Related papers: Random Projection using Random Quantum Circuits
Supervised dimensionality reduction strategies have been of great interest. However, current supervised dimensionality reduction approaches are difficult to scale for situations characterized by large datasets given the high computational…
We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…
Wideband communication receivers often deal with the problems of detecting weak signals from distant sources received together with strong nearby interferers. When the techniques of random modulation are used in communication system…
Quantum circuit optimization - the process of transforming a quantum circuit into an equivalent one with reduced time and space requirements - is crucial for maximizing the utility of current and near-future quantum devices. While most…
Recurrent quantum models (RQMs) realize sequential quantum processes through repeated application of a unitary operation on a memory system coupled with a series of output registers. However, such models often rely on unnecessarily large…
Random data sketching (or projection) is now a classical technique enabling, for instance, approximate numerical linear algebra and machine learning algorithms with reduced computational complexity and memory. In this context, the…
The trust region method is an algorithm traditionally used in the field of derivative free optimization. The method works by iteratively constructing surrogate models (often linear or quadratic functions) to approximate the true objective…
Differential privacy has become a cornerstone in the development of privacy-preserving learning algorithms. This work addresses optimizing differentially private kernel learning within the empirical risk minimization (ERM) framework. We…
Quaternion matrices are employed successfully in many color image processing applications. In particular, a pure quaternion matrix can be used to represent red, green and blue channels of color images. A low-rank approximation for a pure…
We study the role of the constraint set in determining the solution to low-rank, positive semidefinite (PSD) matrix sensing problems. The setting we consider involves rank-one sensing matrices: In particular, given a set of rank-one…
We reduce the memory footprint of popular large-scale online learning methods by projecting our weight vector onto a coarse discrete set using randomized rounding. Compared to standard 32-bit float encodings, this reduces RAM usage by more…
Several variational quantum circuit approaches to machine learning have been proposed in recent years, with one promising class of variational algorithms involving tensor networks operating on states resulting from local feature maps. In…
Motivated by the recent experimental demonstrations of quantum supremacy, proving the hardness of the output of random quantum circuits is an imperative near term goal. We prove under the complexity theoretical assumption of the…
Pseudorandom circuits generate quantum states and unitary operators which are approximately distributed according to the unitarily invariant Haar measure. We explore how several design parameters affect the efficiency of pseudo-random…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
We extend our work for compression of currents and varifolds to a compression algorithm for the embedded normal cycles representation of shape, restricted to the constant normal kernel case, using the Nystrom approximation in Reproducing…
We study the level-spacing statistics in the entanglement spectrum of output states of random universal quantum circuits where qubits are subject to a finite probability of projection to the computational basis at each time step. We…
A fast algorithm for the approximation of a low rank LU decomposition is presented. In order to achieve a low complexity, the algorithm uses sparse random projections combined with FFT-based random projections. The asymptotic approximation…
We present a quantum random number generator (QRNG) based on the random outcomes inherent in projective measurements on a superposition of quantum states of light. Firstly, we use multiplexed holograms encoded on a spatial light modulator…
Quantum Reservoir Computing (QRC) harnesses quantum systems to tackle intricate computational problems with exceptional efficiency and minimized energy usage. This paper presents a QRC framework that utilizes a minimalistic quantum…