arXiv subjects

Ming-Yang Tan

Publications and source records attributed to Ming-Yang Tan.

5 recordsLinked to original sources

arXiv2026

oracq: A Modular Framework for Implementing and Analyzing Quantum Scientific Computing Algorithms

Quantum algorithms for scientific computing are specified against access models such as block-encodings, sparse oracles, state preparations, and quantum random-access memories. Their concrete realization is deliberately left open, yet it is a research variable that changes both the numerical behavior and the resource cost of the program, so every reported conclusion is attributable to one realization. In this paper, we present oracq, a Python framework that makes this choice a managed and checkable decision. Our claim is linguistic rather than infrastructural. Algorithms are stored as persistent register-level programs whose oracle slots are declared and typed but unimplemented. A separate binding pass links compatible realizations, so one stored algorithm can be re-bound to a gate network, a QRAM-backed table, or compiled reversible arithmetic and compared across them. Typed QRAM resources, a compiler from pure Python numerical formulas to reversible fixed-point circuits, and block-encoding algebra with qubitization and QSVT-style kernels supply the constructions. Two end-to-end workflows exercise the framework, a quantum finite-volume pipeline for the compressible Euler equations and a quantum homotopy-analysis pipeline that lifts nonlinear PDEs to composable linear input models. The verification methodology separates implementation error from method error, and logical resource accounts cover programs before and after binding. The framework is openly available at https://github.com/IAI-USTC-Quantum/oracq.

quant-ph↗

arXiv2026

Classical simulation of amplitude-damped bucket-brigade quantum random access memories via predictable branch evolution

Classical simulation of quantum random access memory (QRAM) under noise can be accelerated dramatically by branch pruning: noise histories are sampled as trajectory ensembles, and good branches, whose routing paths avoid every sampled fault, need not be evolved because their final states are analytically predictable. Under amplitude damping this predictability is not automatic, because the no-jump operator $K_0$ acts on every branch at every time slice. Here we give a complete account of damping-channel predictability in bucket-brigade QRAM simulation, for both qutrit and qubit encodings. For the qutrit encoding, $K_0$ is diagonal in the node basis, and the wait state $|W\rangle$ is its fixed point, so a good branch follows the noiseless orbit up to a scalar attenuation. In the qubit encoding, phase-kickback memory fetching between two Hadamard walls makes $K_0$ no longer diagonal, yet the resulting structure is exactly solvable in closed form. Conditional on no jump, the in-branch infidelity of a good branch is second order in the damping rate $γ$, with coherent leakage $\sim n^2γ^2/4$ per data qubit, and the closed form captures it without approximation. We also revise the pruning criterion for the qubit encoding. The resulting algorithm evolves only the bad branches plus one reference branch and shares every other cost with the full evolution it replaces. It is validated by end-to-end benchmarks with pruned-over-full speedups up to $285\times$ and by trajectory-level tests confirming every closed form to machine precision.

quant-ph↗

arXiv2025

Quantum homotopy analysis method with quantum-compatible linearization for nonlinear partial differential equations

Nonlinear partial differential equations (PDEs) are crucial for modeling complex fluid dynamics and are foundational to many computational fluid dynamics (CFD) applications. However, solving these nonlinear PDEs is challenging due to the vast computational resources they demand, highlighting the pressing need for more efficient computational methods. Quantum computing offers a promising but technically challenging approach to solving nonlinear PDEs. Recently, Liao proposed a framework that leverages quantum computing to accelerate the solution of nonlinear PDEs based on the homotopy analysis method (HAM), a semi-analytical technique that transforms nonlinear PDEs into a series of linear PDEs. However, the no-cloning theorem in quantum computing poses a major limitation, where directly applying quantum simulation to each HAM step results in exponential complexity growth with the HAM truncation order. This study introduces a ``quantum-compatible linearization'' approach that maps the whole HAM process into a system of linear PDEs, allowing for a one-time solution using established quantum PDE solvers. Our method preserves the exponential speedup of quantum linear PDE solvers while ensuring that computational complexity increases only polynomially with the HAM truncation order. We demonstrate the efficacy of our approach by applying it to the Burgers' equation and the Korteweg-de Vries (KdV) equation. Our approach provides a novel pathway for transforming nonlinear PDEs into linear PDEs, with potential applications to fluid dynamics. This work thus lays the foundation for developing quantum algorithms capable of solving the Navier-Stokes equations, ultimately offering a promising route to accelerate their solutions using quantum computing.

quant-ph↗

arXiv2025

A Pathway to Practical Quantum Advantage in Solving Navier-Stokes Equations

The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity. Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation. Our approach integrates a spectral-based input/output algorithm, an explicit and synthesized quantum circuit, and a refined error-correction protocol. The algorithm achieves an end-to-end exponential speedup in asymptotic complexity, meeting the lower bound for general quantum linear system solvers. Through symmetry-based circuit synthesis and optimized error correction, we reduce the required logical and physical resources by two orders of magnitude. Our concrete resource analysis demonstrates that solving NSE on a $2^{80}$-grid is feasible with 8.71 million physical qubits (at an error rate of $5 \times 10^{-4}$) in 42.6 days -- outperforming a state-of-the-art supercomputer, which would require over a century. This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing.

quant-ph↗

arXiv2024

Enabling Large-Scale and High-Precision Fluid Simulations on Near-Term Quantum Computers

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method "Iterative-QLS" that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than $0.2\%$, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum-classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.

physics.comp-ph↗