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

arXiv:quant-ph/0406209 · Journal of Optics B Quantum and Semiclassical Optics

Modularization of a multi-qubit controlled phase gate and its nuclear magnetic resonance implementation

Jingfu Zhang, Wenzhang Liu, Zhiwei Deng, Zhiheng Lu, Gui Lu Long

Published Dec 4, 2004• 25 citations
arXivHTMLPDF

Abstract

A quantum circuit network is a set of circuits that implements a certain computation task. Being at the centre of the quantum circuit network, the multi-qubit controlled phase shift is one of the most important quantum gates. In this paper, we apply the method of modular structuring in classical computer architecture to the quantum computer and give a recursive realization of the multi-qubit phase gate. This realization of the controlled phase shift gate is convenient in realizing certain quantum algorithms. We have experimentally implemented this modularized multi-qubit controlled phase gate in a three-qubit nuclear magnetic resonance (NMR) quantum system. The network is demonstrated experimentally using line selective pulses in the NMR technique. The procedure has the advantage of being simple and easy to implement.

DOI
10.1088/1464-4266/7/1/005

Related papers

NMR experimental realization of seven-qubit D-J algorithm and controlled phase-shift gates with improved precision

Daxiu Wei, J. L. Luo, Xianping Sun +4 more

In this study, we report the experimental realization of seven-qubit Deutsch-Jozsa (D-J) algorithm and controlled phase-shift gates with improved precision using liquid state nuclear magnetic resonance (NMR). The experimental results have shown that transformationsU f in the seven-qubit D-J algorithm have been implemented with different pulse sequences, and whetherf is constant or balanced is determined by using only a single function call (U f ). Furthermore, we propose an experimental method to measure and correct the error in the controlled phase-shift gate that is simple and feasible in experiments, and can have precise phase shifts. These may offer the possibility of surmounting the difficulties of low signal-to-noise ratio (SNR) in multi-qubit NMR quantum computers, more complicated experimental techniques, and the increase of gate errors due to using a large number of imperfect selective pulses. These are also applied to more complicated quantum algorithms with more qubits, such as quantum Fourier transformation and Shor’s algorithm.

Chinese Science Bulletin•Jan 1, 2003•6 citations

Experimental technique for multi-qubit nuclear magnetic resonance system

Pan Jian, Yu Qi, Xinhua Peng

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.

Acta Physica Sinica•Jan 1, 2017•2 citations

Experimental implementation of quantum gates with one and two qubits using Nuclear Magnetic Resonance

José Luis Figueiredo

Nuclear Magnetic Ressonance (NMR) is a widely used technique, with a long history of applications in chemestry, medicine, and material science. Twenty years ago, it emerged as a reliable source for quantum computing too, since the work of Cory. One of its major advantage is the ease with which arbitrary unitary transformations can be implemented, together with its experimental simplicity, that can be traced back to very simple NMR routines, which were being extensively used long before. However, some disadvantages came along, mostly related to experimental effort in the initialisation and measure processes, and scalability. In this work, we have successfully probed some simple quantum gates (Pauli-Z, Pauli-X and Hadamard) in one and two-qubit systems, realised in a NMR experiment. The work comprised a pseudo-pure state preparation, followed by the application of the gates, and a quantum tomography method, necessary to reconstruct the density matrix. The experiments were conducted with a chloroform sample, placed in a 300 MHz Bruker Avance II spectrometer, equipped with a superconducting magnet with a 7 T magnetic field.

arXiv:2102.11213•Feb 22, 2021•0 citations

Generalized methods for the development of quantum logic gates for an NMR quantum information processor

Mark D. Price, Shyamal S. Somaroo, A. E. Dunlop +2 more

Logic gates such as the controlled-NOT (c-NOT) and Toffoli gates play a key role in quantum information processing (QIP) and quantum computing. A natural extension of such gates would necessarily operate on one quantum bit (qubit) conditional on the state of the remaining qubits in the system. We show that such selective gates, termed $(\mathrm{controlled}{)}^{n}\ensuremath{-}\mathrm{NOT}$ gates, or ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates, are convenient in nuclear magnetic resonance (NMR) implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometric algebra. These methods yield equivalent NMR pulse sequences for the generation of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for any number of control spins. In this work, a catalog of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for systems of as many as 16 spins is provided along with an experimental implementation of a ${\mathrm{c}}^{3}\ensuremath{-}\mathrm{N}\mathrm{O}\mathrm{T}$ gate on a four spin system, ${}^{13}\mathrm{C}$ alanine.

