Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

IEEE Transactions on Electron Devices

A Quantum-Computing-Based Method for Solving Quantum Confinement Problem in Semiconductor

Ning Yang, Jing Hua Guo

Published Jan 11, 2023• 10 citations
Publisher

Abstract

Technology computer-aided design (TCAD) of semiconductor devices relies on the numerical solution of differential equations in devices. Recent advances in quantum computing provide a new opportunity for TCAD simulations to be performed on a quantum computer. Based on a variational quantum algorithm, we develop a quantum-computing-based method to solve quantum confinement problems in semiconductor nanostructures. As the number of numerical discretization grid points for solving the Schrödinger equation increases, the number of qubits needed scales only logarithmically, ~${O}[\log(N)]$. The method is applied to solve quantum confinement problems at all dimensions, which are related to confinement in a quantum well, semiconductor nanowire, and semiconductor quantum dot structures. The method can treat an anisotropic band structure and electrostatic potential in semiconductor nanostructures. We further show that the design of ansatz plays an important role in the performance of the method in terms of solution accuracy. The quantum-computing-based method can compute the energies and wave functions of both the ground and excited states with high accuracy.

DOI
10.1109/ted.2023.3234887

Related papers

Variational Quantum Linear Solver for Simulating Quantum Transport in Nanoscale Semiconductor Devices

Qimao Yang, Jing Hua Guo

This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor device simulations focuses on solving the Poisson equation, where the coefficient matrix of the sparse linear system is real and symmetric. Solving the quantum transport equation, however, leads to coefficient matrices that are complex and non-symmetric. This work addresses the challenges of applying VQLS to quantum transport simulations. We propose new forms of cost functions to solve complex and non-symmetric linear systems with faster computing speed. We further develop efficient decomposition methods for cost function evaluation, which target reducing the quantum circuit complexity and improving noise robustness when solving the quantum transport equation using the nonequilibrium Green's function method. While classical computation faces the challenge of the “curse of dimensionality” as the spatial-energy numerical grid dimensions grow, the proposed quantum-computing-based method scales logarithmically with the grid size, which offers a promising opportunity for addressing the computational challenges of solving quantum transport in semiconductor devices.

arXiv:2509.07005•IEEE International Conference on Quantum Computing and Engineering (QCE)•Aug 30, 2025•0 citations

Variational Quantum Algorithm for Solving Quantum Transport Equation in Semiconductor Device

Qimao Yang, Jing Hua Guo

As semiconductor feature sizes continue to shrink, accurate and efficient simulations of quantum transport become increasingly critical in device design and manufacturing. The nonequilibrium Green’s function (NEGF) formalism is a widely used method for simulating quantum transport in semiconductor devices, but it is computationally demanding. Quantum computing offers a promising solution, in this work, we pioneer the application of the variational quantum linear solver (VQLS) to the NEGF problem, addressing the challenges associated with handling complex numbers inherent in quantum transport equations. We introduce a new cost function tailored to this framework, demonstrating improved performance over existing approaches. Furthermore, we show that VQLS can efficiently parallelize the computation across different energy levels, significantly reducing computational costs. Our results highlight the potential of variational quantum algorithms (VQAs) in enhancing the scalability and efficiency of quantum transport simulations.

IEEE Transactions on Electron Devices•Apr 18, 2025•1 citation

Quantum variational solving of nonlinear and multidimensional partial differential equations

Abhijat Sarma, Thomas W. Watts, Mudassir Moosa +2 more

A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. [Phys. Rev. A 101, 010301(R) (2020)]. In this paper we generalize the method introduced by Lubasch et al. to cover a broader class of nonlinear PDEs as well as multidimensional PDEs and study the performance of the variational quantum algorithm on several example equations. Specifically, we show via numerical simulations that the algorithm can solve instances of the single-asset Black-Scholes equation with a nontrivial nonlinear volatility model, the double-asset Black-Scholes equation, the Buckmaster equation, and the deterministic Kardar-Parisi-Zhang equation. Our simulations use up to $n=12$ Ansatz qubits, computing PDE solutions with ${2}^{n}$ grid points. We also perform proof-of-concept demonstrations with a trapped-ion quantum processor from IonQ [Nat. Commun. 10, 5464 (2019)], showing accurate computation of two representative expectation values needed for the calculation of a single time step of the nonlinear Black-Scholes equation. Through our classical simulations and demonstrations on quantum hardware, we identify and discuss several open challenges for using quantum variational methods to solve PDEs in a regime with a large number (much greater than ${2}^{20}$) of grid points, but also a practical number of gates per circuit and circuit shots.

arXiv:2311.01531•Physical Review A•Jun 21, 2024•38 citations

DEVELOPMENT OF ALGORITHMS AND SIMULATIONS FOR QUANTUM COMPUTERS AND THEIR POTENTIAL APPLICATIONS IN SOLVING QUANTUM PROBLEMS

