Quantum State Tomography and Quantum Logical Operations in a Three Qubits NMR Quadrupolar System

Abstract

In this work, we present an implementation of quantum logic gates and algorithms in a three effective qubits system, represented by a (I = 7/2) NMR quadrupolar nuclei. To implement these protocols we have used the strong modulating pulses (SMP). The various stages of each implementation were verified by quantum state tomography (QST). It is presented here the results for the computational base states, Toffolli logic gates, and Deutsch-Jozsa and Grover algorithms.Also, we discuss the difficulties and advantages of implementing such protocols using the SMP technique in quadrupolar systems.

Quantum simulation of interaction blockade in a two-site Bose–Hubbard system with solid quadrupolar crystal

“…Consequently, the quadrupolar NMR quantum information processing has already attracted the interest of researchers [10,11]. Several basic experiments have been done in recent years, including the pseudo-pure state preparation [12], quantum state tomography [13], relaxation study [14], quantum algorithms [15] and some quantum simulation experiments [16,17]. In contrast to the systems with the spin-1 2 nuclei, the main obstacles of using quadrupolar nuclei as quantum information processors are as follows: firstly, the higher spin quantum number results in more energy levels, which makes the operations more difficult; secondly, the first-order quadrupolar Hamiltonian exists only in the solid and liquid crystalline states for the first-order quadrupolar coupling dynamically averaged to zero in the liquid states, which usually results in shorter decoherence times [18]; finally, the dipolar coupling between different quadrupolar nuclei is usually small which is a challenge for its scalability.…”

Classical bifurcation in a quadrupolar NMR system

“…,44 with τ = 5 μs. At each step, the pseudo-NSCS is tomographed by the quantum state tomography (QST) procedure [26,27]. QST enables us to reconstruct the deviation density matrix ( ρ) corresponding to the last stage of the system evolution.…”

Implementation of a quantum adiabatic algorithm for factorization on two qudits

“…The operators with one particle interactions can be implemented by a sequence of operators of selective z rotations in the following way: (10) for integer spins I, where and (11) for half integer spins I. For the squares of one particle operators for integer spins I, we obtain (13) for half integer spins I, we have (14) Operators with two particle interactions, (15) are constructed by combining several intervals of free evolution under Hamiltonian (1), whose lengths are multiples of periods 2π/q 1 , 2π/q 2 , 2π/ω 1 , and 2π/ω 2 , and the sets of operators of 180 degree y rotations. For such lengths, only the contribution of the spin-spin interaction remains in the evolution operator: (16) Both operators (15) and (16) are represented by diag onal matrices with matrix elements in the form of exponential functions exp(-iΦ m ), m = 1, 2, …, d 1 d 2 , with different phases.…”

“…The implementation of quantum algo rithms directly on multilevel systems (on qudits, in the presence of d levels) seems to be even more promising [7,8]. The conception of virtual qubits allows one to perform quantum computations even on the level of a single qudit: a quadrupole nucleus [9][10][11][12][13][14], a molecu lar magnetics [15], or a Rydberg atom [16]. However, to implement all the advantages of quantum computa tions over classical ones, one should apply multiqudit systems and multilevel logic [7,8,[17][18][19][20][21][22].…”