相关论文: Comments on quant-ph/0609176
Withdrawn; replaced by longer, more detailed paper quant-ph/0010065.
In a recent paper (quant-ph/0506105), A S Gupta, M. Gupta and A. Pathak proposed a modified Grover algorithm that would exponentially accelerate the unsorted database search problem if the number of marked items is known. If this were true,…
The attempt to equate operator quantum error correction (quant-ph/0504189v1) with the quantum computer condition (quant-ph/0507141) in version two of quant-ph/0504189 is shown to be invalid.
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,…
Grover's quantum search algorithm, involving a large number of qubits, is highly sensitive to errors in the physical implementation of the unitary operators. This poses an intrinsic limitation to the size of the database that can be…
We study the characterisation of efficient and non-efficient families of Grover's algorithms according to the majorization principle. We develop a geometrical interpretation based on the parameters that appears on these algorithms. Using…
Recently, Andreas de Vries proposed a quantum algorithm that would find an element in an unsorted database exponentially faster than Grover's algorithm. We show that de Vries' algorithm does not work as intended and does not give any clue…
We consider Grover's unstructured search problem in the setting where each oracle call has some small probability of failing. We show that no quantum speed-up is possible in this case.
We study the influence of errors and decoherence on both the performance of Shor's factoring algorithm and Grover's search algorithm, and on the amount of interference in these algorithms using a recently proposed interference measure. We…
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…
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…
Grover's algorithm is a primary algorithm offered as evidence that quantum computers can provide an advantage over classical computers. It involves an "oracle" specified for a given application whose structure is not part of the formal…
We consider quantum computation efficiency from a new perspective. The efficiency is reduced to its classical counterpart by imposing the semi-classical limit. We show that this reduction is caused by the fact that any elementary quantum…
Demonstration of quantum advantage remains challenging due to the increased overhead of controlling large quantum systems. While significant effort has been devoted to qubit-based devices, qudits ($d$-level systems) offer potential…
An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some…
There is a serious flaw in the proposal [arXiv:1603.06857] for the achievement of unity efficiency in SPDC. This is a replacement due to mistakes in the table of probabilities. Numbers have been corrected.
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…
In this brief comment on `Grover search with pairs of trapped Ions' [Phys. Rev. A 63, 052308, (2001)], we show that Grover's algorithm may be performed exactly using the gate set given provided that small changes are made to the gate…
Grover's algorithm is usually described in terms of the iteration of a compound operator of the form $Q = - H I_{0} H I_{x_0}$. Although it is quite straightforward to verify the algebra of the iteration, this gives little insight into why…
Two additional reasons are suggested for the seeming lack of progress in producing quantum algorithms.