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ANALYTIC SOLUTIONS FOR QUANTUM LOGIC GATES AND MODELING PULSE ERRORS IN A QUANTUM COMPUTER WITH A HEISENBERG INTERACTION

Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

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D. I. KAMENEV

Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA

Corresponding author.

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V. I. TSIFRINOVICH

IDS Department, Polytechnic University, Six Metrotech Center, Brooklyn, New York 11201, USA

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https://doi.org/10.1142/S0219749904000237Cited by:0 (Source: Crossref)

Abstract

We analyze analytically and numerically quantum logic gates in a one-dimensional spin chain with Heisenberg interaction. Analytic solutions for basic one-qubit gates and swap gate are obtained for a quantum computer based on logical qubits. We calculated the errors caused by imperfect pulses which implement the quantum logic gates. It is numerically demonstrated that the probability error is proportional to ε⁴, while the phase error is proportional to ε, where ε is the characteristic deviation from the perfect pulse duration.

Keywords:

PACS: 03.67.Lx, 75.10.Jm

References

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When the subsequent pulses of the protocol contribute to the same unwanted state, the probability amplitude generated by the pulse (whose phase can be assumed to be random) should be added to the probability amplitude of the unwanted state before the pulse. The result of the action of many pulses on one unwanted state can be presented as a multiple algebraic addition of complex numbers with random phases, and the change of the probability amplitude of each unwanted state can be described by the random walk model in two-dimensional (complex) plane. Due to this model, the probability amplitudes of the unwanted states grows as $\sqrt{M}$, where M is the number of pulses, and the total probability error is proportional to M . Google Scholar