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Intrinsic randomness under general quantum measurements
Published in ArXiv Preprint, 2022
Quantum measurements can produce randomness arising from the uncertainty principle. When measuring a state with von Neumann measurements, the intrinsic randomness can be quantified by the quantum coherence of the state on the measurement basis. Unlike projection measurements, there are additional and possibly hidden degrees of freedom in apparatus for generic measurements. We propose an adversary scenario for general measurements with arbitrary input states, based on which, we characterize the intrinsic randomness. Interestingly, we discover that under certain measurements, such as the symmetric and information-complete measurement, all states have nonzero randomness, inspiring a new design of source-independent random number generators without state characterization. Furthermore, our results show that intrinsic randomness can quantify coherence under general measurements, which generalizes the result in the standard resource theory of state coherence.
Recommended citation: Dai, H., Chen, B., Zhang, X., & Ma, X. (2022). Intrinsic randomness under general quantum measurements. arXiv preprint arXiv:2203.08624. https://arxiv.org/pdf/2203.08624.pdf
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A Convergence Theory for Over-parameterized Variational Quantum Eigensolvers
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The Variational Quantum Eigensolver (VQE) is a promising candidate for quantum applications on near-term Noisy Intermediate-Scale Quantum (NISQ) computers. Despite a lot of empirical studies and recent progress in theoretical understanding of VQE’s optimization landscape, the convergence for optimizing VQE is far less understood. We provide the first rigorous analysis of the convergence of VQEs in the over-parameterization regime. By connecting the training dynamics with the Riemannian Gradient Flow on the unit-sphere, we establish a threshold on the sufficient number of parameters for efficient convergence, which depends polynomially on the system dimension and the spectral ratio, a property of the problem Hamiltonian, and could be resilient to gradient noise to some extent. We further illustrate that this over-parameterization threshold could be vastly reduced for specific VQE instances by establishing an ansatz-dependent threshold paralleling our main result. We showcase that our ansatz-dependent threshold could serve as a proxy of the trainability of different VQE ansatzes without performing empirical experiments, which hence leads to a principled way of evaluating ansatz design. Finally, we conclude with a comprehensive empirical study that supports our theoretical findings.