Quasi non-Markovian Approach to the Study of Decoherence of a Controlled-Not Quantum Gate in a Chain of Few Nuclear Spins Quantum Computer

The effect of frequency noise on correct operation of the multiple-control Toffoli, Fredkin, and Peres gates has been discussed. In the framework of the Ising model, the energy spectrum of a chain of atoms with nuclear spins one-half in a spinless semiconductor matrix has been obtained, and allowed transitions corresponding to the operation algorithm of these gates have been determined. The fidelities of the obtained transitions were studied depending on the number of control qubits and parameters of the radio-frequency control pulses. It has been shown that correct operation of the Toffoli and Fredkin gates does not depend on the number of control qubits, while the Peres gate fidelity decreases significantly with the increasing number of control signals. The calculated ratios of the Larmor frequency to the exchange interaction constant correspond with the results of other studies.

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Realization of a holonomic quantum computer in a chain of three-level systems

Physics Letters A ◽

10.1016/j.physleta.2015.10.015 ◽

2015 ◽

Vol 379 (47-48) ◽

pp. 3050-3053 ◽

Cited By ~ 7

Author(s):

Zeynep Nilhan Gürkan ◽

Erik Sjöqvist

Keyword(s):

Quantum Computer ◽

A Chain

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Experimental demonstration of a stimulated polarization wave in a chain of nuclear spins

New Journal of Physics ◽

10.1088/1367-2630/9/4/083 ◽

2007 ◽

Vol 9 (4) ◽

pp. 83-83 ◽

Cited By ~ 12

Author(s):

Jae-Seung Lee ◽

Travis Adams ◽

A K Khitrin

Keyword(s):

Experimental Demonstration ◽

Nuclear Spins ◽

Polarization Wave ◽

A Chain

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IMPLEMENTATION OF QUANTUM LOGIC OPERATIONS AND CREATION OF ENTANGLEMENT BETWEEN TWO NUCLEAR SPIN QUBITS WITH CONSTANT INTERACTION

International Journal of Quantum Information ◽

10.1142/s0219749906002353 ◽

2006 ◽

Vol 04 (06) ◽

pp. 975-1001

Author(s):

G. P. BERMAN ◽

G. W. BROWN ◽

M. E. HAWLEY ◽

D. I. KAMENEV ◽

V. I. TSIFRINOVICH

Keyword(s):

Quantum Logic ◽

Quantum Computer ◽

Magnetic Field Gradient ◽

Exchange Interactions ◽

Conditional Logic ◽

Perturbation Approach ◽

Nuclear Spins ◽

Logic Operations ◽

Quantum Protocol ◽

Silicon Based

We describe how to implement quantum logic operations in a silicon-based quantum computer with phosphorus atoms serving as qubits. The information is stored in the states of nuclear spins and the conditional logic operations are implemented through the electron spins using nuclear–electron hyperfine and electron–electron exchange interactions. The electrons in our computer should stay coherent only during implementation of one Controlled-NOT gate. The exchange interaction is constant, and selective excitations are provided by a magnetic field gradient. The quantum logic operations are implemented by rectangular radio-frequency pulses. This architecture is scalable and does not require manufacturing nanoscale electronic gates. As shown in this paper, parameters of a quantum protocol can be derived analytically even for a computer with a large number of qubits using our perturbation approach. We present the protocol for initialization of the nuclear spins and the protocol for creation of entanglement. All analytical results are tested numerically using a two-qubit system.

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Universal quantum circuit for n-qubit quantum gate: a programmable quantum gate

Quantum Information and Computation ◽

10.26421/qic7.3-4 ◽

2007 ◽

Vol 7 (3) ◽

pp. 228-242

Author(s):

P.B.M. Sousa ◽

R.V. Ramos

Keyword(s):

Quantum Computer ◽

Quantum Circuit ◽

Quantum Gate ◽

Quantum Circuits ◽

Unitary Matrices ◽

Quantum Operations ◽

Universal Quantum ◽

Np Problems ◽

Universal Quantum Circuit ◽

Specific Quantum

Quantum computation has attracted much attention, among other things, due to its potentialities to solve classical NP problems in polynomial time. For this reason, there has been a growing interest to build a quantum computer. One of the basic steps is to implement the quantum circuit able to realize a given unitary operation. This task has been solved using decomposition of unitary matrices in simpler ones till reach quantum circuits having only single-qubits and CNOTs gates. Usually the goal is to find the minimal quantum circuit able to solve a given problem. In this paper we go in a different direction. We propose a general quantum circuit able to implement any specific quantum circuit by just setting correctly the parameters. In other words, we propose a programmable quantum circuit. This opens the possibility to construct a real quantum computer where several different quantum operations can be realized in the same hardware. The configuration is proposed and its optical implementation is discussed.

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