,000 (in the STO-3G basis with a naive Unitary Coupled Cluster ansatz) to approximately 12,000, using 26 qubits. Thus, the proposed combination of optimization methods can reduce the number of two-qubit operations by nearly two orders of magnitude. Although, we present alternative approaches that are of interest in the context of the further optimization in the number of two-qubit operation, we note that these approaches do not perform well enough in terms of the convergence to required energies. While these challenges persist, our resource analysis represents a valuable step towards the practical use of quantum computers and the development of better methods for optimizing computing resources.

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