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:0710.3196 · Journal of Physics B Atomic Molecular and Optical Physics

Simulation of Grover's quantum search algorithm in an Ising-nuclear-spin-chain quantum computer with first- and second-nearest-neighbour couplings

Gustavo V. López, T. Gorin, Lorena Lara

Published Feb 26, 2008• 9 citations
arXivHTMLPDF

Abstract

We implement Grover's quantum search algorithm on a nuclear spin-chain quantum computer, taking Ising-type interactions between nearest and second-nearest neighbours into account. The performance of this implementation is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtain pronounced maxima at frequencies which fulfil the condition of the 2π k -method with respect to the second-nearest- neighbour interactions.

DOI
10.1088/0953-4075/41/5/055504

Related papers

Simulation of static and random errors on Grover's search algorithm implemented in an Ising nuclear spin chain quantum computer with a few qubits

T. Gorin, Lorena Lara, Gustavo V. López

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first- and second-neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called the fidelity. We analyse the behaviour of the fidelity as a function of the noise intensity for static and random noise on either the Larmor frequencies or the Rabi frequency, and we compare our results to theoretical predictions and numerical simulations which are based on more abstract quantum computer models.

arXiv:0902.0471•Journal of Physics B Atomic Molecular and Optical Physics•Apr 6, 2010•3 citations

Simulation of Grover's algorithm with position-variation of the ancilla qubit

Neris Ilano, Ronald S. Banzon, Cristine Dlr. Villagonzalo

We simulate Grover’s quantum search algorithm in an Ising spin chain quantum computer with nearest and second-nearest neighbour interactions. We determine the optimum Rabi frequency that satisfies the 2πk method by selecting a high fidelity value in the frequency scan for each database size. Also, we vary the position of the ancilla qubit and investigate the effect on the fidelity for different sizes of the database. The behavior of the fidelity as a function of the number of Grover iterations during the algorithm is considered. For a fixed location of the ancilla qubit, the overall fidelity decreases as we increase the size of the database.

Proceedings of the Samahang Pisika ng Pilipinas•Jun 3, 2015•0 citations

Chain of nuclear spins system quantum computer taking into account second neighbor Ising spins interaction and numerical simulation of Shor factorization of N=4

Gustavo V. López, Lorena Lara

For a one-dimensional chain of four nuclear spins (1/2) and taking into account first and second neighbor interactions among the spin system, we make the numerical simulation of Shor prime factorization algorithm of the integer number N=4 to study the influence of the second neighbor interaction on the performance of this algorithm. It is shown that the optimum Rabi's frequency to control the non-resonant effects is dominated by the second neighbor interaction coupling parameter ($J'$), and that a good Shor quantum factorization is achieved for a ratio of second to first coupling constant of $J'/J\ge 0.04$.

arXiv:quant-ph/0608148•Aug 18, 2006•0 citations

Simulation of quantum algorithm using modified qubit rotation

Neris I. Sombillo

We study the implementation of Grover’s algorithm in an Ising spin chain quantum computer. In our scheme, we removed the application of time delay whenever a qubit operation is performed. Instead, we introduced a set of modified pulses that utilizes the interaction of the neighboring qubit. In principle, the absence of time delay pulses allows the overall rotation pulses to be applied simultaneously to execute a gate. We show that the fidelity remains high after continuous application of π/2 pulses. The error arising from the unitary evolution is minimized by using soft pulses. Finally, the probability of finding the target state remain bounded through the application of fixed-point quantum search scheme.

AIP conference proceedings•Jan 1, 2023•0 citations

Simulation of the statical and dynamical noise on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer

T. Gorin, Lorena Lara, Gustavo V. López

•Feb 3, 2009•0 citations

Numerical simulation of Quantum Teleportation in a chain of three nuclear spins system taking into account second neighbor interaction

Gustavo V. López, Lorena Lara

For a one-dimensional chain of three nuclear spins (one half), we make the numerical simulation of quantum teleportation of a given state from one end of the chain to the other end, taking into account first and second neighbor interactions among the spins. It is shown that a well defined teleportation protocol is achieved for a ratio of the first to second neighbor interaction coupling constant of $J'/J\ge 0.04$. We also show that the optimum Rabi's frequency to control the non-resonant effects is dominated by the second neighbor interaction coupling parameter ($J'$).

arXiv:quant-ph/0608194•Aug 24, 2006•0 citations
We implement Grover's quantum search algorithm on a nuclear spin-chain quantum computer, taking Ising-type interactions between nearest and second-nearest neighbours into account. The performance of this implementation is studied by numerical simulations with four spins. We determine the temporal behaviour of the fidelity during the algorithm, and we compute the final fidelity as a function of the Rabi frequency. For the latter, we obtain pronounced maxima at frequencies which fulfil the condition of the 2π k -method with respect to the second-nearest- neighbour interactions.
We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first- and second-neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called the fidelity. We analyse the behaviour of the fidelity as a function of the noise intensity for static and random noise on either the Larmor frequencies or the Rabi frequency, and we compare our results to theoretical predictions and numerical simulations which are based on more abstract quantum computer models.
We simulate Grover’s quantum search algorithm in an Ising spin chain quantum computer with nearest and second-nearest neighbour interactions. We determine the optimum Rabi frequency that satisfies the 2πk method by selecting a high fidelity value in the frequency scan for each database size. Also, we vary the position of the ancilla qubit and investigate the effect on the fidelity for different sizes of the database. The behavior of the fidelity as a function of the number of Grover iterations during the algorithm is considered. For a fixed location of the ancilla qubit, the overall fidelity decreases as we increase the size of the database.
For a one-dimensional chain of four nuclear spins (1/2) and taking into account first and second neighbor interactions among the spin system, we make the numerical simulation of Shor prime factorization algorithm of the integer number N=4 to study the influence of the second neighbor interaction on the performance of this algorithm. It is shown that the optimum Rabi's frequency to control the non-resonant effects is dominated by the second neighbor interaction coupling parameter (J′J'J′), and that a good Shor quantum factorization is achieved for a ratio of second to first coupling constant of J′/J≥0.04J'/J\ge 0.04J′/J≥0.04.
We study the implementation of Grover’s algorithm in an Ising spin chain quantum computer. In our scheme, we removed the application of time delay whenever a qubit operation is performed. Instead, we introduced a set of modified pulses that utilizes the interaction of the neighboring qubit. In principle, the absence of time delay pulses allows the overall rotation pulses to be applied simultaneously to execute a gate. We show that the fidelity remains high after continuous application of π/2 pulses. The error arising from the unitary evolution is minimized by using soft pulses. Finally, the probability of finding the target state remain bounded through the application of fixed-point quantum search scheme.
For a one-dimensional chain of three nuclear spins (one half), we make the numerical simulation of quantum teleportation of a given state from one end of the chain to the other end, taking into account first and second neighbor interactions among the spins. It is shown that a well defined teleportation protocol is achieved for a ratio of the first to second neighbor interaction coupling constant of J′/J≥0.04J'/J\ge 0.04J′/J≥0.04. We also show that the optimum Rabi's frequency to control the non-resonant effects is dominated by the second neighbor interaction coupling parameter (J′J'J′).