Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Nanomanufacturing

Spin coupling damp decay of force cantilever microscopy design based on Grover's algorithm magnetic resonance quantum computing

R. Ren, Weiren Wang, Xuan Li, Zhongxia Zhao, Lin Liu, Song Chen

Published Jan 1, 2014• 0 citations
Publisher

Abstract

We displayed the nuclear spin coupling and dipole polarisation in magnetic resonance microscopy based on quantum calculation. When radio frequency (rf) probing operated nuclear spins on the nanometer localisation, Grover’s quantum algorithm can be realised by polarisation enhanced states using pulse sequence and width according to the interaction between RF and spins. We theoretically proposed two-qubits quantum system of density matrix to achieve quantum Grover’s algorithm in spin damp and frequency shift based on magnetic resonance microscopy. The nuclear spins were operated by pulse time sequences of cyclic adiabatic inversion, and controlled the quantum spin magnetic moment state to achieve the superposition. The resonance spins excited by radio frequency coil and magnetic tip were measured by the nuclear magnetic moment, spectrum and density matrix. The results indicated that the density matrix was used to read out quantum spectrum image. Grover’s algorithm can perform search faster than their classical counterparts. The force microscopy properties of spin damp decay holds great promise of magnetic resonance in quantum computing, quantum communication. Theoretically the algorithm is accelerated but not 100% in a rate of success.

DOI
10.1504/ijnm.2014.059010

Related papers

Application of magnetic resonance force microscopy cyclic adiabatic inversion for a single-spin measurement

G. P. Berman, F. Borgonovi, George Chapline +5 more

We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) with a cyclic adiabatic inversion (CAI). This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a cantilever modelled by a quantum oscillator in a coherent state in a quasi-classical range of parameters. The entire system is treated rigorously within the framework of the Schrödinger equation. For a many-spin system our equations accurately describe conventional MRFM experiments involving CAI of the spin system. Our computer simulations of the quantum spin–cantilever dynamics show that the probability distribution for the cantilever position develops two asymmetric peaks with the total relative probabilities mainly dependent on the initial angle between the directions of the average spin and the effective magnetic field, in the rotating frame. We show that each of the peaks is correlated with the direction of the average spin (being along or opposite to the direction of the effective magnetic field). This generates two possible outcomes of a single-spin measurement, similar to the Stern–Gerlach effect. We demonstrate that the generation of the second peak can be significantly suppressed by turning on adiabatically the amplitude of the rf magnetic field. We also show that MRFM CAI can be used both for detecting a signal from a single spin, and for measuring the single-spin state by measuring the phase of the cantilever driving oscillations.

arXiv:quant-ph/0108025•Journal of Physics A Mathematical and General•Apr 2, 2003•12 citations

Quantum computation in a one-dimensional crystal lattice with NMR force microscopy

Thaddeus D. Ladd, J. R. Goldman, Aykutlu Dâna +2 more

A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar couplings with decoupling and selective recoupling RF pulse sequences. Magnetic resonance force microscopy is used for readout. As many as 300 qubits can be implemented in the laboratory extremes of T=10 mK and B_0=20 T with the existing sensitivity of force microscopy.

arXiv:quant-ph/0009122•Sep 28, 2000•8 citations

Solid-state nuclear-spin quantum computer based on magnetic resonance force microscopy

G. P. Berman, G. D. Doolen, P. C. Hammel +1 more

We propose a nuclear-spin quantum computer based on magnetic resonance force microscopy (MRFM). It is shown that an MRFM single-electron spin measurement provides three essential requirements for quantum computation in solids: (a) preparation of the ground state, (b) one- and two-qubit quantum logic gates, and (c) a measurement of the final state. The proposed quantum computer can operate at temperatures up to 1 K.

arXiv:quant-ph/9909033•Physical review. B, Condensed matter•Jun 1, 2000•54 citations

Modelling Molecular Technologies for Nuclear Magnetic Resonance Quantum Computing

Mario Simoni

Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.

