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Researcher profile

Yuri Alexeev

Yuri Alexeev contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
quant-phData Structures and AlgorithmsMachine Learningphysics.chem-phArtificial Intelligencecond-mat.othercond-mat.str-elhep-lathep-thmath-phmath.MPMathematical Softwarenucl-thphysics.comp-phq-fin.CPSymbolic Computation

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Published work

18 published item(s)

preprint2026arXiv

SCALAR: A Neurosymbolic Framework for Automated Conjecture and Reasoning in Quantum Circuit Analysis

In this paper, we present SCALAR (Symbolic Conjecture and LLM-Assisted Reasoning), a neurosymbolic framework for automated conjecture generation in quantum circuit analysis built on top of the CUDA-Q open source framework. The system integrates quantum simulation, symbolic conjecture generation, and LLM-based interpretation. We evaluate SCALAR on 82 MaxCut instances from the MQLib benchmark dataset and extend the analysis to 2,000 randomly generated graphs across four topologies: regular, Erdos-Renyi, Barabasi-Albert, and Watts-Strogatz. The framework generates conjectured bounds relating optimal QAOA parameters to graph invariants, including known relationships such as periodicity constraints on the phase separation parameter $γ$. SCALAR also recovers previously reported parameter transfer phenomena across structurally similar instances. Additionally, the system identifies correlations between graph structural features and optimization landscape properties, which we characterize through invariant-based descriptors. Using CUDA-Q tensor network simulator, we scale experiments to instances of up to 77 qubits. We discuss the accuracy, generality, and limitations of the generated conjectures, including sensitivity to graph class and quantum circuit depth.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

A Survey of Quantum Computing for Finance

Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems, such as derivative pricing, risk modeling, portfolio optimization, natural language processing, and fraud detection, more efficiently and accurately. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Constructing Optimal Contraction Trees for Tensor Network Quantum Circuit Simulation

One of the key problems in tensor network based quantum circuit simulation is the construction of a contraction tree which minimizes the cost of the simulation, where the cost can be expressed in the number of operations as a proxy for the simulation running time. This same problem arises in a variety of application areas, such as combinatorial scientific computing, marginalization in probabilistic graphical models, and solving constraint satisfaction problems. In this paper, we reduce the computationally hard portion of this problem to one of graph linear ordering, and demonstrate how existing approaches in this area can be utilized to achieve results up to several orders of magnitude better than existing state of the art methods for the same running time. To do so, we introduce a novel polynomial time algorithm for constructing an optimal contraction tree from a given order. Furthermore, we introduce a fast and high quality linear ordering solver, and demonstrate its applicability as a heuristic for providing orderings for contraction trees. Finally, we compare our solver with competing methods for constructing contraction trees in quantum circuit simulation on a collection of randomly generated Quantum Approximate Optimization Algorithm Max Cut circuits and show that our method achieves superior results on a majority of tested quantum circuits. Reproducibility: Our source code and data are available at https://github.com/cameton/HPEC2022_ContractionTrees.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers

Combinatorial optimization on near-term quantum devices is a promising path to demonstrating quantum advantage. However, the capabilities of these devices are constrained by high noise or error rates. In this paper, we propose an iterative Layer VQE (L-VQE) approach, inspired by the Variational Quantum Eigensolver (VQE). We present a large-scale numerical study, simulating circuits with up to 40 qubits and 352 parameters, that demonstrates the potential of the proposed approach. We evaluate quantum optimization heuristics on the problem of detecting multiple communities in networks, for which we introduce a novel qubit-frugal formulation. We numerically compare L-VQE with Quantum Approximate Optimization Algorithm (QAOA) and demonstrate that QAOA achieves lower approximation ratios while requiring significantly deeper circuits. We show that L-VQE is more robust to finite sampling errors and has a higher chance of finding the solution as compared with standard VQE approaches. Our simulation results show that L-VQE performs well under realistic hardware noise.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Localized Quantum Chemistry on Quantum Computers

