Method for Implementation of Universal Quantum Logic Gates in a Scalable Ising Spin Quantum Computer

Berman, G. P.; Kamenev, D. I.; Kassman, R. B.; Pineda, Carlos; Tsifrinovich, V. I.

doi:10.1142/s0219749903000085

Cited by 23 publications

(46 citation statements)

References 24 publications

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“…The F-gates for the left addend qubit are defined in Table VI. We must note that the sets of phases ϕ in the Tables V and VI are not unique since the number of linear equations (which is equal to 8) for finding the phases is smaller than the number of variables, N, in these equations [1]. [N = 13 for F (0) and N = 15 for F (1).]…”

Section: Quantum Protocols For F-gatesmentioning

confidence: 99%

“…The gate F(1) also needs one more Control-Not gate and Not gate [3,14]. Implementation of only one Control-Not gate requires 15 or less pulses [1]. In…”

Section: Quantum Protocols For F-gatesmentioning

confidence: 99%

“…(18) are characterized by the large detuning |D| ≈ |k − k ′ |δω [1,2,4,9], which is approximately equal to the distance between the kth and k ′ th spins measured in the frequency units.…”

Section: A Probability Amplitudes For the Nonresonant Transitionsmentioning

confidence: 99%

“…(ii) Due to the nonlocality of interaction of the rf pulses with the qubits, the direct simulation of the dynamics requires either the solution of large system of coupled differential equations for a long period of time or the diagonalization of large matrices. In order to overcome these difficulties a perturbation theory was developed in our previous papers [1][2][3][4][5][6][7][8][9]. In this paper we apply our perturbation approach to simulate the dynamics of a full adder with 1000 qubits.…”

Section: Introductionmentioning

confidence: 99%

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Modeling Full Adder in Ising Spin Quantum Computer With 1000 Qubits Using Quantum Maps

Kamenev

Berman

Kassman

et al. 2004

Int. J. Quantum Inform.

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The quantum adder is an essential attribute of a quantum computer, just as classical adder is needed for operation of a digital computer. We model the quantum full adder as a realistic complex algorithm on a large number of qubits in an Ising-spin quantum computer. Our results are an important step toward effective modeling of the quantum modular adder which is needed for Shor's and other quantum algo- This allows us to reduce the calculation time to a reasonable value.

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Section: Quantum Protocols For F-gatesmentioning

confidence: 99%

“…The gate F(1) also needs one more Control-Not gate and Not gate [3,14]. Implementation of only one Control-Not gate requires 15 or less pulses [1]. In…”

Section: Quantum Protocols For F-gatesmentioning

confidence: 99%

Section: A Probability Amplitudes For the Nonresonant Transitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modeling Full Adder in Ising Spin Quantum Computer With 1000 Qubits Using Quantum Maps

Kamenev

Berman

Kassman

et al. 2004

Int. J. Quantum Inform.

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“…One of the promising candidates is an Ising spin chain. Implementations of Grover's search and other quantum algorithms in an Ising spin chain are done in [7,8]. In this paper, we modify the quantum search algorithm applied to an Ising spin chain using radio frequency pulses to suppress the oscillation.…”

Section: Introductionmentioning

confidence: 99%

Measurement-enhanced quantum search

Sombillo¹,

Banzon²,

Villagonzalo³

2017

AIP Conference Proceedings

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Abstract. The oscillatory nature of the unitary Grover operator makes quantum searching difficult if one has no prior knowledge of the number of target states in the database. In this work, we coupled the database to an external qubit to transfer the target state in a space where the quantum search operation is not applied. This is followed by a measurement of the external and the ancilla qubit which result to a mixed state with a higher probability of finding the target state. The algorithm is simulated in a spin chain having first and second order neighbor interactions. The result shows that the oscillation is suppressed and the probability of success generally increased with iteration number.

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Quantum Computation in a Ising Spin Chain Taking into Account Second Neighbor Couplings

2007

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We consider the realization of a quantum computer in a chain of nuclear spins coupled by an Ising interaction. Quantum algorithms can be performed with the help of appropriate radio-frequency pulses. In addition to the standard nearest-neighbor Ising coupling, we also allow for a second neighbor coupling. It is shown, how to apply the 2πk method in this more general setting, where the additional coupling eventually allows to save a few pulses. We illustrate our results with two numerical simulations: the Shor prime factorization of the number 4 and the teleportation of a qubit along a chain of 3 qubits. In both cases, the optimal Rabi frequency (to suppress non-resonant effects) depends primarily on the strength of the second neighbor interaction.

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Method for Implementation of Universal Quantum Logic Gates in a Scalable Ising Spin Quantum Computer

Cited by 23 publications

References 24 publications

Modeling Full Adder in Ising Spin Quantum Computer With 1000 Qubits Using Quantum Maps

Modeling Full Adder in Ising Spin Quantum Computer With 1000 Qubits Using Quantum Maps

Measurement-enhanced quantum search

Quantum Computation in a Ising Spin Chain Taking into Account Second Neighbor Couplings

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