•Apr 1, 2020•0 citations

Experimental realization of a continuous version of the Grover algorithm

Vladimir L. Ermakov, B. M. Fung

A continuous, analog version of the Grover algorithm is realized using NMR. The system studied is ${}^{23}\mathrm{Na}$ in a liquid-crystal medium. The presence of quadrupolar coupling makes the spin $I=3/2$ nucleus a two-qubit system. Applying a specially designed pulse sequence, the time evolution of the spin-density operator is described in an interaction representation that has no external time-dependent radio-frequency fields. This approach is used to implement one instance of the continuous Grover search for the transform of a uniform state to a target state, and the implementation provides a clear physical interpretation of the algorithm. The experimental results are in good agreement with the theory.

arXiv:quant-ph/0208145•Physical Review A•Oct 15, 2002•45 citations

Quantum dynamics of the oscillating cantilever-driven adiabatic reversals in magnetic resonance force microscopy

G. P. Berman, F. Borgonovi, V. I. Tsifrinovich

We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schr\"odinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.

arXiv:quant-ph/0306107•Quantum Information and Computation•Mar 1, 2004•7 citations
We displayed the nuclear spin coupling and dipole polarisation in magnetic resonance microscopy based on quantum calculation. When radio frequency (rf) probing operated nuclear spins on the nanometer localisation, Grover’s quantum algorithm can be realised by polarisation enhanced states using pulse sequence and width according to the interaction between RF and spins. We theoretically proposed two-qubits quantum system of density matrix to achieve quantum Grover’s algorithm in spin damp and frequency shift based on magnetic resonance microscopy. The nuclear spins were operated by pulse time sequences of cyclic adiabatic inversion, and controlled the quantum spin magnetic moment state to achieve the superposition. The resonance spins excited by radio frequency coil and magnetic tip were measured by the nuclear magnetic moment, spectrum and density matrix. The results indicated that the density matrix was used to read out quantum spectrum image. Grover’s algorithm can perform search faster than their classical counterparts. The force microscopy properties of spin damp decay holds great promise of magnetic resonance in quantum computing, quantum communication. Theoretically the algorithm is accelerated but not 100% in a rate of success.
We consider the process of a single-spin measurement using magnetic resonance force microscopy (MRFM) with a cyclic adiabatic inversion (CAI). This technique is also important for different applications, including a measurement of a qubit state in quantum computation. The measurement takes place through the interaction of a single spin with a cantilever modelled by a quantum oscillator in a coherent state in a quasi-classical range of parameters. The entire system is treated rigorously within the framework of the Schrödinger equation. For a many-spin system our equations accurately describe conventional MRFM experiments involving CAI of the spin system. Our computer simulations of the quantum spin–cantilever dynamics show that the probability distribution for the cantilever position develops two asymmetric peaks with the total relative probabilities mainly dependent on the initial angle between the directions of the average spin and the effective magnetic field, in the rotating frame. We show that each of the peaks is correlated with the direction of the average spin (being along or opposite to the direction of the effective magnetic field). This generates two possible outcomes of a single-spin measurement, similar to the Stern–Gerlach effect. We demonstrate that the generation of the second peak can be significantly suppressed by turning on adiabatically the amplitude of the rf magnetic field. We also show that MRFM CAI can be used both for detecting a signal from a single spin, and for measuring the single-spin state by measuring the phase of the cantilever driving oscillations.
A proposal for a scalable, solid-state implementation of a quantum computer is presented. Qubits are fluorine nuclear spins in a solid crystal of fluorapatite [Ca_5 F(PO_4)_3] with resonant frequencies separated by a large field gradient. Quantum logic is accomplished using nuclear-nuclear dipolar couplings with decoupling and selective recoupling RF pulse sequences. Magnetic resonance force microscopy is used for readout. As many as 300 qubits can be implemented in the laboratory extremes of T=10 mK and B_0=20 T with the existing sensitivity of force microscopy.
