Problem-Specific Basis Quantum State Readout via Proper Orthogonal Decomposition

arXiv:2605.27915 · quant-ph · Submitted 2026-05-27 · Read on arXiv

quant-ph

Submitted: 2026-05-27

Updated: 2026-09-24

Terminology

• Accuracy — 16× in this paper · explained in 1 episode
• Core — 9× in this paper · explained in 2 episodes
• Benchmark — 6× in this paper · explained in 2 episodes
• Quantum Circuits — 4× in this paper · explained in 2 episodes
• Hilbert Space — 3× in this paper · explained in 2 episodes
• Fidelity — 2× in this paper · explained in 2 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Matrix Product States (MPS) — 2× in this paper · explained in 2 episodes
• Adaptive Sampling — 1× in this paper · explained in 1 episode
• Benchmarking — 1× in this paper · explained in 3 episodes
• Chebyshev Polynomials — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Diffusion Model — 1× in this paper · explained in 8 episodes
• Diffusion Models — 1× in this paper · explained in 6 episodes
• Feature Extraction — 1× in this paper · explained in 2 episodes
• Singular Value Decomposition (SVD) — 1× in this paper · explained in 2 episodes

Sources

• Fast quantum algorithm for differential equations
• A probabilistic imaginary-time evolution quantum algorithm for advection-diffusion equation: Explicit gate-level implementation and comparisons to quantum linear system algorithms
• Quantum Computing and AI: Perspectives on Advanced Automation in Science and Engineering
• A Gateway to Quantum Computing for Industrial Engineering
• Quantum State Readout via Overlap-Based Feature Extraction
• Efficient quantum state tomography with Chebyshev polynomials
• Quantum Chebyshev Transform: Mapping, Embedding, Learning and Sampling Distributions
• PolyQROM: Orthogonal-Polynomial-Based Quantum Reduced-Order Model for Flow Field Analysis
• Fourier space readout method for efficiently recovering functions encoded in quantum states
• Real and Fourier space readout methods: Comparison of complexity and applications to CFD problems
• Benchmarking Autoregressive Conditional Diffusion Models for Turbulent Flow Simulation
• Learning to Control PDEs with Differentiable Physics
• Quantum computing with Qiskit
• Tensor Train Multiplication
• A Quantum Inspired Approach to Exploit Turbulence Structures

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity