arXiv subjects

Eleftherios Mastorakis

Publications and source records attributed to Eleftherios Mastorakis.

5 recordsLinked to original sources

arXiv2026

Quantum Variational Approaches to Plasma Equilibrium: Cost Function Design for the Grad-Shafranov Equation

The solution of nonlinear partial differential equations constitutes an important application domain for variational quantum algorithms (VQAs). In this work, we extend the application of VQAs to plasma physics by solving the two-dimensional Grad-Shafranov equation, which describes the equilibrium state of a plasma fluid within the framework of ideal magnetohydrodynamics. For this problem, we develop and investigate two distinct cost function formulations and compare their performance in terms of solution fidelity, convergence speed and quantum resource requirements. Our results, obtained from noiseless simulations, show that the choice of cost function formulation significantly affects the performance of the variational algorithm. The Weak and Picard formulations exhibit complementary characteristics: the former consistently converges faster, whereas the latter achieves slightly lower final infidelities. Exploiting these complementary properties, we introduce a hybrid optimization strategy that combines the rapid initial convergence of the Weak formulation with the higher final accuracy of the Picard formulation. In addition, the two approaches display different quantum resource requirements due to their distinct implementations of boundary conditions. These results highlight the importance of cost function design in the development of efficient VQAs for nonlinear partial differential equations.

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arXiv2026

Minimum Toffoli depth for the multi-controlled Toffoli gate via teleportation

The decomposition of complex quantum operations into experimentally feasible gate sets has been a central challenge since the early development of quantum computing. The multi-controlled Toffoli (MCT) gate is a key example, with applications across a wide range of quantum algorithms, whose decomposition into smaller gates, however, typically leads to deep circuits. In this work, we introduce a teleportation-based decomposition that implements an MCT gate. This decomposition has unit Toffoli depth, independent of the number of controls, while achieving the lowest Toffoli count among existing approaches for more than five controls at the cost of a linear overhead in ancilla qubits. We also investigate the parameter regimes in which the teleportation-based decomposition is preferable by analyzing the relative quality of distributed entanglement and Toffoli gates. We further demonstrate the advantages of this implementation in circuits that rely on MCT gates, such as the adder operator, quantum read-only memory, quantum neurons, and quantum decision trees.

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arXiv2026

Resource-Efficient Hadamard Test Tailored Variational Framework for Nonlinear Dynamics on Quantum Computers

Resource-efficient, low-depth implementations of quantum circuits remain a promising strategy for achieving reliable and scalable computation on quantum hardware, as they reduce gate resources and limit the accumulation of noisy operations. Here, we propose a low-depth implementation of a class of Hadamard test circuits, complemented by the development of a parameterized quantum ansatz specifically tailored for variational algorithms that exploit the underlying Hadamard test framework. Our findings demonstrate a significant reduction in single- and two-qubit gate counts, suggesting a reliable circuit architecture for noisy intermediate-scale quantum (NISQ) devices. Building on this foundation, we tested our low-depth scheme to investigate the expressive capacity of the proposed parameterized ansatz in simulating nonlinear Burgers' dynamics. The resulting variational quantum states faithfully capture the shockwave feature of the turbulent regime and maintain high overlaps with classical benchmarks, underscoring the practical effectiveness of our framework. Furthermore, we evaluate the effect of hardware noise by modeling the error properties of real quantum processors and by executing the variational algorithm on a trapped-ion-based IBEX Q1 device. The outcomes of our demonstrations highlight the resilience of our low-depth scheme in the turbulent regime, consistently preparing high-fidelity variational states that exhibit strong agreement with classical benchmarks. Our work contributes to the advancement of resource-efficient strategies for quantum computation, offering a robust framework for tackling a range of computationally intensive problems across numerous applications.

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arXiv2024

Efficient Estimation and Sequential Optimization of Cost Functions in Variational Quantum Algorithms

Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its derivatives, coupled with their effective utilization, facilitates faster convergence by enabling smooth navigation through complex landscapes, ensuring the algorithm's success in addressing challenging variational problems. In this work, we introduce a novel optimization methodology that conceptualizes the parameterized quantum circuit as a weighted sum of distinct unitary operators, enabling the cost function to be expressed as a sum of multiple terms. This representation facilitates the efficient evaluation of nonlocal characteristics of cost functions, as well as their arbitrary derivatives. The optimization protocol then utilizes the nonlocal information on the cost function to facilitate a more efficient navigation process, ultimately enhancing the performance in the pursuit of optimal solutions. We utilize this methodology for two distinct cost functions. The first is the squared residual of the variational state relative to a target state, which is subsequently employed to examine the nonlinear dynamics of fluid configurations governed by the one-dimensional Burgers' equation. The second cost function is the expectation value of an observable, which is later utilized to approximate the ground state of the nonlinear Schrödinger equation. Our findings reveal substantial enhancements in convergence speed and accuracy relative to traditional optimization methods, even within complex, high-dimensional landscapes. Our work contributes to the advancement of optimization strategies for variational quantum algorithms, establishing a robust framework for addressing a range of computationally intensive problems across numerous applications.

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arXiv2024

Probing the limits of variational quantum algorithms for nonlinear ground states on real quantum hardware: The effects of noise

A recently proposed variational quantum algorithm has expanded the horizon of variational quantum computing to nonlinear physics and fluid dynamics. In this work, we probe the ability of such approaches to capture the ground state of the nonlinear Schrödinger equation for a range of parameters on real superconducting quantum processors. Specifically, we study the expressivity of real-amplitude, hardware-efficient ansatz to capture the ground state of this nonlinear system across various interaction regimes and implement different noise scenarios in both simulators and cloud processors. Our investigation reveals that although quantum hardware noise impairs the evaluation of the energy cost function, certain small instances of the problem consistently converge to the ground state. We test for a variety of cases on IBM Q superconducting devices and analyze the discrepancies in the energy cost function evaluation due to quantum hardware noise. These discrepancies are absent in the state fidelity estimation because of the shallow state preparation circuit. Our comprehensive analysis offers valuable insights into the practical implementation and advancement of the variational algorithms for nonlinear problems.

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