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International Journal of Modern Physics B

STATE EVOLUTION AND INFORMATION PROCESSING IN Mn 12 QUANTUM MAGNET

Bin Zhou, Ruibao Tao, Shun-Qing Shen

Published Jul 30, 2004• 0 citations
Publisher

Abstract

Following an alternative version of Grover's algorithm, we propose a scheme to read- in information in Mn 12 molecular magnets with the help of multi-frequency magnetic pulses in two separate steps: first to realize an intermediate state |Ψ(T1)> and then to reach the state |Ψ(T2)> to encode information. All controllable parameters are calculated to implement read-in of information, and the durations of magnetic pulses are less than the dephasing time of quantum states in Mn 12. It is also shown that all the states of information can be initialized back to the intermediate state.

DOI
10.1142/s0217979204025439

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Following an alternative version of Grover's algorithm, we propose a scheme to read- in information in Mn 12 molecular magnets with the help of multi-frequency magnetic pulses in two separate steps: first to realize an intermediate state |Ψ(T1)> and then to reach the state |Ψ(T2)> to encode information. All controllable parameters are calculated to implement read-in of information, and the durations of magnetic pulses are less than the dephasing time of quantum states in Mn 12. It is also shown that all the states of information can be initialized back to the intermediate state.
Quantum computation in molecular magnets is studied by solving the time-dependent Schr\"odinger equation numerically. Following Leuenberger and Loss [Nature (London) 410,410,410, 789 (2001)], an external alternating magnetic field is applied to populate and manipulate a superposition of single-spin states in molecular magnet Mn12.{\mathrm{Mn}}_{12}.Mn12​. The conditions to realize parallel recording and reading databases of Grover algorithms in molecular magnets are discussed in detail. It is found that an accurate time duration of the magnetic pulse as well as the discrete frequency spectrum and the amplitudes are required to design a quantum computing device.
A single-step operation is proposed to produce multiqubit maximally entangled states in the NMR model. In the scheme, all qubits are initially in the ground state, and one single pulse of a multifrequency coherent magnetic radiation is applied to manipulate simultaneously the ``active states'' that satisfy the resonant conditions while all other ``inactive states'' remain unchanged. An effective Hamiltonian is derived in a generalized rotating frame, which allows us to predict the time evolution of ``active states'' generated by the magnetic pulse. The magnetic pulse parameters, such as frequencies, phases, amplitudes, and duration time, are obtained analytically to implement a Bell state of two qubits and a Greenberger-Horne-Zeilinger state of three qubits. The scheme has been generalized to create an NNN-qubit entangled state. Two rules are found to calculate the magnetic pulse parameters numerically, which are required to realize entangled states for even and odd qubits, respectively. The rules are successfully checked in the cases of $4\ensuremath{\leqslant}N\ensuremath{\leqslant}10$. The relation of lnt0\mathrm{ln}\phantom{\rule{0.3em}{0ex}}{t}_{0}lnt0​ and lnN\mathrm{ln}\phantom{\rule{0.3em}{0ex}}NlnN is found to be linear, and the duration time t0{t}_{0\phantom{\rule{0.3em}{0ex}}}t0​is approximately proportional to N\sqrt{N}N​.
We propose a scheme to realize a controlled-NOT quantum logic gate in a dimer of exchange coupled single-molecule magnets, [Mn 4 ] 2 . We chosen the ground state and the three low-lying excited states of a dimer in a finite longitudinal magnetic field as the quantum computing bases and introduced a pulsed transverse magnetic field with a special frequency. The pulsed transverse magnetic field induces the transitions between the quantum computing bases so as to realize a controlled-NOT quantum logic gate. The transition rates between a pair of the four quantum computing bases and between the quantum computing bases and excited states are evaluated and analysed.
