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

Computer Engineering and Science

NMR Simulation of the Multi-Qubit Grover Quantum Search Algorithm

Chunhong Lu

Published Jan 1, 2007• 1 citation
OpenAlex

Abstract

Currently,the NMR technology is one of the effective physical systems to realize quantum computation.As the multiple-quantum operator algebra theory mentions,any unitary transformation can be decomposed into a sequence of a limited number of one-qubit quantum gates and two-qubit diagonal gates.Based on these backgrounds,we propose a method to form NMR pulse sequences to realize the multi-qubit Grover quantum search algorithm.Experiments finish the algorithm with three-qubit,on a Quantum Computer Emulator.

Related papers

Modelling of Grover’s quantum search algorithms: implementations of Simple quantum simulators on classical computers

Sergey Victorovich Ulyanov, Andrey G. Reshetnikov, Olga Tyatyushkina

Models of Grover’s search algorithm is reviewed to build the foundation for the other algorithms. Thereafter, some preliminary modifications of the original algorithms by others are stated, that increases the applicability of the search procedure. A general quantum computation on an isolated system can be represented by a unitary matrix. In order to execute such a computation on a quantum computer, it is common to decompose the unitary into a quantum circuit, i.e., a sequence of quantum gates that can be physically implemented on a given architecture. There are different universal gate sets for quantum computation. Here we choose the universal gate set consisting of CNOT and single-qubit gates. We measure the cost of a circuit by the number of CNOT gates as they are usually more difficult to implement than single qubit gates and since the number of single-qubit gates is bounded by about twice the number of CNOT’s.

System Analysis in Science and Education•Sep 30, 2020•4 citations

Experimental NMR implementation of a robust quantum search algorithm

Avik Mitra, Avatar Tulsi, Anil Kumar

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 practically searched. The lack of robustness of Grover's algorithm for a large number of qubits is due to quite stringent "phase-matching" condition. To overcome this limitation, Tulsi suggested a modified search algorithm [PRA 78, 022332] which succeeds as long as the errors are reproducible and reversible while Grover's algorithm fails. Such systematic errors arise often from imperfections in apparatus setup e.g. the errors arising from imperfect pulse calibration and offset effect in NMR systems. In this paper, we report the experimental NMR implementation of the modified search algorithm and its comparison with the original Grover's algorithm. We experimentally validate the theoretical predictions made by Tulsi.

arXiv:0912.4071•Dec 21, 2009•1 citation

Circuits and simulation of multi-qubit quantum wavelet transforms

Zhu Xuan-yi

Because of the prominent advantages of quantum computation compared to classic computation,implementation of quantum wavelet transforms has profound significance to its completion and application,which based on the circuits of those transforms.In this paper,the circuits of 3-qubit Haar and D(4) wavelet transforms are designed by way of multiple-quantum operator algebra theory.Furthermore,the circuits are evolved into pulse sequences,which can be implemented in a real NMR system.Finally,based on the simulation on a Quantum Computer Emulator,the circuits are verified to be reasonable.

Computer Engineering and Applications Journal•Jan 1, 2008•0 citations

Solving the quantum search problem in polynomial time on an NMR quantum computer

Xijia Miao

The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in polynomial time on an NMR quantum computer. The NMR ensemble quantum computation is based on the quantum mechanical unitary dynamics that both a closed quantum system and its ensemble obey the same quantum mechanical unitary dynamics instead of on the pseudopure state or the effective pure state of the classical NMR quantum computation. Based on the new principle the conventional NMR multiple-quantum spectroscopy has been developed to solve experimentally the search problem. The solution information of the search problem is first loaded on the unitary evolution propagator which is constructed with the oracle unitary operation and oracle-independent unitary operations and is used to excite the multiple-quantum coherence in a spin ensemble. Then the multiple- quantum spectroscopy is used to extract experimentally the solution information. It has been discussed how to enhance the output NMR signal of the quantum search NMR multiple-quantum pulse sequence and some approaches to enhancing the NMR signal are also proposed. The present work could be helpful for conventional high field NMR machines to solve efficiently the quantum search problem.

arXiv:quant-ph/0206102•Jun 16, 2002•4 citations

Orchestrating an NMR quantum computation: the N=3 Deutsch-Jozsa algorithm

David C. Collins, K. W. Kim, William C. Holton +2 more

A detailed description of the development of a three qubit NMR realization of the Deutsch-Jozsa algorithm [Collins et.al., Phys. Rev. A 62, 022304 (2000)] is provided. The theoretical and experimental techniques used for the reduction of the algorithm's evolution steps into a sequence of NMR pulses are discussed at length. This includes the description of general pulse sequence compilation techniques, various schemes for indirectly coupled gate realizations, experimental pulse parameterization techniques and bookkeeping methods for pulse phases.