Quantum chemistry calculations of large, strongly correlated systems are typically limited by the computation cost that scales exponentially with the size of the system. Quantum algorithms, designed specifically for quantum computers, can alleviate this, but the resources required are still too large for today's quantum devices. Here we present a quantum algorithm that combines a localization of multireference wave functions of chemical systems with quantum phase estimation (QPE) and variational unitary coupled cluster singles and doubles (UCCSD) to compute their ground state energy. Our algorithm, termed "local active space unitary coupled cluster" (LAS-UCC), scales linearly with system size for certain geometries, providing a polynomial reduction in the total number of gates compared with QPE, while providing accuracy above that of the variational quantum eigensolver using the UCCSD ansatz and also above that of the classical local active space self-consistent field. The accuracy of LAS-UCC is demonstrated by dissociating (H$_2$)$_2$ into two H$_2$ molecules and by breaking the two double bonds in trans-butadiene and resources estimates are provided for linear chains of up to 20 H$_2$ molecules.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Performance Evaluation and Acceleration of the QTensor Quantum Circuit Simulator on GPUs

This work studies the porting and optimization of the tensor network simulator QTensor on GPUs, with the ultimate goal of simulating quantum circuits efficiently at scale on large GPU supercomputers. We implement NumPy, PyTorch, and CuPy backends and benchmark the codes to find the optimal allocation of tensor simulations to either a CPU or a GPU. We also present a dynamic mixed backend to achieve optimal performance. To demonstrate the performance, we simulate QAOA circuits for computing the MaxCut energy expectation. Our method achieves $176\times$ speedup on a GPU over the NumPy baseline on a CPU for the benchmarked QAOA circuits to solve MaxCut problem on a 3-regular graph of size 30 with depth $p=4$.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

QuYBE -- An Algebraic Compiler for Quantum Circuit Compression

QuYBE is an open-source algebraic compiler for the compression of quantum circuits. It has been applied for the efficient simulation of the Heisenberg Hamiltonian on quantum computers. Currently, it can simulate the time dynamics of one-dimensional chains. It includes modules to generate the quantum circuits for the above as well as produce the compressed circuits, which are independent of the time step. It utilizes the Yang-Baxter equation (YBE) to perform the compression. QuYBE enables users to seamlessly design, execute, and analyze the time dynamics of the Heisenberg Hamiltonian on quantum computers. QuYBE is the first step toward making the YBE technique available to a broader community of scientists from multiple domains. The QuYBE compiler is available at https://github.com/ZichangHe/QuYBE

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Tensor Network Quantum Simulator With Step-Dependent Parallelization

In this work, we present a new large-scale quantum circuit simulator. It is based on the tensor network contraction technique to represent quantum circuits. We propose a novel parallelization algorithm based on \stepslice . In this paper, we push the requirement on the size of a quantum computer that will be needed to demonstrate the advantage of quantum computation with Quantum Approximate Optimization Algorithm (QAOA). We computed 210 qubit QAOA circuits with 1,785 gates on 1,024 nodes of the the Cray XC 40 supercomputer Theta. To the best of our knowledge, this constitutes the largest QAOA quantum circuit simulations reported to this date.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Unitary Selective Coupled-Cluster Method

Simulating molecules using the Variational Quantum Eigensolver method is one of the promising applications for NISQ-era quantum computers. Designing an efficient ansatz to represent the electronic wave function is crucial in such simulations. Standard unitary coupled-cluster with singles and doubles (UCCSD) ansatz tends to have a large number of insignificant terms that do not lower the energy of the system. In this work, we present a unitary selective coupled-cluster method, a way to construct a unitary coupled-cluster ansatz iteratively using a selection procedure with excitations up to fourth order. This approach uses the electronic Hamiltonian matrix elements and the amplitudes for excitations already present in the ansatz to find the important excitations of higher order and to add them to the ansatz. The important feature of the method is that it systematically reduces the energy error with increasing ansatz size for a set of test molecules. The main advantage of the proposed method is that the effort to increase the ansatz does not require any additional measurements on a quantum computer.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Quantum time dynamics of 1D-Heisenberg models employing the Yang-Baxter equation for circuit compression

