Related papers: Quantum block encoding for semiseparable matrices
A quantum circuit must be preprocessed before implementing on NISQ devices due to the connectivity constraint. Quantum circuit mapping (QCM) transforms the circuit into an equivalent one that is compliant with the NISQ device's architecture…
Image-based data is a popular arena for testing quantum machine learning algorithms. A crucial factor in realizing quantum advantage for these applications is the ability to efficiently represent images as quantum states. Here we present a…
Quantum tokens envision to store unclonable quantum states in a physical device, with the goal of being used for personal authentication protocols, as required by banks. Still, the experimental realization of such devices faces many…
Quantum machine learning is an emerging field that combines machine learning with advances in quantum technologies. Many works have suggested great possibilities of using near-term quantum hardware in supervised learning. Motivated by these…
We propose a quantum data fitting algorithm for non-sparse matrices, which is based on the Quantum Singular Value Estimation (QSVE) subroutine and a novel efficient method for recovering the signs of eigenvalues. Our algorithm generalizes…
One of the key considerations in the development of Quantum Machine Learning (QML) protocols is the encoding of classical data onto a quantum device. In this chapter we introduce the Matrix Product State representation of quantum systems…
Quantum algorithms present a quadratically improved complexity over classical ones for certain sampling tasks. For instance, the Quantum Amplitude Estimation (QAE) algorithm promises to speedup the estimation of the mean of certain…
The class of quasiseparable matrices is defined by the property that any submatrix entirely below or above the main diagonal has small rank, namely below a bound called the order of quasiseparability. These matrices arise naturally in…
We present a quantum error correction code which protects a qubit of information against general one qubit errors which maybe caused by the interaction with the environment. To accomplish this, we encode the original state by distributing…
The basic idea of quantum computing is surprisingly similar to that of kernel methods in machine learning, namely to efficiently perform computations in an intractably large Hilbert space. In this paper we explore some theoretical…
Recent years have seen rapid development in the subject of quantum coding theory, with breakthroughs on many exciting classes of codes, including quantum LDPC codes, quantum locally testable codes, and quantum codes with interesting…
To improve the efficiency of the encoding and the decoding is the important problem in the quantum error correction. In a preceding work, a general algorithm for decoding the stabilizer code is shown. This paper will show an decoding which…
Quantum based systems are a relatively new research area for that different modelling languages including process calculi are currently under development. Encodings are often used to compare process calculi. Quality criteria are used then…
The LINPACK benchmark reports the performance of a computer for solving a system of linear equations with dense random matrices. Although this task was not designed with a real application directly in mind, the LINPACK benchmark has been…
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This…
We develop a unified quantum framework for subgraph counting in graphs. We encode a graph on $N$ vertices into a quantum state on $2\lceil \log_2 N \rceil$ working qubits and $2$ ancilla qubits using its adjacency list, with worst-case gate…
Vectorized quantum block encoding provides a way to embed classical data into Hilbert space, offering a pathway for quantum models, such as Quantum Transformers (QT), that replace classical self-attention with quantum circuit simulations to…
In the span of four decades, quantum computation has evolved from an intellectual curiosity to a potentially realizable technology. Today, small-scale demonstrations have become possible for quantum algorithmic primitives on hundreds of…
Quantum Error Correction (QEC) is essential for building robust, fault-tolerant quantum computers; however, the decoding process often presents a significant computational bottleneck. Tesseract is a novel Most-Likely-Error (MLE) decoder for…
Any architecture for practical quantum computing must be scalable. An attractive approach is to create multiple cores, computing regions of fixed size that are well-spaced but interlinked with communication channels. This exploded…