Perturbation approach for nuclear magnetic resonance solid‐state quantum computation

Berman, G. P.; Kamenev, D. I.; Tsifrinovich, V. I.

doi:10.1155/s1110757x03110182

Cited by 4 publications

(11 citation statements)

References 16 publications

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“…First, we simulate the full adder protocol for a small number of qubits using an exact numerical solution [2,4] in order to calculate the phase errors and to test the quantum map approach. For the relation between the numerical and physical parameters see Refs.…”

Section: Numerical Resultsmentioning

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%

“…The probability amplitudes for the nonresonant transitions were calculated in Ref. [9]. If the state |i is initially populated, C i (t 0 ) = 1, then after application of one rectangular pulse with duration τ and frequency ν, resonant or near-resonant with the transition frequency of the kth spin, the probability amplitudes for the nonresonant transitions associated with…”

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%

“…For solution of problem (ii), we formulate the quantum dynamics in terms of quantum maps. We use the analytic formulas from [9] of the perturbation theory for the transition amplitudes of unwanted transitions. In this approach, one pulse of the protocol corresponds to one discrete step of the map.…”

Section: Introductionmentioning

confidence: 99%

See 4 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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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: Numerical Resultsmentioning

confidence: 99%

Section: A Probability Amplitudes For the Nonresonant Transitionsmentioning

confidence: 99%

Section: A Probability Amplitudes For the Nonresonant Transitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits

2006

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Creation of entanglement is considered theoretically and numerically in an ensemble of spin chains with dipole-dipole interaction between the spins. The unwanted effect of the long-range dipole interaction is compensated by the optimal choice of the parameters of radio-frequency pulses implementing the protocol. The errors caused by ͑i͒ the influence of the environment, ͑ii͒ nonselective excitations, ͑iii͒ influence of different spin chains on each other, ͑iv͒ displacements of qubits from their perfect locations, and ͑v͒ fluctuations of the external magnetic field are estimated analytically and calculated numerically. For the perfectly entangled state the z component M of the magnetization of the whole system is equal to zero. The errors lead to a finite value of M. If the number of qubits in the system is large, M can be detected experimentally. Using the fact that M depends differently on the parameters of the system for each kind of error, varying these parameters would allow one to experimentally determine the most significant source of errors and to optimize correspondingly the quantum computer design in order to decrease the errors and ͉M͉. Using our approach one can benchmark the quantum computer, decrease the errors, and prepare the quantum computer for implementation of more complex quantum algorithms.

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Minimization of Nonresonant Effects in a Scalable Ising Spin Quantum Computer

Berman

Kamenev

Tsifrinovich³

2004

Int. J. Quantum Inform.

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The errors caused by the transitions with large frequency offsets (nonresonant transitions) are calculated analytically for a scalable solid-state quantum computer based on a one-dimensional spin chain with Ising interactions between neighboring spins. Selective excitations of the spins are enabled by a uniform gradient of the external magnetic field. We calculate the probabilities of all unwanted nonresonant transitions associated with the flip of each spin with nonresonant frequency and with flips of two spins: one with resonant and one with nonresonant frequencies.It is shown that these errors oscillate with changing the gradient of the external magnetic field. Choosing the optimal values of this gradient allows us to decrease these errors by 50%.

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Perturbation approach for nuclear magnetic resonance solid‐state quantum computation

Cited by 4 publications

References 16 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

Creation of entanglement in a scalable spin quantum computer with long-range dipole-dipole interaction between qubits

Minimization of Nonresonant Effects in a Scalable Ising Spin Quantum Computer

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