# Is partial quantum search of a database any easier?

@inproceedings{Grover2004IsPQ, title={Is partial quantum search of a database any easier?}, author={Lov K. Grover and Jaikumar Radhakrishnan}, booktitle={ACM Symposium on Parallelism in Algorithms and Architectures}, year={2004} }

We consider the partial database search problem where given a quantum database <i>f</i> : {0,1}<sup>n</sup>→{0,1} such that <i>f</i>(<i>x</i>) =1 for a unique <i>x</i> ∈ {0,1}<sup>n</sup>, we are required to determine <i>only</i> the first <i>k</i> bits of the address <i>x</i>. We present an algorithm and derive a lower bound for this problem. Let <i>q</i>(<i>k,n</i>) be the minimum number of queries needed to find the first <i>k</i> bits of the required address <i>x</i> with certainty (or with…

## 50 Citations

### Simple Algorithm for Partial Quantum Search

- Computer ScienceQuantum Inf. Process.
- 2006

A quantum algorithm is presented for this problem of partial search that takes about 0.34 $$\sqrt{b}$$ fewer iterations than the quantum search algorithm.

### Quantum Algorithm for Dynamic Programming Approach for DAGs. Applications for Zhegalkin Polynomial Evaluation and Some Problems on DAGs

- Computer ScienceUCNC
- 2019

A quantum algorithm for dynamic programming approach for problems on directed acyclic graphs (DAGs) that can solve problems that use OR, AND, NAND, MAX and MIN functions as the main transition steps and is useful for a couple of problems.

### HIERARCHICAL QUANTUM SEARCH

- Computer Science
- 2005

It is proved that the optimized version of the algorithm discovered by Grover and Radhakrishnan and called GRK, which is applied to a database with a single target item, is faster than the full search.

### Quantum partial search algorithm with smaller oracles for multiple target items

- Computer ScienceQuantum Information Processing
- 2022

This paper presents a punctuated version of the quantum partial search algorithm with smaller oracles, which reduces the difficulty of designing oracles without errors and is practical for running on a quantum computer and solving many real problems, such as the Hamiltonian circuit problem and solving systems of nonlinear equations.

### Performance Analysis and Parameter Optimization of the Optimal Fixed-Point Quantum Search

- Computer Science, MathematicsApplied Sciences
- 2019

This paper derives the sufficient and necessary condition on the number of feasible iterations, based on which the exact least number of iterations can be obtained, and analytically derives the optimal δ which minimizes the query complexity.

### Binary quantum search

- Computer ScienceSPIE Defense + Commercial Sensing
- 2007

A database with one target item and number of queries necessary for sequential searches is calculated and it is shown that sequential partial search can be done faster the first one.

### 06 03 13 6 v 1 1 5 M ar 2 00 6 Sure success partial search

- Computer Science
- 2018

An optimal version of the partial search algorithm, known as GRK algorithm is reviewed and a modification to the phases for the final step is proposed to guarantee sure success of thepartial search algorithm.

### Quantum Algorithm for Dynamic Programming Approach for DAGs and Applications

- Computer Science
- 2022

A quantum algorithm for the dynamic programming approach for problems on directed acyclic graphs (DAGs) that can solve problems that use OR, AND, NAND, MAX, and MIN functions as the main transition steps and is useful for a couple of problems.

### Quest for Fast Partial Search Algorithm

- Computer ScienceQuantum Inf. Process.
- 2006

This work considers different partial search algorithms and argues that the algorithm originally suggested by Grover and Radhakrishnan and modified by Korepin is the optimal one.

### First experimental demonstration of an exact quantum search algorithm in nuclear magnetic resonance system

- Computer ScienceScience China Physics, Mechanics & Astronomy
- 2015

The first experimental realization of the improved Grover algorithm is given, which finds a marked state with certainty, in a nuclear magnetic resonance system, and the experimental results agree well with the theoretical predictions.

## References

SHOWING 1-9 OF 9 REFERENCES

### Simple Algorithm for Partial Quantum Search

- Computer ScienceQuantum Inf. Process.
- 2006

A quantum algorithm is presented for this problem of partial search that takes about 0.34 $$\sqrt{b}$$ fewer iterations than the quantum search algorithm.

### Family of sure-success quantum algorithms for solving a generalized Grover search problem

- Computer Science
- 2002

An infinite family of sure-success quantum algorithms are introduced here to solve Grover's search problem, each member for a different range of f, and are particularly useful when the cost of failure of a search is very high, and for multistage searches with a different search criterion for each stage.

### Tight bounds on quantum searching

- Computer Science
- 1996

A lower bound on the efficiency of any possible quantum database searching algorithm is provided and it is shown that Grover''s algorithm nearly comes within a factor 2 of being optimal in terms of the number of probes required in the table.

### GROVER'S QUANTUM SEARCHING ALGORITHM IS OPTIMAL

- Computer Science
- 1999

I show that for any number of oracle lookups up to about {pi}/4thinsp{radical} (N) , Grover{close_quote}s quantum searching algorithm gives the maximal possible probability of finding the desired…

### Grover algorithm with zero theoretical failure rate

- Mathematics
- 2001

In a standard Grover's algorithm for quantum searching, the probability of finding the marked item is not exactly 1. In this paper we present a modified version of Grover's algorithm that searches a…

### Quantum computation and quantum information

- Physics, Computer Science
- 2000

This chapter discusses quantum information theory, public-key cryptography and the RSA cryptosystem, and the proof of Lieb's theorem.

### Quantum Amplitude Amplification and Estimation

- Mathematics
- 2000

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…

### Strengths and Weaknesses of Quantum Computing

- Computer ScienceSIAM J. Comput.
- 1997

It is proved that relative to an oracle chosen uniformly at random with probability 1 the class $\NP$ cannot be solved on a quantum Turing machine (QTM) in time $o(2^{n/2})$.

### A Grover-based quantum search of optimal order for an unknown number of marked elements

- Computer Science, Mathematics
- 1999

For every prescribed success probability I give an algorithm consisting of several runs of Grover's algorithm that matches a recent bound by Buhrman and de Wolf on the order of the number of queries to the black box.