Related papers: Efficient Computation of the Quantum Rate-Distorti…
Consider the following distributed optimization scenario. A worker has access to training data that it uses to compute the gradients while a server decides when to stop iterative computation based on its target accuracy or delay…
In this paper we study the topic of signal restoration using complexity regularization, quantifying the compression bit-cost of the signal estimate. While complexity-regularized restoration is an established concept, solid practical methods…
Symmetry is an important and unifying notion in many areas of physics. In quantum mechanics, it is possible to eliminate degrees of freedom from a system by leveraging symmetry to identify the possible physical transitions. This allows us…
We present a quantum algorithm that analyzes risk more efficiently than Monte Carlo simulations traditionally used on classical computers. We employ quantum amplitude estimation to evaluate risk measures such as Value at Risk and…
Mirror descent (MD) is a powerful first-order optimization technique that subsumes several optimization algorithms including gradient descent (GD). In this work, we develop a semi-definite programming (SDP) framework to analyze the…
Decoherence and loss will limit the practicality of quantum cryptography and computing unless successful error correction techniques are developed. To this end, we have discovered a new scheme for perfectly detecting and rejecting the error…
We consider the problem of simultaneously learning to linearly combine a very large number of kernels and learn a good predictor based on the learnt kernel. When the number of kernels $d$ to be combined is very large, multiple kernel…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
In recent years, the compression of large language models (LLMs) has emerged as a key problem in facilitating LLM deployment on resource-limited devices, reducing compute costs, and mitigating the environmental footprint due to large-scale…
Quantization has proven effective in high-resolution and large-scale simulations, which benefit from bit-level memory saving. However, identifying a quantization scheme that meets the requirement of both precision and memory efficiency…
We analyse dissipation in quantum computation and its destructive impact on efficiency of quantum algorithms. Using a general model of decoherence, we study the time evolution of a quantum register of arbitrary length coupled with an…
In many quantization problems, the distortion function is given by the Euclidean metric to measure the distance of a source sample to any given reproduction point of the quantizer. We will in this work regard distortion functions, which are…
We consider the problem of multiple description scalar quantizers and describing the achievable rate-distortion tuples in that setting. We formulate it as a combinatorial optimization problem of arranging numbers in a matrix to minimize the…
It is known that quantum computers can speed up Monte Carlo simulation compared to classical counterparts. There are already some proposals of application of the quantum algorithm to practical problems, including quantitative finance. In…
In this paper, we propose Image Downscaling Assessment by Rate-Distortion (IDA-RD), a novel measure to quantitatively evaluate image downscaling algorithms. In contrast to image-based methods that measure the quality of downscaled images,…
For a Gaussian source under mean-squared error (MSE), classical transform coding is rate--distortion (RD) optimal: the Karhunen--Loeve transform (KLT) diagonalizes the covariance, reverse waterfilling allocates the bits, and scalar…
Using convex optimization, we propose entanglement-assisted quantum error correction procedures that are optimized for given noise channels. We demonstrate through numerical examples that such an optimized error correction method achieves…
We propose a random coordinate descent algorithm for optimizing a non-convex objective function subject to one linear constraint and simple bounds on the variables. Although it is common use to update only two random coordinates…
In this thesis, we investigate whether quantum algorithms can be used in the field of machine learning for both long and near term quantum computers. We will first recall the fundamentals of machine learning and quantum computing and then…
This article presents the first complete application of a quantum time-marching algorithm for simulating multidimensional linear transport phenomena with arbitrary boundaries, whereby the success probabilities are problem intrinsic. The…