Physical Review A•Oct 1, 1999•65 citations

Experimental realization of 7-qubit universal perfect controlled-NOT and controlled square-root NOT gates

Daxiu Wei, Xiaodong Yang, Jun Luo +4 more

The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.

arXiv:quant-ph/0109002•Sep 1, 2001•1 citation

Implementation of Quantum Logic Gates by Nuclear Magnetic Resonance Spectroscopy

Jiangfeng Du, Jihui Wu, Ming-Jun Shi +5 more

Using nuclear magnetic resonance techniques with a solution of cytosine molecules, we show an implementation of certain quantum logic gates (including NOT gate, square-root of NOT gate and controlled-NOT gate), which have central importance in quantum computing. In addition, experimental results show that nuclear magnetic resonance spectroscopy can efficiently measure the result of quantum computing without attendant wave-function collapse.

Chinese Physics Letters•Jan 1, 2000•10 citations
A quantum circuit network is a set of circuits that implements a certain computation task. Being at the centre of the quantum circuit network, the multi-qubit controlled phase shift is one of the most important quantum gates. In this paper, we apply the method of modular structuring in classical computer architecture to the quantum computer and give a recursive realization of the multi-qubit phase gate. This realization of the controlled phase shift gate is convenient in realizing certain quantum algorithms. We have experimentally implemented this modularized multi-qubit controlled phase gate in a three-qubit nuclear magnetic resonance (NMR) quantum system. The network is demonstrated experimentally using line selective pulses in the NMR technique. The procedure has the advantage of being simple and easy to implement.
In this study, we report the experimental realization of seven-qubit Deutsch-Jozsa (D-J) algorithm and controlled phase-shift gates with improved precision using liquid state nuclear magnetic resonance (NMR). The experimental results have shown that transformationsU f in the seven-qubit D-J algorithm have been implemented with different pulse sequences, and whetherf is constant or balanced is determined by using only a single function call (U f ). Furthermore, we propose an experimental method to measure and correct the error in the controlled phase-shift gate that is simple and feasible in experiments, and can have precise phase shifts. These may offer the possibility of surmounting the difficulties of low signal-to-noise ratio (SNR) in multi-qubit NMR quantum computers, more complicated experimental techniques, and the increase of gate errors due to using a large number of imperfect selective pulses. These are also applied to more complicated quantum algorithms with more qubits, such as quantum Fourier transformation and Shor’s algorithm.
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.
Nuclear Magnetic Ressonance (NMR) is a widely used technique, with a long history of applications in chemestry, medicine, and material science. Twenty years ago, it emerged as a reliable source for quantum computing too, since the work of Cory. One of its major advantage is the ease with which arbitrary unitary transformations can be implemented, together with its experimental simplicity, that can be traced back to very simple NMR routines, which were being extensively used long before. However, some disadvantages came along, mostly related to experimental effort in the initialisation and measure processes, and scalability. In this work, we have successfully probed some simple quantum gates (Pauli-Z, Pauli-X and Hadamard) in one and two-qubit systems, realised in a NMR experiment. The work comprised a pseudo-pure state preparation, followed by the application of the gates, and a quantum tomography method, necessary to reconstruct the density matrix. The experiments were conducted with a chloroform sample, placed in a 300 MHz Bruker Avance II spectrometer, equipped with a superconducting magnet with a 7 T magnetic field.
Logic gates such as the controlled-NOT (c-NOT) and Toffoli gates play a key role in quantum information processing (QIP) and quantum computing. A natural extension of such gates would necessarily operate on one quantum bit (qubit) conditional on the state of the remaining qubits in the system. We show that such selective gates, termed $(\mathrm{controlled}{)}^{n}\ensuremath{-}\mathrm{NOT}$ gates, or ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates, are convenient in nuclear magnetic resonance (NMR) implementations of QIP and are straightforward to implement. NMR pulse sequences for these gates can be built using classical methods as well as insights from geometric algebra. These methods yield equivalent NMR pulse sequences for the generation of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for any number of control spins. In this work, a catalog of ${\mathrm{c}}^{n}\ensuremath{-}\mathrm{NOT}$ gates for systems of as many as 16 spins is provided along with an experimental implementation of a ${\mathrm{c}}^{3}\ensuremath{-}\mathrm{N}\mathrm{O}\mathrm{T}$ gate on a four spin system, 13C{}^{13}\mathrm{C}13C alanine.
The controlled-NOT gate and controlled square-root NOT gate play an important role in quantum algorithm. This article reports the experimental results of these two universal quantum logic gates (controlled square-root NOT gate and controlled-NOT gate) on a 7-qubit NMR quantum computer. Further, we propose a simple experimental method to measure and correct the error in the controlled phase-shift gate, which is helpful to construct a more perfect phase-shift gate experimentally and can also be used in more qubits discrete Fourier transformation.