K. Sabeeh, Gul Rahman

Quantum computing has emerged as a transformative paradigm capable of solving complex computational problems that are intractable for classical computers. Central to the advancement of this technology is the development of efficient quantum algorithms and high fidelity simulations that enable the design, testing, and optimization of quantum solutions before deployment on physical hardware. This study focuses on the design and implementation of quantum algorithms tailored for solving a variety of quantum problems, including quantum chemistry, optimization, and cryptography. Using state of the art simulation platforms such as Qiskit, Cirq, and Pennylane, algorithm performance was evaluated in terms of accuracy, execution time, scalability, and resilience to noise. Benchmarks demonstrate that algorithms such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) achieve significant speedups in problem specific domains, while hybrid quantum–classical methods provide robust pathways for near term quantum advantage. Simulation results reveal that algorithmic efficiency can be significantly improved through optimized circuit depth, qubit connectivity mapping, and advanced error mitigation techniques. The findings highlight the potential of simulation driven quantum algorithm development in accelerating the practical realization of quantum computing applications across disciplines such as materials discovery, molecular modeling, secure communications, and complex optimization tasks.

•Dec 1, 2025•0 citations

Quantum topology optimization of ground structures for near-term devices

Yuki Sato, Ruho Kondo, Satoshi Koide +1 more

Product development processes frequently use numerical simulations and mathematical programming techniques. Structural optimization, especially topology optimization, is one of the most promising techniques for generating insightful design choices. Topology optimization for discrete structures, such as truss structures, can be formulated as a combinatorial optimization problem, where the combination of the existence or absence of the material is optimized. In this study, we examine the usage of quantum computers as a potential solution to discrete topology optimization problems. The proposed method consists of two variational quantum algorithms (VQAs); the first solves the state equilibrium equation for all possible structures, and the second amplifies the probability of the optimal structure in quantum superposition. Several experiments, including a real device experiment, show that the proposed method successfully obtained the optimal structure. These findings suggest that quantum computers could be a potential tool for solving topology optimization problems.

arXiv:2207.09181•IEEE International Conference on Quantum Computing and Engineering (QCE)•Sep 17, 2023•11 citations

Depth analysis of variational quantum algorithms for the heat equation

Nikita Guseynov, Andrei A. Zhukov, W. V. Pogosov +1 more

Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution is finite-difference schemes, which can be reduced to the linear algebra problem. We consider three approaches to solve the heat equation on a quantum computer. Using the direct variational method we minimize the expectation value of a Hamiltonian with its ground state being the solution of the problem under study. Typically, an exponential number of Pauli products in the Hamiltonian decomposition does not allow for the quantum speedup to be achieved. The Hadamard-test-based approach solves this problem, however, the performed simulations do not evidently prove that the Ansatz circuit has a polynomial depth with respect to the number of qubits. The Ansatz tree approach exploits an explicit form of the matrix that makes it possible to achieve an advantage over classical algorithms. In our numerical simulations with up to $n=11$ qubits, this method reveals the exponential speedup.

