Related papers: A Grover-compatible manifold optimization algorith…
Quantum advantage is the core of quantum computing. Grover's search algorithm is the only quantum algorithm with proven advantage to any possible classical search algorithm. However, realizing this quantum advantage in practice is quite…
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…
Grover's algorithm is a well-known unstructured quantum search algorithm run on quantum computers. It constructs an oracle and calls the oracle O($\sqrt N$) times to locate specific data out of N unsorted data. This represents a quadratic…
This paper discusses an improvement to Grover's algorithm for searches where target states are Hamming weight eigenstates and search space is not ordered. It is shown that under these conditions search efficiency depends on the smaller…
The search problem is to find a state satisfying certain properties out of a given set. Grover's algorithm drives a quantum computer from a prepared initial state to the target state and solves the problem quadratically faster than a…
Run-times of quantum algorithms are often studied via an asymptotic, worst-case analysis. Whilst useful, such a comparison can often fall short: it is not uncommon for algorithms with a large worst-case run-time to end up performing well on…
Grover's search algorithm is one of the first quantum algorithms to exhibit a provable quantum advantage. It forms the backbone of numerous quantum applications and is widely used in benchmarking efforts. Here, we report…
Developing hardware-efficient implementations of quantum algorithms is crucial in the NISQ era to achieve practical quantum advantage. Here, we construct a generic quantum solver for NP problems based on Grover's search algorithm,…
Solving optimisation problems is a promising near-term application of quantum computers. Quantum variational algorithms leverage quantum superposition and entanglement to optimise over exponentially large solution spaces using an…
We analyze inexact Riemannian gradient descent (RGD) where Riemannian gradients and retractions are inexactly (and cheaply) computed. Our focus is on understanding when inexact RGD converges and what is the complexity in the general…
In this paper, we consider the problem of minimizing a smooth function on a Riemannian manifold and present a Riemannian gradient method with momentum. The proposed algorithm represents a substantial and nontrivial extension of a recently…
Manifold-valued datasets are widely encountered in many computer vision tasks. A non-linear analog of the PCA, called the Principal Geodesic Analysis (PGA) suited for data lying on Riemannian manifolds was reported in literature a decade…
Grover's algorithm is a well-known contribution to quantum computing. It searches one value within an unordered sequence faster than any classical algorithm. A fundamental part of this algorithm is the so-called oracle, a quantum circuit…
The quantum approximate optimization algorithm, also known in its generalization as the quantum alternating operator ansatz, (QAOA) is a heuristic hybrid quantum-classical algorithm for finding high-quality approximate solutions to…
Searching a database is a central task in computer science and is paradigmatic of transport and optimization problems in physics. For an unstructured search, Grover's algorithm predicts a quadratic speedup, with the search time…
Grover's quantum search algorithm evolves a quantum system from a known source state $|s\rangle$ to an unknown target state $|t\rangle$ using the selective phase inversions, $I_{s}$ and $I_{t}$, of these two states. In one of the…
The Grover search algorithm is a pivotal advancement in quantum computing, promising a remarkable speedup over classical algorithms in searching unstructured large databases. Here, we report results for the implementation and…
Finding a maximum or minimum is a fundamental building block in many mathematical models. Compared with classical algorithms, Durr, Hoyer's quantum algorithm (DHA) achieves quadratic speed. However, its key step, the quantum exponential…
We study the complexity of finding the global solution to stochastic nonconvex optimization when the objective function satisfies global Kurdyka-Lojasiewicz (KL) inequality and the queries from stochastic gradient oracles satisfy mild…
The translation of Grover's search algorithm from its standard version, designed for implementation on a single quantum system amenable to projective measurements, into one suitable for an ensemble of quantum computers, whose outputs are…