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We review here the recent success in quantum annealing, i.e., optimization of the cost or energy functions of complex systems utilizing quantum fluctuations. The concept is introduced in successive steps through the studies of mapping of…

Quantum Physics · Physics 2010-09-21 Arnab Das , Bikas K. Chakrabarti

We exhibit a simple, systematic procedure for detecting and correcting errors using any of the recently reported quantum error-correcting codes. The procedure is shown explicitly for a code in which one qubit is mapped into five. The…

Quantum Physics · Physics 2009-10-30 David P. DiVincenzo , Peter W. Shor

We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to…

Data Structures and Algorithms · Computer Science 2016-08-16 Vincent Lefèvre

We present quantum algorithms for the estimation of n-time correlation functions, the local and non-local density of states, and dynamical linear response functions. These algorithms are all based on block-encodings - a versatile technique…

Quantum Physics · Physics 2020-08-19 Patrick Rall

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…

Machine Learning · Computer Science 2024-01-17 Fabien Geyer , Johannes Freitag , Tobias Schulz , Sascha Uhrig

Here we show how universal quantum computers based on the quantum circuit model can handle mathematical analysis calculations for functions with continuous domains, without any digitalization, and with remarkably few qubits. The basic…

Quantum Physics · Physics 2022-10-10 Pablo Bermejo , Roman Orus

Quantum error correction is widely thought to be the key to fault-tolerant quantum computation. However, determining the most suited encoding for unknown error channels or specific laboratory setups is highly challenging. Here, we present a…

In order to use quantum error-correcting codes to actually improve the performance of a quantum computer, it is necessary to be able to perform operations fault-tolerantly on encoded states. I present a general theory of fault-tolerant…

Quantum Physics · Physics 2011-07-19 Daniel Gottesman

Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…

Distributed, Parallel, and Cluster Computing · Computer Science 2022-04-14 Johannes de Fine Licht , Christopher A. Pattison , Alexandros Nikolaos Ziogas , David Simmons-Duffin , Torsten Hoefler

Quantum bits have technological imperfections. Additionally, the capacity of a component that can be implemented feasibly is limited. Therefore, distributed quantum computation is required to scale up quantum computers. This dissertation…

Quantum Physics · Physics 2017-04-11 Shota Nagayama

This thesis examines a modern concept for machine numbers based on interval arithmetic called 'Unums' and compares it to IEEE 754 floating-point arithmetic, evaluating possible uses of this format where floating-point numbers are…

Numerical Analysis · Computer Science 2017-01-04 Laslo Hunhold

This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…

Computer Vision and Pattern Recognition · Computer Science 2024-06-11 Vincenzo Liguori

Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…

Reducing hardware overhead of neural networks for faster or lower power inference and training is an active area of research. Uniform quantization using integer multiply-add has been thoroughly investigated, which requires learning many…

Numerical Analysis · Computer Science 2018-11-06 Jeff Johnson

Floating point multiplication is a crucial operation in high power computing applications such as image processing, signal processing etc. And also multiplication is the most time and power consuming operation. This paper proposes an…

Hardware Architecture · Computer Science 2019-12-17 S Arish , R. K. Sharma

The fastest quantum algorithms (for the solution of classical computational tasks) known so far are basically variations of the hidden subgroup problem with {$f(U[x])=f(x)$}. Following a discussion regarding which tasks might be solved…

Quantum Physics · Physics 2007-05-23 R. Schützhold , W. G. Unruh

Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…

Quantum Physics · Physics 2024-09-26 Marcel Niedermeier , Jose L. Lado , Christian Flindt

Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…

Machine Learning · Computer Science 2026-05-08 Stanislav Budzinskiy , Marian Gloser , Tolunay Yilmaz , Ying Hong Tham , Yuanyi Lin , Wenyi Fang , Fan Wu , Philipp Petersen

A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…

Quantum Physics · Physics 2017-11-07 Xun Gao , Zhengyu Zhang , Luming Duan

We describe a scheme for quantum error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols…

Quantum Physics · Physics 2009-11-10 Mohan Sarovar , Charlene Ahn , Kurt Jacobs , Gerard J. Milburn