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arXiv:quant-ph/0603227 · Physical Review A

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

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

Published Jun 29, 2006• 5 citations
arXivHTMLPDF

Abstract

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 (i) the influence of the environment, (ii) nonselective excitations, (iii) influence of different spin chains on each other, (iv) displacements of qubits from their perfect locations, and (v) 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 $\ensuremath{\mid}M\ensuremath{\mid}$. Using our approach one can benchmark the quantum computer, decrease the errors, and prepare the quantum computer for implementation of more complex quantum algorithms.

DOI
10.1103/physreva.73.062336

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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 (i) the influence of the environment, (ii) nonselective excitations, (iii) influence of different spin chains on each other, (iv) displacements of qubits from their perfect locations, and (v) fluctuations of the external magnetic field are estimated analytically and calculated numerically. For the perfectly entangled state the zzz component MMM of the magnetization of the whole system is equal to zero. The errors lead to a finite value of MMM. If the number of qubits in the system is large, MMM can be detected experimentally. Using the fact that MMM 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 \ensuremath∣M\ensuremath∣\ensuremath{\mid}M\ensuremath{\mid}\ensuremath∣M\ensuremath∣. Using our approach one can benchmark the quantum computer, decrease the errors, and prepare the quantum computer for implementation of more complex quantum algorithms.
We consider a one-dimensional chain of many superconducting quantum interference devices (SQUIDs), serving as charge qubits. Each SQUID is coupled to its nearest neighbor through constant capacitances. We study the quantum logic operations and implementation of entanglement in this system. Arrays with two and three qubits are considered in detail. We show that the creation of entanglement with an arbitrary number of qubits can be implemented, without systematic errors, even when the coupling between qubits is not small. A relatively large coupling constant allows one to increase the clock speed of the quantum computer. We analytically and numerically demonstrate the creation of the entanglement for this case, which can be a good test for the experimental implementation of a relatively simple quantum protocol with many qubits. The logic operations in a system with long-range interaction are not universal. We discuss a possible application of our approach for implementing universal quantum logic for more complex algorithms by decreasing the coupling constant and, correspondingly, decreasing the clock speed. The errors introduced by the long-range interaction for the universal logic gates are estimated analytically and calculated numerically. Our results can be useful for experimental implementation of quantum algorithms using controlled magnetic fluxes and gate voltages applied to the SQUIDs. The algorithms discussed in this paper can be implemented using already existing technologies in superconducting systems with constant interqubit coupling.
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We present protocols for implementation of universal quantum gates on an arbitrary superposition of quantum states in a scalable solid-state Ising spin quantum computer. The spin chain is composed of identical spins 1/2 with the Ising interaction between the neighboring spins. The selective excitations of the spins are provided by the gradient of the external magnetic field. The protocols are built of rectangular radio-frequency pulses. The phase and probability errors caused by unwanted transitions are minimized and computed numerically.