With the development of quantum information and quantum computation science, quantum information processor has been widely used in different areas such as quantum simulation, quantum computation and quantum metrology and so on. To make quantum computer come true, we need to increase the number of controllable qubits of the system and improve the controllability to perform complex quantum manipulation. As a good experimental testbed for quantum information processing, nuclear magnetic resonance (NMR) spin system provides rich and sophisticated quantum control methods. In recent years a lot of multi-qubit experiments have been performed on the platform and a series of experimental technologies have been developed. In this paper, we firstly explain the difficulties of multi-qubit NMR experiments. Then by focusing on the experiment of 7-qubit labelled pseudo-pure state preparation and other relevant experiments, we review the technologies in multi-qubit experiments. Using the radio frequency selective method, the inhomogeneities of the radio frequency pulses are reduced and the spectral resolution is improved. After performing 1/2 spin selective sequence, we can regard the three methyl protons in the sample of crotonic acid as a single 1/2 spin nucleus and treat the whole molecule as a 7-qubit quantum information processor. We utilize Gauss pulses, Hermite pulses, composite pulses and gradient ascent pulse engineering (GRAPE) pulses to implement basic /2 and rotation operations. The GRAPE pulses are calculated by subspace GRAPE program to speed up the computation greatly. The errors of the basic pulses caused by chemical shift and J-coupling evolution can be estimated by the program of pulse compilation. It divides the errors of the pulses into a series of post-errors and pre-errors. A program of sequence compilation is used to eliminate the accumulated error of the whole pulse sequence, reduce the number of pulses and optimize the experimental duration. A variety of methods of quantum state tomography have been proposed to improve the efficiency of reading out information about quantum state. As an experimental example, we combine the above experimental technologies and perform the experiment of 7-qubit labelled pseudo-pure state preparation by using the method of cat state preparation. The sequence of cat state preparation consists of three steps:encoding procedure, phase cycling and decoding procedure. We use 14 experiments to realize the phase cycling and acquire the final 7-qubit labelled pseudo-pure state. The total duration of experimental sequence is about 132 ms. All the readout spectra have the similar shapes to the theoretical expectations. Finally we give an outlook for further research in this direction.
Abstract Molecular Nanomagnets may enable the implementation of qudit-based quantum error-correction codes which exploit the many spin levels naturally embedded in a single molecule, a promising step towards scalable quantum processors. To fully realize the potential of this approach, a microscopic understanding of the errors corrupting the quantum information encoded in a molecular qudit is essential, together with the development of tailor-made quantum error correction strategies. We address these central points by first studying dephasing effects on the molecular spin qudit produced by the interaction with surrounding nuclear spins, which are the dominant source of errors at low temperatures. Numerical quantum error correction codes are then constructed, by means of a systematic optimization procedure based on simulations of the coupled system-bath dynamics, that provide a striking enhancement of the coherence time of the molecular computational unit. The sequence of pulses needed for the experimental implementation of the codes is finally proposed.
Physical implementation of quantum-information processing by liquid-state nuclear magnetic resonance, using weakly coupled spin-12\frac{1}{2}21​ nuclei of a molecule, is well established. Nuclei with spin>1/2\mathrm{spin}>1/2spin>1/2 oriented in liquid-crystalline matrices is another possibility. Such systems have multiple qubits per nuclei and large quadrupolar couplings resulting in well separated lines in the spectrum. So far, creation of pseudopure states and logic gates has been demonstrated in such systems using transition selective radio-frequency pulses. In this paper we report two developments. First, we implement a quantum algorithm that needs coherent superposition of states. Second, we use evolution under quadrupolar coupling to implement multiqubit gates. We implement the Deutsch-Jozsa algorithm on a spin-32\frac{3}{2}23​ (2 qubit) system. The controlled-NOT operation needed to implement this algorithm has been implemented here by evolution under the quadrupolar Hamiltonian. To the best of our knowledge, this method has been implemented for the first time in quadrupolar systems. Since the quadrupolar coupling is several orders of magnitude greater than the coupling in weakly coupled spin-12\frac{1}{2}21​ nuclei, the gate time decreases, increasing the clock speed of the quantum computer.