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

Feedback Error Correction Method of Creating Pseudo-Pure States for NMR Quantum Computers

Minaru Kawamura

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

In this paper, a feedback error correction method of creating pseudo-pure states for large scale nuclear magnetic resonance quantum computers (NMR-QC) is proposed that is aimed at creating the initial states asymptotically within a specified error tolerance by using a spatial averaging method. The present method enables almost complete error correction and even enhances the NMR signal compared with the initial state. An implementation of this method was successfully demonstrated on a five-qubit NMR-QC.

Related papers

Effective pure states for bulk quantum computation

Emanuel H. Knill, Isaac L. Chuang, Raymond Laflamme

In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) [Science 275, 350 (1997)] and Cory et al. (spatial averaging) [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)] for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla quantum bits, and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high-temperature and low-temperature bulk quantum computing and analyze the signal-to-noise behavior of each. Most of these algorithms require only a constant multiple of the number of experiments needed by the other methods for creating effective pure states.

arXiv:quant-ph/9706053•Physical Review A•May 1, 1998•245 citations

Preparation of pseudo-pure states by line-selective pulses in Nuclear Magnetic Resonance

Xinhua Peng, Xiwen Zhu, Ximing Fang +4 more

A new method of preparing the pseudo-pure state of a spin system for quantum computation in liquid nuclear magnetic resonance (NMR) was put forward and demonstrated experimentally. Applying appropriately connected line-selective pulses simultaneously and a field gradient pulse techniques we acquired straightforwardly all pseudo-pure states for two qubits in a single experiment much efficiently. The signal intensity with the pseudo-pure state prepared in this way is the same as that of temporal averaging. Our method is suitable for the system with arbitrary numbers of qubits. As an example of application, a highly structured search algorithm—-Hogg’s algorithm was also performed on the pseudo-pure state | 00 〉 prepared by our method.

•Jan 1, 2000•38 citations

Ensemble quantum computing by NMR spectroscopy: product operators, pseudopure states, and an implementation of quantum error correction

Timothy F. Havel, Shyamal S. Somaroo, David G. Cory

Quantum computers are able to operate on coherent superpositions of states, and to isolate a single global property of the set of computed quantities via interference. In principle, this permits them to solve certain problems exponentially faster thana classical computer, but not one has yet succeeded in implementing a true quantum computer on more than two quantum bits. Recently, however, it has been found that an ensemble of independent and identical quantum computers can perform mots of the same feats than a single quantum computer could, while at the same time bringing massive classical parallelism to bear on its computations. Such an ensemble quantum computer can be realized, to a limited extent, by nuclear magnetic resonance (NMR) spectroscopy on ordinary liquids at room temperature and pressure. This simple implementation depends on special kinds of mixed states, called pseudo-pure states, whose preparation entails a loss of signal that is exponential in the number of spins. While this would appear to limit such an implementation to ca. 8-10 spins in the foreseeable future, NMR spectroscopy has now permitted the first experimental demonstrations of all the basic features of quantum computing. We claim, moreover, that the product operator formalism, on which the theory of NM R spectroscopy is based, provides an efficient framework within which to analyze algorithms and decoherence effects in quantum computing more generally. This is illustrated by presenting our recent experimentally implementation of a quantum error correcting code.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jul 6, 1998•0 citations

Quantum computation using NMR

Kavita Dorai, T. S. Mahesh, Arvind Arvind +1 more

This article reviews recent work done by us an some initial steps towards the implementation of quantum computation using liquid state NMR. We describe how special kinds of states required for such computation (called pseudo-pure states) can be created from a thermal ensemble of spins. We demonstrate the implementation of several quantum logic gates through one- and two-dimensional NMR methods, using transition- and spin- selective pulses. Finally, we discuss the implementation of the Deutsch-Jozsa algorithm using NMR.

•Nov 1, 2000•5 citations

Linear Preparation Method of Pseudo-Pure States while Correcting Errors and Enhancing Signals for NMR Quantum Computer

Minaru Kawamura, H. Sakai, Yoshinori Manmoto +1 more

AIP conference proceedings•Jan 1, 2009•0 citations

Preparation of effective pure states $\mid 00 \cdots 0 \rangle$ on an NMR quantum computer with any number of spins (Analytical Study of Quantum Information and Related Fields)

Ushio Sakaguchi, Hiroshi Ozawa, Toshio Fukumi

A method is proposed to prepare an effective pure state corresponding to the pure state $|0\rangle$ $|0\rangle$ $\cdots|0\rangle$ for any number of spins on a nuclear magnetic resonance quantum computer, where $|0\rangle$ stands for the spin-up state of a nuclear spin.The method is based on the spatial labeling proposed by Cory et al.

