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The question of which resources drive the advantages in quantum algorithms has long been a fundamental challenge. While entanglement and coherence are critical to many quantum algorithms, our results indicate that they do not fully explain…
A generalized quantum search algorithm, where phase inversions for the marked state and the prepared state are replaced by $\pi/2$ phase rotations, is realized in a 2-qubit NMR heteronuclear system. The quantum algorithm searches a marked…
Given two unsorted lists each of length N that have a single common entry, a quantum computer can find that matching element with a work factor of $O(N^{3/4}\log N)$ (measured in quantum memory accesses and accesses to each list). The…
In the Grover-type quantum search process a search operator is iteratively applied, say, k times, on the initial database state. We present an additive decomposition scheme such that the iteration process is expressed, in the computational…
We present a method for realizing efficiently Grover's search algorithm in an array of coupled cavities doped with three-level atoms. We show that by encoding information in the lowest two ground states of the dopants and through the…
The difference between classical and quantum algorithms (QA) is following: problem solved by QA is coded in the structure of the quantum operators. Input to QA in this case is always the same. Output of QA says which problem coded. In some…
As the engineering endeavour to realise quantum computers progresses, we consider that such machines need not rely on binary as their de facto unit of information. We investigate Grover's algorithm under a generalised quantum circuit model,…
Noise dominates every aspect of near-term quantum computers, rendering it exceedingly difficult to carry out even small computations. In this paper we are concerned with the modelling of noise in Noisy Intermediate-Scale Quantum (NISQ)…
We consider the Grover search algorithm implementation for a quantum register of size $N = 2^k$ using k (or k +1) microwave- and laser-driven Rydberg-blockaded atoms, following the proposal by M{\o}lmer, Isenhower, and Saffman [J. Phys. B…
Current technological advancements of quantum computers highlight the need for application-driven, practical and well-defined methods of benchmarking their performance. As the existing NISQ device's quality of two-qubit gate errors rate is…
We present a systematic construction of quantum circuits implementing Grover's database search algorithm for arbitrary number of targets. We introduce a new operator which flips the sign of the targets and evaluate its circuit complexity.…
We propose a scalable implementation of Grover's quantum search algorithm in a trapped-ion quantum information processor. The system is initialized in an entangled Dicke state by using simple adiabatic techniques. The…
We study the status of fair sampling on Noisy Intermediate Scale Quantum (NISQ) devices, in particular the IBM Q family of backends. Using the recently introduced Grover Mixer-QAOA algorithm for discrete optimization, we generate fair…
We assess the potential of quantum computing to accelerate computation of central tasks in genomics, focusing on often-neglected theoretical limitations. We discuss state-of-the-art challenges of quantum search, optimization, and machine…
While limitations on quantum computation by Markovian environmental noise are well-understood in generality, their behavior for different quantum circuits and noise realizations can be less universal. Here we consider a canonical quantum…
Grover's algorithm relies on the superposition and interference of quantum mechanics, which is more efficient than classical computing in specific tasks such as searching an unsorted database. Due to the high complexity of quantum…
Quantum algorithms are conventionally formulated for implementation on a single system of qubits amenable to projective measurements. However, in expectation value quantum computation, such as nuclear magnetic resonance realizations, the…
A simple circuit implementation of the oracle for Grover's quantum search of a real unstructured classical database is proposed. The oracle contains a kind of quantumly accessible classical memory, which stores the database.
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
Replication of DNA and synthesis of proteins are studied from the view-point of quantum database search. Identification of a base-pairing with a quantum query gives a natural (and first ever) explanation of why living organisms have 4…