Quantum time dynamics (QTD) is considered a promising problem for quantum supremacy on near-term quantum computers. However, QTD quantum circuits grow with increasing time simulations. This study focuses on simulating the time dynamics of 1-D integrable spin chains with nearest neighbor interactions. We show how the quantum Yang-Baxter equation can be exploited to compress and produce a shallow quantum circuit. With this compression scheme, the depth of the quantum circuit becomes independent of step size and only depends on the number of spins. We show that the compressed circuit scales quadratically with system size, which allows for the simulations of time dynamics of very large 1-D spin chains. We derive the compressed circuit representations for different special cases of the Heisenberg Hamiltonian. We compare and demonstrate the effectiveness of this approach by performing simulations on quantum computers.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Full-State Quantum Circuit Simulation by Using Data Compression

Quantum circuit simulations are critical for evaluating quantum algorithms and machines. However, the number of state amplitudes required for full simulation increases exponentially with the number of qubits. In this study, we leverage data compression to reduce memory requirements, trading computation time and fidelity for memory space. Specifically, we develop a hybrid solution by combining the lossless compression and our tailored lossy compression method with adaptive error bounds at each timestep of the simulation. Our approach optimizes for compression speed and makes sure that errors due to lossy compression are uncorrelated, an important property for comparing simulation output with physical machines. Experiments show that our approach reduces the memory requirement of simulating the 61-qubit Grover's search algorithm from 32 exabytes to 768 terabytes of memory on Argonne's Theta supercomputer using 4,096 nodes. The results suggest that our techniques can increase the simulation size by 2 to 16 qubits for general quantum circuits.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Multilevel Combinatorial Optimization Across Quantum Architectures

Emerging quantum processors provide an opportunity to explore new approaches for solving traditional problems in the post Moore's law supercomputing era. However, the limited number of qubits makes it infeasible to tackle massive real-world datasets directly in the near future, leading to new challenges in utilizing these quantum processors for practical purposes. Hybrid quantum-classical algorithms that leverage both quantum and classical types of devices are considered as one of the main strategies to apply quantum computing to large-scale problems. In this paper, we advocate the use of multilevel frameworks for combinatorial optimization as a promising general paradigm for designing hybrid quantum-classical algorithms. In order to demonstrate this approach, we apply this method to two well-known combinatorial optimization problems, namely, the Graph Partitioning Problem, and the Community Detection Problem. We develop hybrid multilevel solvers with quantum local search on D-Wave's quantum annealer and IBM's gate-model based quantum processor. We carry out experiments on graphs that are orders of magnitudes larger than the current quantum hardware size, and we observe results comparable to state-of-the-art solvers in terms of quality of the solution.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quantum Computer Systems for Scientific Discovery

The great promise of quantum computers comes with the dual challenges of building them and finding their useful applications. We argue that these two challenges should be considered together, by co-designing full-stack quantum computer systems along with their applications in order to hasten their development and potential for scientific discovery. In this context, we identify scientific and community needs, opportunities, a sampling of a few use case studies, and significant challenges for the development of quantum computers for science over the next 2--10 years. This document is written by a community of university, national laboratory, and industrial researchers in the field of Quantum Information Science and Technology, and is based on a summary from a U.S. National Science Foundation workshop on Quantum Computing held on October 21--22, 2019 in Alexandria, VA.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quantum Divide and Compute: Hardware Demonstrations and Noisy Simulations

Noisy, intermediate-scale quantum computers come with intrinsic limitations in terms of the number of qubits (circuit "width") and decoherence time (circuit "depth") they can have. Here, for the first time, we demonstrate a recently introduced method that breaks a circuit into smaller subcircuits or fragments, and thus makes it possible to run circuits that are either too wide or too deep for a given quantum processor. We investigate the behavior of the method on one of IBM's 20-qubit superconducting quantum processors with various numbers of qubits and fragments. We build noise models that capture decoherence, readout error, and gate imperfections for this particular processor. We then carry out noisy simulations of the method in order to account for the observed experimental results. We find an agreement within 20% between the experimental and the simulated success probabilities, and we observe that recombining noisy fragments yields overall results that can outperform the results without fragmentation.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Evaluating Quantum Approximate Optimization Algorithm: A Case Study

