Related papers: Amplitude amplification and estimation require inv…
This paper presents an enhancement to Grover's search algorithm for instances where the number of items (or the size of the search problem) $N$ is not a power of 2. By employing an efficient algorithm for the preparation of uniform quantum…
Quantum amplitude amplification and quantum phase estimation are two fundamental quantum algorithms. All known quantum algorithms are derived from these two algorithms. Even the adiabatic quantum algorithms can also be efficiently simulated…
We investigate the use of amplitude amplification on the gate-based model of quantum computing as a means for solving combinatorial optimization problems. This study focuses primarily on QUBO (quadratic unconstrained binary optimization)…
Grover's Search algorithm was a breakthrough at the time it was introduced, and its underlying procedure of amplitude amplification has been a building block of many other algorithms and patterns for extracting information encoded in…
Quantum algorithms theoretically outperform classical algorithms in solving problems of increasing size, but computational errors must be kept to a minimum to realize this potential. Despite the development of increasingly capable quantum…
We propose a scheme for translating metrological precision bounds into lower bounds on query complexity of quantum search algorithms. Within the scheme the link between quadratic performance enhancement in idealized quantum metrological and…
We examine how amplitude noise in queries to the oracle degrades a performance of quantum search algorithm. The Grover search and similar techniques are widely used in various quantum algorithms, including cases where rival parties are…
Access to the time-reverse $U^{-1}$ of an unknown quantum unitary process $U$ is widely assumed in quantum learning, metrology, and many-body physics. The fundamental task of unitary time-reversal dictates implementing $U^{-1}$ to within…
A new approach to the classical limit of Grover's algorithm is discussed by assuming a very rapid dephasing of a system between consecutive Grover's unitary operations, which drives pure quantum states to decohered mixed states. One can…
Some quantum algorithms have "quantum speedups": improved time complexity as compared with the best-known classical algorithms for solving the same tasks. Can we understand what fuels these speedups from an entropic perspective? Information…
This paper introduces a quantum-classical hybrid algorithm for generalized pattern search (GPS) algorithms. We introduce a quantum search step algorithm using amplitude amplification, which reduces the number of oracle calls needed during…
A simpler quantum counting algorithm based on amplitude amplification is presented. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator where M is the number of marked states and N is the total number of states…
Multi-armed bandits are one of the theoretical pillars of reinforcement learning. Recently, the investigation of quantum algorithms for multi-armed bandit problems was started, and it was found that a quadratic speed-up (in query…
Reversing an unknown quantum evolution is of central importance to quantum information processing and fundamental physics, yet it remains a formidable challenge as conventional methods necessitate an infinite number of queries to fully…
For quantum state preparation, a non-unitary operator is typically designed to decay undesirable states contained in an initial state using ancilla qubits and a probabilistic action. Probabilistic algorithms do not accelerate the…
Quantum algorithm involves the manipulation of amplitudes and computational basis, of which manipulating basis is largely a quantum analogue of classical computing that is always a major contributor to the complexity. In order to make full…
Consider a Boolean function $\chi: X \to \{0,1\}$ that partitions set $X$ between its good and bad elements, where $x$ is good if $\chi(x)=1$ and bad otherwise. Consider also a quantum algorithm $\mathcal A$ such that $A |0\rangle=…
The quantum simulation of classical fluids often involves the use of probabilistic algorithms that encode the result of the dynamics in the form of the amplitude of the selected quantum state. In most cases, however, the amplitude…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…