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Quantum Generative Diffusion Model: A Fully Quantum-Mechanical Model for Generating Quantum State Ensemble
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Classical diffusion models have shown superior generative results. Exploring them in the quantum domain can advance the field of quantum generative learning. This work introduces Quantum Generative Diffusion Model (QGDM) as their simple and elegant quantum counterpart. Through a non-unitary forward process, any target quantum state can be transformed into a completely mixed state that has the highest entropy and maximum uncertainty about the system. A trainable backward process is used to recover the former from the latter. The design requirements for its backward process includes non-unitarity and small parameter count. We introduce partial trace operations to enforce non-unitary and reduce the number of trainable parameters by using a parameter-sharing strategy and incorporating temporal information as an input in the backward process. We present QGDM's resource-efficient version to reduce auxiliary qubits while preserving generative capabilities. QGDM exhibits faster convergence than Quantum Generative Adversarial Network (QGAN) because its adopted convex-based optimization can result in better convergence. The results of comparing it with QGAN demonstrate its effectiveness in generating both pure and mixed quantum states. It can achieve 53.02% higher fidelity in mixed-state generation than QGAN. The results highlight its great potential to tackle challenging quantum generation tasks.
Forward citations
Cited by 8 Pith papers
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Generating quantum ensembles via reverse-time quantum diffusions
The paper establishes a reverse-time quantum diffusion framework that generates complex quantum ensembles from simple distributions by deriving and learning a feedback Hamiltonian from forward trajectory data.
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Intrinsic Flow Matching on Quantum Pure-State Manifolds with Phase-Aligned Transport
IFM learns deterministic tangent velocity fields on CP^{d-1} via Pancharatnam phase-aligned paths, recovering marginal transport with endpoint and stability guarantees while showing empirical gains over Euclidean flow...
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Photonic-Implemented Efficient Deep Quantum Neural Network via Virtual-Driven Hilbert Space Expansion
A deep photonic QNN achieves nonlinear operations via virtual Hilbert space expansion on a linear chip with four entanglement sources, demonstrated on classification, generation, and state preparation tasks.
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Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold
SSDMs realize Riemannian diffusion on CP^{d-1} via a stochastic Schrödinger equation forward process and train the reverse process with a local Euclidean Ornstein-Uhlenbeck approximation to the Riemannian score.
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Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold
SSDMs introduce an intrinsic score-based diffusion framework on the Fubini-Study manifold to sample quantum pure-state ensembles without classical re-preparation.
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Measurement-Based Quantum Diffusion Models
Measurement-based quantum diffusion models are introduced to recover pure and mixed quantum states via weak measurements, quantum score matching, and Petz recovery maps with error bounds, bridging to classical stochas...
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Local-Time Riemannian Score Matching on the Quantum Pure-State Manifold
Score-based diffusion built intrinsically on the quantum pure-state manifold CP^{d-1}, trained with a local-time Gaussian teacher, matches pure-state ensembles far better than Euclidean baselines in the local-cluster ...
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Quantum Reversibility Meets Classical Reverse Diffusion
The semiclassical limit of the Petz-reversed Lindblad equation reproduces the Bayes-rule reverse-time diffusion equation, with the reference state's Wigner function playing the role of the classical score distribution.
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