Related papers: Demonstration of algorithmic quantum speedup
Quantum computing has noteworthy speedup over classical computing by taking advantage of quantum parallelism, i.e., the superposition of states. In particular, quantum search is widely used in various computationally hard problems. Grover's…
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
We introduce Quantum Index Algebra (QIA) as a finite, index-based algebraic framework for representing and manipulating quantum operators on Hilbert spaces of dimension $2^m$. In QIA, operators are expressed as structured combinations of…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…
Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization…
Quantum error detection can produce unbiased expectation values that exponentially converge to noiseless results as the code distance is increased. Despite this, its performance as an error mitigation technique is relatively understudied on…
The thesis deals with Quantum Algorithms for solving Hard Constrained Optimization Problems. It shows how quantum computers can solve difficult everyday problems such as finding the best schedule for social workers or the path of a robot…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
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…
Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…
The development of small-scale digital and analog quantum devices raises the question of how to fairly assess and compare the computational power of classical and quantum devices, and of how to detect quantum speedup. Here we show how to…
The successful implementation of algorithms on quantum processors relies on the accurate control of quantum bits (qubits) to perform logic gate operations. In this era of noisy intermediate-scale quantum (NISQ) computing, systematic…
One of the main aims in the field of quantum simulation is to achieve a quantum speedup, often referred to as "quantum computational supremacy", referring to the experimental realization of a quantum device that computationally outperforms…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
Quantum computing holds promise across various fields, particularly with the advent of Noisy Intermediate-Scale Quantum (NISQ) devices, which can outperform classical supercomputers in specific tasks. However, challenges such as noise and…
Quantum computing leverages quantum mechanics to achieve computational advantages over classical hardware, but the use of third-party quantum compilers in the Noisy Intermediate-Scale Quantum (NISQ) era introduces risks of intellectual…
We propose a new method for evaluating NISQ devices. This paper has three distinct parts. First, we present a new quantum algorithm that solves a two hundred year old problem of finding quadratic nonresidues (QNR) in polynomial time. We…
Machines are possible to have some artificial intelligence like human beings owing to particular algorithms or software. Such machines could learn knowledge from what people taught them and do works according to the knowledge. In practical…
Quantum algorithms are getting extremely popular due to their potential to significantly outperform classical algorithms. Yet, applying quantum algorithms to optimization problems meets challenges related to the efficiency of quantum…