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We analyze the problem of a quantum computer in a correlated environment protected from decoherence by QEC using a perturbative renormalization group approach. The scaling equation obtained reflects the competition between the dimension of…
Quantum autoencoders which aim at compressing quantum information in a low-dimensional latent space lie in the heart of automatic data compression in the field of quantum information. In this paper, we establish an upper bound of the…
Overdamped Langevin dynamics are reversible stochastic differential equations which are commonly used to sample probability measures in high-dimensional spaces, such as the ones appearing in computational statistical physics and Bayesian…
This paper concerns the reconstruction of a diffusion coefficient in an elliptic equation from knowledge of several power densities. The power density is the product of the diffusion coefficient with the square of the modulus of the…
Many trace inequalities can be expressed either as concavity/convexity theorems or as monotonicity theorems. A classic example is the joint convexity of the quantum relative entropy which is equivalent to the Data Processing Inequality. The…
This thesis focuses on the intersection of mathematical and computational optimization and quantum information. Main contributions are open-source software code: A hybrid approach mixing "traditional" nonconvex and convex methods can make…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
Upper bounds are given for the weight distribution of binary weakly self-dual codes. To get these new bounds, we introduce a novel method of utilizing unitary operations on Hilbert spaces. This method is motivated by recent progress on…
Recent advances in the efficiency and robustness of algorithms solving convex quadratically constrained quadratic programming (QCQP) problems motivate developing techniques for creating convex quadratic relaxations that, although more…
Quantum machine learning models incorporating data re-uploading circuits have garnered significant attention due to their exceptional expressivity and trainability. However, their ability to generate accurate predictions on unseen data,…
The configuration space, i.e. the Hilbert space, of compound quantum systems grows exponentially with the number of its subsystems: its dimensionality is given by the product of the dimensions of its constituents. Therefore a full quantum…
One of the key challenges in quantum machine learning is finding relevant machine learning tasks with a provable quantum advantage. A natural candidate for this is learning unknown Hamiltonian dynamics. Here, we tackle the supervised…
Quantiles are very important statistics information used to describe the distribution of datasets. Given the quantiles of a dataset, we can easily know the distribution of the dataset, which is a fundamental problem in data analysis.…
Quantum channel capacity is a fundamental quantity in order to understand how good can quantum information be transmitted or corrected when subjected to noise. However, it is generally not known how to compute such quantities, since the…
The process of state preparation, its transmission and subsequent measurement can be classically simulated through the communication of some amount of classical information. Recently, we proved that the minimal communication cost is the…
Computational methods are the most effective tools we have besides scientific experiments to explore the properties of complex biological systems. Progress is slowing because digital silicon computers have reached their limits in terms of…
A basic problem of approximation theory, the approximation of functions from the Sobolev space W_p^r([0,1]^d) in the norm of L_q([0,1]^d), is considered from the point of view of quantum computation. We determine the quantum query…
Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…
In their seminal work, Bennett et al. [IEEE Trans. Inf. Theory (2002)] showed that, with sufficient shared randomness, one noisy channel can simulate another at a rate equal to the ratio of their capacities. We establish that when coding…
The weak converse coding theorems have been proved for the quantum source and channel. The results give the lower bound for capacity of source and the upper bound for capacity of channel. The monotonicity of mutual quantum information have…