Quantum Approximate Optimization Algorithm (QAOA) is one of the most promising quantum algorithms for the Noisy Intermediate-Scale Quantum (NISQ) era. Quantifying the performance of QAOA in the near-term regime is of utmost importance. We perform a large-scale numerical study of the approximation ratios attainable by QAOA is the low- to medium-depth regime. To find good QAOA parameters we perform 990 million 10-qubit QAOA circuit evaluations. We find that the approximation ratio increases only marginally as the depth is increased, and the gains are offset by the increasing complexity of optimizing variational parameters. We observe a high variation in approximation ratios attained by QAOA, including high variations within the same class of problem instances. We observe that the difference in approximation ratios between problem instances increases as the similarity between instances decreases. We find that optimal QAOA parameters concentrate for instances in out benchmark, confirming the previous findings for a different class of problems.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Learning to Optimize Variational Quantum Circuits to Solve Combinatorial Problems

Quantum computing is a computational paradigm with the potential to outperform classical methods for a variety of problems. Proposed recently, the Quantum Approximate Optimization Algorithm (QAOA) is considered as one of the leading candidates for demonstrating quantum advantage in the near term. QAOA is a variational hybrid quantum-classical algorithm for approximately solving combinatorial optimization problems. The quality of the solution obtained by QAOA for a given problem instance depends on the performance of the classical optimizer used to optimize the variational parameters. In this paper, we formulate the problem of finding optimal QAOA parameters as a learning task in which the knowledge gained from solving training instances can be leveraged to find high-quality solutions for unseen test instances. To this end, we develop two machine-learning-based approaches. Our first approach adopts a reinforcement learning (RL) framework to learn a policy network to optimize QAOA circuits. Our second approach adopts a kernel density estimation (KDE) technique to learn a generative model of optimal QAOA parameters. In both approaches, the training procedure is performed on small-sized problem instances that can be simulated on a classical computer; yet the learned RL policy and the generative model can be used to efficiently solve larger problems. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our proposed RL- and KDE-based approaches reduce the optimality gap by factors up to 30.15 when compared with other commonly used off-the-shelf optimizers.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Network Community Detection On Small Quantum Computers

In recent years a number of quantum computing devices with small numbers of qubits became available. We present a hybrid quantum local search (QLS) approach that combines a classical machine and a small quantum device to solve problems of practical size. The proposed approach is applied to the network community detection problem. QLS is hardware-agnostic and easily extendable to new quantum computing devices as they become available. We demonstrate it to solve the 2-community detection problem on graphs of size up to 410 vertices using the 16-qubit IBM quantum computer and D-Wave 2000Q, and compare their performance with the optimal solutions. Our results demonstrate that QLS perform similarly in terms of quality of the solution and the number of iterations to convergence on both types of quantum computers and it is capable of achieving results comparable to state-of-the-art solvers in terms of quality of the solution including reaching the optimal solutions.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Reinforcement-Learning-Based Variational Quantum Circuits Optimization for Combinatorial Problems

Quantum computing exploits basic quantum phenomena such as state superposition and entanglement to perform computations. The Quantum Approximate Optimization Algorithm (QAOA) is arguably one of the leading quantum algorithms that can outperform classical state-of-the-art methods in the near term. QAOA is a hybrid quantum-classical algorithm that combines a parameterized quantum state evolution with a classical optimization routine to approximately solve combinatorial problems. The quality of the solution obtained by QAOA within a fixed budget of calls to the quantum computer depends on the performance of the classical optimization routine used to optimize the variational parameters. In this work, we propose an approach based on reinforcement learning (RL) to train a policy network that can be used to quickly find high-quality variational parameters for unseen combinatorial problem instances. The RL agent is trained on small problem instances which can be simulated on a classical computer, yet the learned RL policy is generalizable and can be used to efficiently solve larger instances. Extensive simulations using the IBM Qiskit Aer quantum circuit simulator demonstrate that our trained RL policy can reduce the optimality gap by a factor up to 8.61 compared with other off-the-shelf optimizers tested.

0 citations0 reviewsNo code linkedOpen access