Related papers: Exponential Quantum Speed-ups are Generic
Simon as extended by Brassard and H{\o}yer shows that there are tasks on which polynomial-time quantum machines are exponentially faster than each classical machine infinitely often. The present paper shows that there are tasks on which…
Quantum computing has shown promise for solving complex optimization problems in databases, such as join ordering and index selection. Prior work often submits formulated problems directly to black-box quantum or quantum-inspired solvers…
We discuss classical and quantum algorithms for solvability testing and finding integer solutions x,y of equations of the form af^x + bg^y = c over finite fields GF(q). A quantum algorithm with time complexity q^(3/8) (log q)^O(1) is…
Proposed quantum advantage in electronic structure has so far required significant fine-tuning to find problems where classical heuristics fail. We describe how to obtain robust quantum speedups for correlated electronic structure and…
Let $f$ denote length preserving function on words. A classical algorithm can be considered as $T$ iterated applications of black box representing $f$, beginning with input word $x$ of length $n$. It is proved that if $T=O(2^{n/(7+e)}), e…
On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation…
Demonstrations of quantum advantage for certain sampling problems have generated considerable excitement for quantum computing and have further spurred the development of circuit-model quantum computers, which represent quantum programs as…
I provide an alternative way of seeing quantum computation. First, I describe an idealized classical problem solving machine that, thanks to a many body interaction, reversibly and nondeterministically produces the solution of the problem…
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 computers allow a near-exponential speed-up for specific applications when compared to classical computers. Despite recent advances in the hardware of quantum computers, their practical usage is still severely limited due to a…
Quantum processing unit (QPU) has to satisfy highly demanding quantity and quality requirements on its qubits to produce accurate results for problems at useful scales. Furthermore, classical simulations of quantum circuits generally do not…
Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical…
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
Due to the expected disparity in quantum vs. classical clock speeds, quantum advantage for branch and bound algorithms is more likely achievable in settings involving large search trees and low operator evaluation costs. Therefore, in this…
Quantum hardware continues to advance, yet finding new quantum algorithms - quantum software - remains a challenge, with classically trained computer programmers having little intuition of how computational tasks may be performed in the…
Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods to find optimal values for these parameters. Solving a quantum computational problem with such…
Quantum machine learning has become an area of growing interest but has certain theoretical and hardware-specific limitations. Notably, the problem of vanishing gradients, or barren plateaus, renders the training impossible for circuits…
The architecture of circuital quantum computers requires computing layers devoted to compiling high-level quantum algorithms into lower-level circuits of quantum gates. The general problem of quantum compiling is to approximate any unitary…
In this paper we study quantum algorithms for NP-complete problems whose best classical algorithm is an exponential time application of dynamic programming. We introduce the path in the hypercube problem that models many of these dynamic…
Quantum computing promises substantial speedups by exploiting quantum mechanical phenomena such as superposition and entanglement. Corresponding design methods require efficient means of representation and manipulation of quantum…