Related papers: On the Existence of certain Quantum Algorithms
This paper summarizes a quantum algorithm of [R.D. Somma, et.al., Phys. Rev. Lett. 101, 130504 (2008)] that simulates a classical annealing process for solving discrete optimization problems. The complexity of the quantum algorithm scales…
We propose the necessary and sufficient condition for the presence of quantum entanglement in arbitrary symmetric pure states of two-level atomic systems. We introduce a parameter to quantify quantum entanglement in such systems. We express…
Applications such as simulating complicated quantum systems or solving large-scale linear algebra problems are very challenging for classical computers due to the extremely high computational cost. Quantum computers promise a solution,…
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…
Quantum families of maps between quantum spaces are defined and studied. We prove that quantum semigroup (and sometimes quantum group) structures arise naturally on such objects out of more fundamental properties. As particular cases we…
We review the field of Optical Quantum Computation, considering the various implementations that have been proposed and the experimental progress that has been made toward realizing them. We examine both linear and nonlinear approaches and…
Linear differential equations are ubiquitous in science and engineering. Quantum computers can simulate quantum systems, which are described by a restricted type of linear differential equations. Here we extend quantum simulation algorithms…
We explore the implications of restricting the framework of quantum theory and quantum computation to finite fields. The simplest proposed theory is defined over arbitrary finite fields and loses the notion of unitaries. This makes such…
We study some extensions of Grover's quantum searching algorithm. First, we generalize the Grover iteration in the light of a concept called amplitude amplification. Then, we show that the quadratic speedup obtained by the quantum searching…
Recent theoretical results confirm that quantum theory provides the possibility of new ways of performing efficient calculations. The most striking example is the factoring problem. It has recently been shown that computers that exploit…
We introduce a novel algorithm for the task of coherently controlling a quantum mechanical system to implement any chosen unitary dynamics. It performs faster than existing state of the art methods by one to three orders of magnitude…
We study the efficiency of algorithms simulating a system evolving with Hamiltonian $H=\sum_{j=1}^m H_j$. We consider high order splitting methods that play a key role in quantum Hamiltonian simulation. We obtain upper bounds on the number…
This paper discusses the compilation, optimization, and error mitigation of quantum algorithms, essential steps to execute real-world quantum algorithms. Quantum algorithms running on a hybrid platform with QPU and CPU/GPU take advantage of…
A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that…
In seeking out an algorithm to test out the capability of the IBM Quantum Experience quantum computer, we were given a review paper covering various algorithms for solving the subset-sum problem, including both classical and quantum…
The paper considers the problem of finding the largest possible set P(n), a subset of the set N of the natural numbers, with the property that a number is in P(n) if and only if it is a sum of n distinct naturals all in P(n) or none in…
Alongside the development of quantum algorithms and quantum complexity theory in recent years, quantum techniques have also proved instrumental in obtaining results in classical (non-quantum) areas. In this paper we survey these results and…
Residue arithmetic is an elegant and convenient way of computing with integers that exceed the natural word size of a computer. The algorithms are highly parallel and hence naturally adapted to quantum computation. The process differs from…
When a probe qubit is coupled to a quantum register that represents a physical system, the probe qubit will exhibit a dynamical response only when it is resonant with a transition in the system. Using this principle, we propose a quantum…
In this paper, we consider three types of polynomial equations in quantum computer: linear divisibility equation, which belongs to a special type of binary-quadratic Diophantine equation; quadratic congruence equation with restriction in…