arXiv:2212.12375•Physical Review A•May 26, 2023•19 citations
Technology computer-aided design (TCAD) of semiconductor devices relies on the numerical solution of differential equations in devices. Recent advances in quantum computing provide a new opportunity for TCAD simulations to be performed on a quantum computer. Based on a variational quantum algorithm, we develop a quantum-computing-based method to solve quantum confinement problems in semiconductor nanostructures. As the number of numerical discretization grid points for solving the Schrödinger equation increases, the number of qubits needed scales only logarithmically, ~O[log⁡(N)]{O}[\log(N)]O[log(N)]. The method is applied to solve quantum confinement problems at all dimensions, which are related to confinement in a quantum well, semiconductor nanowire, and semiconductor quantum dot structures. The method can treat an anisotropic band structure and electrostatic potential in semiconductor nanostructures. We further show that the design of ansatz plays an important role in the performance of the method in terms of solution accuracy. The quantum-computing-based method can compute the energies and wave functions of both the ground and excited states with high accuracy.
This work develops simulation methods that enable the application of the variational quantum linear solver (VQLS) to simulate quantum transport in nanoscale semiconductor devices. Most previous work on VQLS applications in semiconductor device simulations focuses on solving the Poisson equation, where the coefficient matrix of the sparse linear system is real and symmetric. Solving the quantum transport equation, however, leads to coefficient matrices that are complex and non-symmetric. This work addresses the challenges of applying VQLS to quantum transport simulations. We propose new forms of cost functions to solve complex and non-symmetric linear systems with faster computing speed. We further develop efficient decomposition methods for cost function evaluation, which target reducing the quantum circuit complexity and improving noise robustness when solving the quantum transport equation using the nonequilibrium Green's function method. While classical computation faces the challenge of the “curse of dimensionality” as the spatial-energy numerical grid dimensions grow, the proposed quantum-computing-based method scales logarithmically with the grid size, which offers a promising opportunity for addressing the computational challenges of solving quantum transport in semiconductor devices.
As semiconductor feature sizes continue to shrink, accurate and efficient simulations of quantum transport become increasingly critical in device design and manufacturing. The nonequilibrium Green’s function (NEGF) formalism is a widely used method for simulating quantum transport in semiconductor devices, but it is computationally demanding. Quantum computing offers a promising solution, in this work, we pioneer the application of the variational quantum linear solver (VQLS) to the NEGF problem, addressing the challenges associated with handling complex numbers inherent in quantum transport equations. We introduce a new cost function tailored to this framework, demonstrating improved performance over existing approaches. Furthermore, we show that VQLS can efficiently parallelize the computation across different energy levels, significantly reducing computational costs. Our results highlight the potential of variational quantum algorithms (VQAs) in enhancing the scalability and efficiency of quantum transport simulations.
A variational quantum algorithm for numerically solving partial differential equations (PDEs) on a quantum computer was proposed by Lubasch et al. [Phys. Rev. A 101, 010301(R) (2020)]. In this paper we generalize the method introduced by Lubasch et al. to cover a broader class of nonlinear PDEs as well as multidimensional PDEs and study the performance of the variational quantum algorithm on several example equations. Specifically, we show via numerical simulations that the algorithm can solve instances of the single-asset Black-Scholes equation with a nontrivial nonlinear volatility model, the double-asset Black-Scholes equation, the Buckmaster equation, and the deterministic Kardar-Parisi-Zhang equation. Our simulations use up to n=12n=12n=12 Ansatz qubits, computing PDE solutions with 2n{2}^{n}2n grid points. We also perform proof-of-concept demonstrations with a trapped-ion quantum processor from IonQ [Nat. Commun. 10, 5464 (2019)], showing accurate computation of two representative expectation values needed for the calculation of a single time step of the nonlinear Black-Scholes equation. Through our classical simulations and demonstrations on quantum hardware, we identify and discuss several open challenges for using quantum variational methods to solve PDEs in a regime with a large number (much greater than 220{2}^{20}220) of grid points, but also a practical number of gates per circuit and circuit shots.
Quantum computing has emerged as a transformative paradigm capable of solving complex computational problems that are intractable for classical computers. Central to the advancement of this technology is the development of efficient quantum algorithms and high fidelity simulations that enable the design, testing, and optimization of quantum solutions before deployment on physical hardware. This study focuses on the design and implementation of quantum algorithms tailored for solving a variety of quantum problems, including quantum chemistry, optimization, and cryptography. Using state of the art simulation platforms such as Qiskit, Cirq, and Pennylane, algorithm performance was evaluated in terms of accuracy, execution time, scalability, and resilience to noise. Benchmarks demonstrate that algorithms such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA) achieve significant speedups in problem specific domains, while hybrid quantum–classical methods provide robust pathways for near term quantum advantage. Simulation results reveal that algorithmic efficiency can be significantly improved through optimized circuit depth, qubit connectivity mapping, and advanced error mitigation techniques. The findings highlight the potential of simulation driven quantum algorithm development in accelerating the practical realization of quantum computing applications across disciplines such as materials discovery, molecular modeling, secure communications, and complex optimization tasks.
Product development processes frequently use numerical simulations and mathematical programming techniques. Structural optimization, especially topology optimization, is one of the most promising techniques for generating insightful design choices. Topology optimization for discrete structures, such as truss structures, can be formulated as a combinatorial optimization problem, where the combination of the existence or absence of the material is optimized. In this study, we examine the usage of quantum computers as a potential solution to discrete topology optimization problems. The proposed method consists of two variational quantum algorithms (VQAs); the first solves the state equilibrium equation for all possible structures, and the second amplifies the probability of the optimal structure in quantum superposition. Several experiments, including a real device experiment, show that the proposed method successfully obtained the optimal structure. These findings suggest that quantum computers could be a potential tool for solving topology optimization problems.
Variational quantum algorithms are a promising tool for solving partial differential equations. The standard approach for its numerical solution is finite-difference schemes, which can be reduced to the linear algebra problem. We consider three approaches to solve the heat equation on a quantum computer. Using the direct variational method we minimize the expectation value of a Hamiltonian with its ground state being the solution of the problem under study. Typically, an exponential number of Pauli products in the Hamiltonian decomposition does not allow for the quantum speedup to be achieved. The Hadamard-test-based approach solves this problem, however, the performed simulations do not evidently prove that the Ansatz circuit has a polynomial depth with respect to the number of qubits. The Ansatz tree approach exploits an explicit form of the matrix that makes it possible to achieve an advantage over classical algorithms. In our numerical simulations with up to n=11n=11n=11 qubits, this method reveals the exponential speedup.