Standard CMOS circuits are expected to be no longer able to satisfy nowadays demand for higher performances and lower power consumption. This commits to look for new solutions. Quantum computation, whose fundamental quantity of information is the qubit, is a thoroughly new way of thinking to electronics. There are at least two main reasons for which quantum computing is expected to broaden computation horizons. First, specific algorithms can be engineered, manipulating the probability amplitudes of different states, to exploit the quantum superposition principle and achieve high parallelism. Second, it is expected to be spontaneously suitable to simulate complex quantum physical systems, as large molecules. Quantum computing requires the cooperation of several scientific fields. The leading idea has been to highlight the operations and algorithms a quantum computer must be able to perform and, then, to propose a hardware solution, providing the rigorous physical treatment mandatory for a deep understanding and for an appropriate modelling, something which is hard to find in nowadays literature. Thus, the first chapters address the quantum algorithms, focusing on Grover's search algorithm and deriving, from fundamentals, the corresponding circuit. The latter is then described in Quantum Assembly (QASM), which can be seen as the quantum equivalent of VHDL, and simulated on IBM Q Experience. The following chapters deal with a possible physical implementation of quantum processors: the encoding of qubits on nuclear spins in diamagnetic molecules. When a static magnetic field is applied to a spin-1/2 nucleus, two well-defined energy eigenstates arise, as a result of the Zeeman effect. Each of them can be associated with a qubit eigenstate. Thanks to nuclear magnetic resonance principles, the probability with which one of the two eigenstates is measured can be handled by the superposition of a radio frequency field at the resonance frequency of the nucleus. This can be interpreted as a rotation of the spin, and so of the qubit, about the RF field and enables the execution of single qubit quantum gates, since they are simple rotations of the state vector. The two-qubit CNOT gate is obtained through the interaction of spins via J-coupling. Considering that these gates constitute a universal set, every quantum algorithm can theoretically be run on an NMR processor. Different nuclei have different resonant frequencies, but the addressing of a specific spin can be achieved also in homonuclear molecules, since the resonant frequency depends also on the nuclear environment (nuclear shielding). While unwanted J-couplings can be removed thanks to refocusing, spin decoherence and relaxation phenomena force an upper limit to the allowed timescale. A main advantage of NMR is that this timescale is long, even at room temperature. Conversely, scalability is still an issue. A simple heteronuclear MATLAB model, based on the relations derived from first principles in the thesis, is proposed to prove the feasibility of NMR quantum processors. The input technological parameters, as chemical shielding and J-coupling, can be computed resorting on ORCA, or obtained from experimental data. The model, able to run a universal set of quantum gates and simple algorithms, can be useful to find an optimal operating point as a compromise between molecule physical properties and the quantities which can be controlled by nowadays NMR instrumentation.
A continuous, analog version of the Grover algorithm is realized using NMR. The system studied is 23Na{}^{23}\mathrm{Na}23Na in a liquid-crystal medium. The presence of quadrupolar coupling makes the spin I=3/2I=3/2I=3/2 nucleus a two-qubit system. Applying a specially designed pulse sequence, the time evolution of the spin-density operator is described in an interaction representation that has no external time-dependent radio-frequency fields. This approach is used to implement one instance of the continuous Grover search for the transform of a uniform state to a target state, and the implementation provides a clear physical interpretation of the algorithm. The experimental results are in good agreement with the theory.
We simulated the quantum dynamics for magnetic resonance force microscopy (MRFM) in the oscillating cantilever-driven adiabatic reversals (OSCAR) technique. We estimated the frequency shift of the cantilever vibrations and demonstrated that this shift causes the formation of a Schr\"odinger cat state which has some similarities and differences from the conventional MRFM technique which uses cyclic adiabatic reversals of spins. The interaction of the cantilever with the environment is shown to quickly destroy the coherence between the two possible cantilever trajectories. We have shown that using partial adiabatic reversals, one can produce a significant increase in the OSCAR signal.