Related papers: Dequantization and Hardness of Spectral Sum Estima…
The algorithm and complexity of approximating the permanent of a matrix is an extensively studied topic. Recently, its connection with quantum supremacy and more specifically BosonSampling draws special attention to the average-case…
Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…
The low-complexity assumption in linear systems can often be expressed as rank deficiency in data matrices with generalized Hankel structure. This makes it possible to denoise the data by estimating the underlying structured low-rank…
We present an exact quantum algorithm for solving the Exact Satisfiability (XSAT) problem, which belongs to the important NP-complete complexity class. The algorithm is based on an intuitive approach that can be divided into two parts:…
This paper presents a computationally efficient decoder for multiple antenna systems. The proposed algorithm can be used for any constellation (QAM or PSK) and any labeling method. The decoder is based on matrix-lifting Semi-Definite…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
Different choices of quantum error-correcting codes can reduce the demands on the physical hardware needed to build a quantum computer. To achieve the full potential of a code, we must develop practical decoding algorithms that can correct…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…
We propose the variational quantum singular value decomposition based on encoding the elements of the considered { $N\times N$} matrix into the state of a quantum system of appropriate dimension. This method doesn't use the expansion of…
We solve the analysis sparse coding problem considering a combination of convex and non-convex sparsity promoting penalties. The multi-penalty formulation results in an iterative algorithm involving proximal-averaging. We then unfold the…
Studies of quantum error correction (QEC) typically focus on stochastic Pauli errors because the existence of a threshold error rate below which stochastic Pauli errors can be corrected implies that there exists a threshold below which…
The ubiquitous presence of shot noise sets a fundamental limit to the measurement precision in classical metrology. Recent advances in quantum devices and novel quantum algorithms utilizing interference effects are opening new routes for…
We introduce a framework of the equivariant convolutional quantum algorithms which is tailored for a number of machine-learning tasks on physical systems with arbitrary SU$(d)$ symmetries. It allows us to enhance a natural model of quantum…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
Even after decades of quantum computing development, examples of generally useful quantum algorithms with exponential speedups over classical counterparts are scarce. Recent progress in quantum algorithms for linear-algebra positioned…
Block encoding is a key ingredient in the recently developed quantum singular value transformation (QSVT) framework, which provides a unifying description for many quantum algorithms. Initially introduced to simplify and optimize resource…
The strongly correlated systems we use to realise quantum error-correcting codes may give rise to high-weight, problematic errors. Encouragingly, we can expect local quantum error-correcting codes with no string-like logical operators $-$…
Treating the effects of a time-dependent classical dephasing environment during quantum logic operations poses a theoretical challenge, as the application of non-commuting control operations gives rise to both dephasing and depolarization…
A widely used method for solving SOS (Sum Of Squares) decomposition problem is to reduce it to the problem of semi-definite programs (SDPs) which can be efficiently solved in theory. In practice, although many SDP solvers can work out some…