Related papers: On the Existence of certain Quantum Algorithms
Machine-learning tasks frequently involve problems of manipulating and classifying large numbers of vectors in high-dimensional spaces. Classical algorithms for solving such problems typically take time polynomial in the number of vectors…
Universal fault-tolerant quantum computers will require error-free execution of long sequences of quantum gate operations, which is expected to involve millions of physical qubits. Before the full power of such machines will be available,…
We propose the use of a quantum algorithm to deal with the problem of searching with errors in the framework of two-person games. Specifically, we present a solution to the Ulam's problem that polynomially reduces its query complexity and…
Fuelled by increasing computer power and algorithmic advances, machine learning techniques have become powerful tools for finding patterns in data. Since quantum systems produce counter-intuitive patterns believed not to be efficiently…
One of the fundamental theories of physics is that of quantum mechanics. Quantum mechanics tries to explain the inconsistencies in the behaviors of systems at the macro and micro scales. Quantum mechanics paved the way for quantum computing…
Quantum algorithms could efficiently solve certain classically intractable problems by exploiting quantum parallelism. To date, whether the quantum entanglement is useful or not for quantum computing is still a question of debate. Here, we…
We construct an algorithm for solving the following problem: given a number field $K$, a positive integer $N$, and a positive real number $B$, determine all points in $\mathbb P^N(K)$ having relative height at most $B$. A theoretical…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
The so-called "threshold" theorem says that, once the error rate per qubit per gate is below a certain value, indefinitely long quantum computation becomes feasible, even if all of the qubits involved are subject to relaxation processes,…
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…
Quantum computers leverage the principles of quantum mechanics to do computation with a potential advantage over classical computers. While a single classical computer transforms one particular binary input into an output after applying one…
We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new,…
Ordinary approach to quantum algorithm is based on quantum Turing machine or quantum circuits. It is known that this approach is not powerful enough to solve NP-complete problems. In this paper we study a new approach to quantum algorithm…
A generalization of recent group-theoretic matrix multiplication algorithms to an analogue of the theory of partial matrix multiplication is presented. We demonstrate that the added flexibility of this approach can in some cases improve…
Quantum computation is based on implementing selected unitary transformations which represent algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The…
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…
We review the investigations on the quantum structure of spactime, to be found at the Planck scale if one takes into account the operational limitations to localization of events which result from the concurrence of Quantum Mechanics and…
Combinatorial optimization is a promising application for near-term quantum computers, however, identifying performant algorithms suited to noisy quantum hardware remains as an important goal to potentially realizing quantum computational…
A quantum algorithm is a set of instructions for a quantum computer, however, unlike algorithms in classical computer science their results cannot be guaranteed. A quantum system can undergo two types of operation, measurement and quantum…