arXiv subjects

Yoshifumi Kawada

Publications and source records attributed to Yoshifumi Kawada.

4 recordsLinked to original sources

arXiv2026

Problem-Specific Basis Quantum State Readout via Proper Orthogonal Decomposition

Quantum computing offers a promising approach to accelerating partial differential equation (PDE) solvers for large-scale, real-world problems. However, reconstructing the classical representation of a solution from a quantum state remains a significant computational bottleneck. We propose a problem-specific method, termed proper orthogonal decomposition-based readout (PODR), to improve this efficiency. This method comprises offline and online stages. In the offline stage, a set of basis functions capturing the dominant features of the target problem is constructed using classical computations. In the online stage, the quantum state is projected onto this reduced basis, and only a small number of coefficients is extracted to reconstruct the solution. PODR is particularly advantageous for simulations involving varying parameters, common in computational fluid dynamics (CFD), because the POD basis functions are constructed only once in the offline stage and reused during the online stage. Applying PODR to benchmark CFD problems demonstrates a significant reduction in online computational cost compared with conventional readout methods.

quant-ph↗

arXiv2025

Real and Fourier space readout methods: Comparison of complexity and applications to CFD problems

Quantum computing is a promising technology that accelerates the partial differential equations solver for practical problems. The reconstruction of solutions (i.e., the readout of quantum states) remains a crucial problem, although numerous efficient quantum algorithms have been proposed. In this paper, we propose and compare several efficient readout methods in the real and the Fourier space. The Fourier space readout (FSR) and the proposed approximate real space readout (ARSR) methods are currently the most efficient and practical ones for the purpose of reconstructing continuous real-valued functions. In contrast, the quantum amplitude estimation (QAE) based methods (especially in the Fourier space) are favorable for mid-term/far-term quantum devices. Besides, we apply the methods for benchmark solutions in computational fluid dynamics (CFD) and demonstrate great improvements compared to the conventional sampling method for large grid numbers. Equipped with efficient readout methods, we further show that a 2D Burgers' equation can be solved efficiently without using the expensive strategy of linearization. It suggests the potential quantum advantages for some practical applications on mid-term quantum devices.

quant-ph↗

arXiv2025

Fourier space readout method for efficiently recovering functions encoded in quantum states

Applying quantum computing in the computer-aided engineering (CAE) problems are highly expected since quantum computers yield potential exponential speedups for the operations between extremely large matrices and vectors. Although efficient quantum algorithms for the above problems have been intensively investigated, it remains a crucial task to extract all the grid-point values encoded in the prepared quantum states, which was believed to eliminate the achieved quantum advantage. In this paper, we propose a quantum-classical hybrid Fourier space readout (FSR) method to efficiently recover the underlying function from its corresponding quantum state. We provide explicit quantum circuits, followed by theoretical and numerical discussions on its complexity. In particular, the complexity on quantum computers has only a logarithmic dependence on the grid number, while the complexity on classical computers has a linear dependence on the number of target points instead of the grid number. Our result implies that the achieved quantum speedups are not necessarily ruined when we read out the solutions to the CAE problems.

quant-ph↗

arXiv2025

A probabilistic imaginary-time evolution quantum algorithm for advection-diffusion equation: Explicit gate-level implementation and comparisons to quantum linear system algorithms

Simulating differential equations on classical computers becomes an intractable problem if the grid size is extremely large. Quantum computers are believed to achieve a possibly exponential speedup in the matrix operation. In this paper, we propose a quantum algorithm for solving the advection-diffusion-reaction equation by employing a novel approximate probabilistic imaginary-time evolution (PITE) operator. First, the effectiveness of the proposed approximate PITE operator is justified by the theoretical evaluation of the error. Next, we construct the explicit quantum circuit to realize the imaginary-time evolution of the Hamiltonian coming from the advection-diffusion equation, whose gate complexity is logarithmic regarding the size of the discretized Hamiltonian matrix. Compared to the existing algorithms for the quantum linear system problem, our algorithm achieves an exponential speedup regarding the matrix size at the cost of a worse dependence on the error bound. Moreover, numerical simulations using gate-based quantum emulator for 1D/2D examples are also provided to verify our algorithm. Finally, we extend our algorithm to the coupled system of advection-diffusion equations to show the prospects for practical applications.

quant-ph↗