arXiv:quant-ph/0105045•May 10, 2001•0 citations

Efficient Grover search with Rydberg blockade

Klaus Mølmer, Larry Isenhower, Mark E. Saffman

We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple π-pulse excitation sequences between ground and Rydberg excited states readily produce the key conditional phase shift and inversion-about-the-mean unitary operations for the Grover search. Multi-qubit implementation schemes suitable for different properties of the atomic interactions are identified and the error scaling of the protocols with system size is found to be promising for experimental investigation.

arXiv:1102.3573•Journal of Physics B Atomic Molecular and Optical Physics•Sep 14, 2011•54 citations
Currently,the NMR technology is one of the effective physical systems to realize quantum computation.As the multiple-quantum operator algebra theory mentions,any unitary transformation can be decomposed into a sequence of a limited number of one-qubit quantum gates and two-qubit diagonal gates.Based on these backgrounds,we propose a method to form NMR pulse sequences to realize the multi-qubit Grover quantum search algorithm.Experiments finish the algorithm with three-qubit,on a Quantum Computer Emulator.
Models of Grover’s search algorithm is reviewed to build the foundation for the other algorithms. Thereafter, some preliminary modifications of the original algorithms by others are stated, that increases the applicability of the search procedure. A general quantum computation on an isolated system can be represented by a unitary matrix. In order to execute such a computation on a quantum computer, it is common to decompose the unitary into a quantum circuit, i.e., a sequence of quantum gates that can be physically implemented on a given architecture. There are different universal gate sets for quantum computation. Here we choose the universal gate set consisting of CNOT and single-qubit gates. We measure the cost of a circuit by the number of CNOT gates as they are usually more difficult to implement than single qubit gates and since the number of single-qubit gates is bounded by about twice the number of CNOT’s.
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 practically searched. The lack of robustness of Grover's algorithm for a large number of qubits is due to quite stringent "phase-matching" condition. To overcome this limitation, Tulsi suggested a modified search algorithm [PRA 78, 022332] which succeeds as long as the errors are reproducible and reversible while Grover's algorithm fails. Such systematic errors arise often from imperfections in apparatus setup e.g. the errors arising from imperfect pulse calibration and offset effect in NMR systems. In this paper, we report the experimental NMR implementation of the modified search algorithm and its comparison with the original Grover's algorithm. We experimentally validate the theoretical predictions made by Tulsi.
Because of the prominent advantages of quantum computation compared to classic computation,implementation of quantum wavelet transforms has profound significance to its completion and application,which based on the circuits of those transforms.In this paper,the circuits of 3-qubit Haar and D(4) wavelet transforms are designed by way of multiple-quantum operator algebra theory.Furthermore,the circuits are evolved into pulse sequences,which can be implemented in a real NMR system.Finally,based on the simulation on a Quantum Computer Emulator,the circuits are verified to be reasonable.
The quantum search problem is an important problem due to the fact that a general NP problem can be solved efficiently by an unsorted quantum search algorithm. Here it has been shown that the quantum search problem could be solved in polynomial time on an NMR quantum computer. The NMR ensemble quantum computation is based on the quantum mechanical unitary dynamics that both a closed quantum system and its ensemble obey the same quantum mechanical unitary dynamics instead of on the pseudopure state or the effective pure state of the classical NMR quantum computation. Based on the new principle the conventional NMR multiple-quantum spectroscopy has been developed to solve experimentally the search problem. The solution information of the search problem is first loaded on the unitary evolution propagator which is constructed with the oracle unitary operation and oracle-independent unitary operations and is used to excite the multiple-quantum coherence in a spin ensemble. Then the multiple- quantum spectroscopy is used to extract experimentally the solution information. It has been discussed how to enhance the output NMR signal of the quantum search NMR multiple-quantum pulse sequence and some approaches to enhancing the NMR signal are also proposed. The present work could be helpful for conventional high field NMR machines to solve efficiently the quantum search problem.
A detailed description of the development of a three qubit NMR realization of the Deutsch-Jozsa algorithm [Collins et.al., Phys. Rev. A 62, 022304 (2000)] is provided. The theoretical and experimental techniques used for the reduction of the algorithm's evolution steps into a sequence of NMR pulses are discussed at length. This includes the description of general pulse sequence compilation techniques, various schemes for indirectly coupled gate realizations, experimental pulse parameterization techniques and bookkeeping methods for pulse phases.
We present efficient methods to implement the quantum computing Grover search algorithm using the Rydberg blockade interaction. We show that simple π-pulse excitation sequences between ground and Rydberg excited states readily produce the key conditional phase shift and inversion-about-the-mean unitary operations for the Grover search. Multi-qubit implementation schemes suitable for different properties of the atomic interactions are identified and the error scaling of the protocols with system size is found to be promising for experimental investigation.