Related papers: Two-sided Quantum Amplitude Amplification and Exac…
With the advent of powerful quantum computers, the quest for more efficient quantum algorithms becomes crucial in attaining quantum supremacy over classical counterparts in the noisy intermediate-scale quantum era. While Grover's search…
We review the basic theoretical underpinnings of the Grover algorithm, providing a rigorous and well motivated derivation. We then present a generalization of Grover's algorithm that searches an arbitrary subspace of the multi-dimensional…
L. K. Grover's search algorithm in quantum computing gives an optimal, square-root speedup in the search for a single object in a large unsorted database. In this paper, we expound Grover's algorithm in a Hilbert-space framework that…
Quantum amplifiers are intrinsically nonlinear systems whose performance limits are set by quantum mechanics. In quantum measurement, amplifier operation is conventionally optimized in the linear regime by maximizing signal-to-noise ratio,…
We present the implementation of Grover's algorithm in a quantum simulator to perform a quantum search for preimages of two scaled hash functions, whose design only uses modular addition, word rotation, and bitwise exclusive or. Our…
Constraint satisfiability problems, crucial to several applications, are solved on a quantum computer using Grover's search algorithm, leading to a quadratic improvement over the classical case. The solutions are obtained with high…
Adiabatic quantum optimization is a procedure to solve a vast class of optimization problems by slowly changing the Hamiltonian of a quantum system. The evolution time necessary for the algorithm to be successful scales inversely with the…
The $n$-point amplitudes of gauge and gravity theory are given as a series in the coupling. The recursive derivative expansion is used to find all of the coupling coefficients. Initial conditions to any bare Lagrangian, or of an improved…
We present a continuous time quantum search algorithm analogous to Grover's. In particular, the optimal search time for this algorithm is proportional to $\sqrt{N}$, where $N$ is the database size. This search algorithm can be implemented…
Estimating quantum amplitude, or the overlap between two quantum states, is a fundamental task in quantum computing and underpins numerous quantum algorithms. In this work, we introduce a novel algorithmic framework for quantum amplitude…
A universal deterministic noiseless quantum amplifier has been shown to be impossible. However, probabilistic noiseless amplification of a certain set of states is physically permissible. Regarding quantum state amplification as quantum…
Quantum Computing offers an entirely new way of doing computation governed by the rules of quantum mechanics like Superposition and Entanglement. These rules allow us to do computation over all the possible states simultaneously. Hence,…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
In this paper, we propose a quantum algorithm that supports a real-valued higher-order unconstrained binary optimization (HUBO) problem. This algorithm is based on the Grover adaptive search that originally supported HUBO with integer…
We re-examine a non-Gaussian quantum error correction code designed to protect optical coherent-state qubits against errors due to an amplitude damping channel. We improve on a previous result [Phys. Rev. A 81, 062344 (2010)] by providing a…
An algebraic analysis of Grover's quantum search algorithm is presented for the case in which the initial state is an arbitrary pure quantum state of n qubits. This approach reveals the geometrical structure of the quantum search process,…
Quantum computers and quantum algorithms have made great strides in the last few years and promise improvements over classical computing for specific tasks. Although the current hardware is not yet ready to make real impacts at the time of…
Overcoming the influence of noise and imperfections is a major challenge in quantum computing. Here, we present an approach based on applying a desired unitary computation in superposition between the system of interest and some auxiliary…
Quantum search algorithms, such as Grover's algorithm, are anticipated to efficiently solve constrained combinatorial optimization problems. However, applying these algorithms to the traveling salesman problem (TSP) on a quantum circuit…
We present a simple and general simulation technique that transforms any black-box quantum algorithm (a la Grover's database search algorithm) to a quantum communication protocol for a related problem, in a way that fully exploits the…