数理解析研究所講究録•Apr 1, 2001•0 citations
In this paper, a feedback error correction method of creating pseudo-pure states for large scale nuclear magnetic resonance quantum computers (NMR-QC) is proposed that is aimed at creating the initial states asymptotically within a specified error tolerance by using a spatial averaging method. The present method enables almost complete error correction and even enhances the NMR signal compared with the initial state. An implementation of this method was successfully demonstrated on a five-qubit NMR-QC.
In bulk quantum computation one can manipulate a large number of indistinguishable quantum computers by parallel unitary operations and measure expectation values of certain observables with limited sensitivity. The initial state of each computer in the ensemble is known but not pure. Methods for obtaining effective pure input states by a series of manipulations have been described by Gershenfeld and Chuang (logical labeling) [Science 275, 350 (1997)] and Cory et al. (spatial averaging) [Proc. Natl. Acad. Sci. USA 94, 1634 (1997)] for the case of quantum computation with nuclear magnetic resonance. We give a different technique called temporal averaging. This method is based on classical randomization, requires no ancilla quantum bits, and can be implemented in nuclear magnetic resonance without using gradient fields. We introduce several temporal averaging algorithms suitable for both high-temperature and low-temperature bulk quantum computing and analyze the signal-to-noise behavior of each. Most of these algorithms require only a constant multiple of the number of experiments needed by the other methods for creating effective pure states.
A new method of preparing the pseudo-pure state of a spin system for quantum computation in liquid nuclear magnetic resonance (NMR) was put forward and demonstrated experimentally. Applying appropriately connected line-selective pulses simultaneously and a field gradient pulse techniques we acquired straightforwardly all pseudo-pure states for two qubits in a single experiment much efficiently. The signal intensity with the pseudo-pure state prepared in this way is the same as that of temporal averaging. Our method is suitable for the system with arbitrary numbers of qubits. As an example of application, a highly structured search algorithm—-Hogg’s algorithm was also performed on the pseudo-pure state | 00 〉 prepared by our method.
Quantum computers are able to operate on coherent superpositions of states, and to isolate a single global property of the set of computed quantities via interference. In principle, this permits them to solve certain problems exponentially faster thana classical computer, but not one has yet succeeded in implementing a true quantum computer on more than two quantum bits. Recently, however, it has been found that an ensemble of independent and identical quantum computers can perform mots of the same feats than a single quantum computer could, while at the same time bringing massive classical parallelism to bear on its computations. Such an ensemble quantum computer can be realized, to a limited extent, by nuclear magnetic resonance (NMR) spectroscopy on ordinary liquids at room temperature and pressure. This simple implementation depends on special kinds of mixed states, called pseudo-pure states, whose preparation entails a loss of signal that is exponential in the number of spins. While this would appear to limit such an implementation to ca. 8-10 spins in the foreseeable future, NMR spectroscopy has now permitted the first experimental demonstrations of all the basic features of quantum computing. We claim, moreover, that the product operator formalism, on which the theory of NM R spectroscopy is based, provides an efficient framework within which to analyze algorithms and decoherence effects in quantum computing more generally. This is illustrated by presenting our recent experimentally implementation of a quantum error correcting code.
This article reviews recent work done by us an some initial steps towards the implementation of quantum computation using liquid state NMR. We describe how special kinds of states required for such computation (called pseudo-pure states) can be created from a thermal ensemble of spins. We demonstrate the implementation of several quantum logic gates through one- and two-dimensional NMR methods, using transition- and spin- selective pulses. Finally, we discuss the implementation of the Deutsch-Jozsa algorithm using NMR.
Preparation of effective pure states ∣00⋯0⟩\mid 00 \cdots 0 \rangle∣00⋯0⟩ on an NMR quantum computer with any number of spins (Analytical Study of Quantum Information and Related Fields)
A method is proposed to prepare an effective pure state corresponding to the pure state ∣0⟩|0\rangle∣0⟩ ∣0⟩|0\rangle∣0⟩ ⋯∣0⟩\cdots|0\rangle⋯∣0⟩ for any number of spins on a nuclear magnetic resonance quantum computer, where ∣0⟩|0\rangle∣0⟩ stands for the spin-up state of a nuclear spin.The method is based on the spatial labeling proposed by Cory et al.