Related papers: Sub-quadratic Decoding of One-point Hermitian Code…
Recently, there has been increasing interest in designing schemes for quantum computations that are robust against errors. Although considerable research has been devoted to developing quantum error correction schemes, much less attention…
In traditional quantum computing, it has been established that real quantum computation augmented with non-Clifford gates is as powerful as universal quantum computation. Here we investigate this phenomenon in the non-Hermitian setting. We…
The surface code is designed to suppress errors in quantum computing hardware and currently offers the most believable pathway to large-scale quantum computation. The surface code requires a 2-D array of nearest-neighbor coupled qubits that…
This paper highlights a formal connection between two families of widely used matrix factorization algorithms in numerical linear algebra. One family consists of the Jacobi eigenvalue algorithm and its variants for computing the Hermitian…
A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and…
We present subquadratic algorithms in the algebraic decision-tree model for several \textsc{3Sum}-hard geometric problems, all of which can be reduced to the following question: Given two sets $A$, $B$, each consisting of $n$ pairwise…
The sum-rank metric generalizes the Hamming and rank metric by partitioning vectors into blocks and defining the total weight as the sum of the rank weights of these blocks, based on their matrix representation. In this work, we explore…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
Quantum computation of vibrational properties of molecules is a promising platform to obtain computational advantages for computational chemistry. However, fault-tolerant quantum computations of vibrational properties remain a relatively…
Starting from a classic financial optimization problem, we first propose a cutting plane algorithm for this problem. Then we use spectral decomposition to tranform the problem into an equivalent D.C. programming problem, and the…
We decode Reed-Solomon codes using soft information provided at the receiver. The Extended Euclidean Algorithm (EEA) is considered as an initial step to obtain an intermediate result. The final decoding result is obtained by interpolating…
Principal component analysis is an important dimension reduction technique in machine learning. In [S. Lloyd, M. Mohseni and P. Rebentrost, Nature Physics 10, 631-633, (2014)], a quantum algorithm to implement principal component analysis…
We present an algorithm for list decoding codewords of algebraic number field codes in polynomial time. This is the first explicit procedure for decoding number field codes whose construction were previously described by Lenstra and…
In this paper we study evaluation codes arising from plane quotients of the Hermitian curve, defined by affine equations of the form $y^q+y=x^m$, $q$ being a prime power and $m$ a positive integer which divides $q+1$. The dual minimum…
We study the complexity of Decoded Quantum Interferometry (DQI), a quantum algorithm for approximate optimization. First, we show that the algorithm resists classical simulation strategies based on locating outputs with large probabilities.…
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…
Four-level systems in quantum optics, and for representing two qubits in quantum computing, are difficult to solve for general time-dependent Hamiltonians. A systematic procedure is presented which combines analytical handling of the…
PhD thesis investigating homological quantum codes derived from curved and higher dimensional geometries. In the first part we will consider closed surfaces with constant negative curvature. We show how such surfaces can be constructed and…
In this paper we present a geometrical characterization for the minimum-weight codewords of the Hermitian codes over the fields $\mathbb{F}_{q^2}$ in the third and fourth phase, namely with distance $d \geq q^2-q$. We consider the unique…
We propose a versatile and efficient algorithmic framework for optimizing fermion-to-qubit mappings by generalizing the idea of randomized block coordinate descent. Our greedy approach, termed Randomized Subsystem Descent, iteratively…