Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:quant-ph/9910076

An intrinsic limitation on the size of quantum database

Long, Gui Lu, Yan Li, Wei Lin Zhang, Chang Cun Tu

Published Oct 16, 1999• 1 citation
arXivHTMLPDF

Abstract

It is found that Grover's quantum search algorithm is not robust against phase inversion and Hadmard transformation inaccuracies. Imperfect phase inversions and Hadmard-Walsh transformations in Grover's quantum search algorithm lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. even in the absence of decoherence. Given the degrees of inaccuracies, we find that to guarantee half rate of success, the size of the database should be in the order of $O({1 \over δ^2})$, where $δ$ is the uncertainty.

DOI
10.48550/arxiv.quant-ph/9910076

Related papers

Dominant gate imperfection in Grover’s quantum search algorithm

Gui Lu Long, Yan Li, Wei Lin Zhang +1 more

It is found that systematic errors in phase inversions and random errors in Hadmard-Walsh transformations are the dominant gate imperfection in Grover's quantum search algorithm. They lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. Given the degree of inaccuracy, we find that to guarantee a half-rate of success, the size of the database should be on the order of $O(1/{\ensuremath{\delta}}^{2}),$ where $\ensuremath{\delta}$ is the uncertainty.

Physical Review A•Mar 10, 2000•81 citations

Gate imperfection in the quantum random-walk search algorithm

Yun Li, Lei Ma, Jie Zhou

We study how imperfect quantum gates affect the quantum random-walk search algorithm. We find that systematic errors in phase inversions result in the reduction of the maximum probability of the marked state and lower the algorithm efficiency with an increasing degree of inaccuracy. The size of the database should be limited due to the inevitable errors. Finally, we compare the phase noise caused by such errors in the random-walk search algorithm with that in the Grover search algorithm.

Journal of Physics A Mathematical and General•Jul 5, 2006•7 citations

An improved phase error tolerance in Quantum search algorithm

Jin-Yuan Hsieh, Che‐Ming Li, Der-San Chuu

As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the generalized and imroved criterion for tolerated error and corresponding size of quantum database under the inevitable gate imperfections. The vanished inaccurancy to this condition has also been shown. Besides, a concise formula for evaluating minimum number of iterations is also presented in this work.

arXiv:quant-ph/0209073•Sep 11, 2002•4 citations

Effects of systematic phase errors on optimized quantum random-walk search algorithm

Yuchao Zhang, Wan‐Su Bao, Xiang Wang +1 more

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm.

arXiv:1501.02098•Chinese Physics B•Jun 1, 2015•6 citations

Phase Matching in Quantum Searching and the Improved Grover Algorithm

Yang Sun

We briefly introduced some of our recent work related to the phase matching condition in quantum searching algorithms and the improved Grover algorithm. When one replaces the two phase inversions in the Grover algorithm with arbitrary phase rotations, the modified algorithm usually fails in searching the marked state unless a phase matching condition is satisfied between the two phases. The Grover algorithm is not 100% in success rate, an improved Grover algorithm with zero-failure rate is given by replacing the phase inversions with angles that depends on the size of the database. Other aspects of the Grover algorithm such as the SO(3) picture of quantum searching, the dominant gate imperfections in the Grover algorithm are also mentioned.

Yuanzihe wuli pinglun•Jan 1, 2004•7 citations

Quantum Searching amidst large uncertainties

D. Li, Xiao-Ming Li, Hongtao Huang +1 more

The quantum search algorithm is a way for finding an item with desired properties in an unsorted database of size N in only$\\sqrt{N}$ steps by means of a sequence of selective inversion and quantum diffusion operations. However, like most quantum algorithms, this requires the algorithm to execute the precise sequence of operations, any further probing into the database only worsens the result. Grover recently showed that by replacing the selective inversion by selective phase shifts of $\\pi /3$, the algorithm converges to the desired item monotonically. This paper builds on that result and considers the problem of retrieving a marked item from a database containing an unknown fraction of marked items, say $\\epsilon $. We derive optimal algorithms for different ranges of $\\epsilon .$ These are similar to Grover's recent algorithm but the phase shift turns out to vary with $\\epsilon $ - this is generally quite different from $\\pi /3$.

•Jan 1, 2006•0 citations
It is found that Grover's quantum search algorithm is not robust against phase inversion and Hadmard transformation inaccuracies. Imperfect phase inversions and Hadmard-Walsh transformations in Grover's quantum search algorithm lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. even in the absence of decoherence. Given the degrees of inaccuracies, we find that to guarantee half rate of success, the size of the database should be in the order of O(1δ2)O({1 \over δ^2})O(δ21​), where δδδ is the uncertainty.
It is found that systematic errors in phase inversions and random errors in Hadmard-Walsh transformations are the dominant gate imperfection in Grover's quantum search algorithm. They lead to reductions in the maximum probability of the marked state and affect the efficiency of the algorithm. Given the degree of inaccuracy, we find that to guarantee a half-rate of success, the size of the database should be on the order of $O(1/{\ensuremath{\delta}}^{2}),$ where $\ensuremath{\delta}$ is the uncertainty.
As the matching condition in Grover search algorithm is transgressed due to inevitable errors in phase inversions, it gives a reduction in maximum probability of success. With a given degree of maximum success, we have derive the generalized and imroved criterion for tolerated error and corresponding size of quantum database under the inevitable gate imperfections. The vanished inaccurancy to this condition has also been shown. Besides, a concise formula for evaluating minimum number of iterations is also presented in this work.
This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm.
We briefly introduced some of our recent work related to the phase matching condition in quantum searching algorithms and the improved Grover algorithm. When one replaces the two phase inversions in the Grover algorithm with arbitrary phase rotations, the modified algorithm usually fails in searching the marked state unless a phase matching condition is satisfied between the two phases. The Grover algorithm is not 100% in success rate, an improved Grover algorithm with zero-failure rate is given by replacing the phase inversions with angles that depends on the size of the database. Other aspects of the Grover algorithm such as the SO(3) picture of quantum searching, the dominant gate imperfections in the Grover algorithm are also mentioned.
The quantum search algorithm is a way for finding an item with desired properties in an unsorted database of size N in onlysqrtN\\sqrt{N}sqrtN steps by means of a sequence of selective inversion and quantum diffusion operations. However, like most quantum algorithms, this requires the algorithm to execute the precise sequence of operations, any further probing into the database only worsens the result. Grover recently showed that by replacing the selective inversion by selective phase shifts of pi/3\\pi /3pi/3, the algorithm converges to the desired item monotonically. This paper builds on that result and considers the problem of retrieving a marked item from a database containing an unknown fraction of marked items, say $\\epsilon $. We derive optimal algorithms for different ranges of epsilon.\\epsilon .epsilon. These are similar to Grover's recent algorithm but the phase shift turns out to vary with $\\epsilon $ - this is generally quite different from pi/3\\pi /3pi/3.