Related papers: Computational speedups using small quantum devices
In the NISQ-era of quantum computing, we should not expect to see quantum devices that provide an exponential improvement in runtime for practical problems, due to the lack of error correction and small number of qubits available.…
A theoretical model of a quantum device which can factorize any number N in two steps i.e. by preparing an input state and performing a measurement is discussed. The analysis reveals that the duration of state preparation and measurement is…
The field of quantum algorithms aims to find ways to speed up the solution of computational problems by using a quantum computer. A key milestone in this field will be when a universal quantum computer performs a computational task that is…
In this paper we discuss analogue computers based on quantum optical systems accelerating dynamic programming for some computational problems. These computers, at least in principle, can be realized by actually existing devices. We estimate…
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…
Recently, it is shown that quantum computers can be used for obtaining certain information about the solution of a linear system Ax=b exponentially faster than what is possible with classical computation. Here we first review some key…
We illustrate the application of Quantum Computing techniques to the investigation of the thermodynamical properties of a simple system, made up of three quantum spins with frustrated pair interactions and affected by a hard sign problem…
The intensive pursuit for quantum advantage in terms of computational complexity has further led to a modernized crucial question: {\it When and how will quantum computers outperform classical computers?} The next milestone is undoubtedly…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
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…
Quantum algorithms speeding up classical counterparts are proposed for the problems: 1. Recognition of eigenvalues with fixed precision. Given a quantum circuit generating unitary mapping $U$ and a complex number the problem is to determine…
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…
Insofar as quantum computation is faster than classical, it appears to be irreversible. In all quantum algorithms found so far the speed-up depends on the extra-dynamical irreversible projection representing quantum measurement. Quantum…
Quantum computing holds great promise for surpassing the limits of classical devices in many fields. Despite impressive developments, however, current research is primarily focused on qubits. At the same time, quantum hardware based on…
Quantum devices use qubits to represent information, which allows them to exploit important properties from quantum physics, specifically superposition and entanglement. As a result, quantum computers have the potential to outperform the…
Large quantum computers promise to solve some critical problems not solvable otherwise. However, modern quantum technologies suffer various imperfections such as control errors and qubit decoherence, inhibiting their potential utility. The…
Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one…
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…
A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum…
Quantum computing is a game-changing technology for global academia, research centers and industries including computational science, mathematics, finance, pharmaceutical, materials science, chemistry and cryptography. Although it has seen…