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 Quantum Chemistry

Gray code and the initialization problem of NMR quantum computers

Ryuichi Sawae, Toshio Sakata, M. Tei, Kenichi Takarabe, Yoshinori Manmoto

Published Jan 1, 2003• 3 citations
Publisher

Abstract

Abstract The initialization of states is of importance in nuclear magnetic resonance quantum computing systems. In this article it is shown that the initialization ofn‐qubits states can be realized via a sequence of controlled‐not quantum gates from any mixed state. We present a general algorithm and its optimization to construct a circuit of controlled‐not quantum gates that realizes the initialization using the concept of Gray Codes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

DOI
10.1002/qua.10631

Related papers

Quantum circuits for an effective pure state in NMR quantum computer

Yoshiyuki Mori, Ryuichi Sawae, Minaru Kawamura +2 more

Abstract In nuclear magnetic resonance (NMR) quantum computing systems, it is very important to prepare an effective pure state rather than a true pure state. Our main objective is to present a general algorithm that provides quantum circuits for preparing an effective pure state from any mixed state, consisting only of controlled‐not (CNOT) quantum gates for homonuclear spin systems. Our algorithm is based on the product operator approach and could be applicable to NMR quantum computing systems with more than eight qubits. Optimization of the number of controlled‐not quantum gates is discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005

International Journal of Quantum Chemistry•Jan 1, 2005•6 citations

Implementation of two‐qubit and three‐qubit quantum computers using liquid‐state nuclear magnetic resonance

Dorothea Golze, Maik Icker, Stefan T. A. Berger

Abstract The field of quantum computing has grown rapidly in the last years. Most realizations of quantum computers were done on liquid‐state NMR quantum computers so far. We present in a didactic approach how to build small NMR quantum computers with two and three qubits. The two‐qubit quantum computer was implemented on α‐D‐methylglucose using 13C spins, whereas the three‐qubit quantum computer was implemented on 4‐bromo‐1,1,2‐trifluoro‐1‐butene using 19F spins. We describe in detail how to initialize these systems by generating pseudo‐pure states. For initialization, we used the spatial averaging method, which has the advantage that it can be easily understood by product operators. Furthermore, the implementation of quantum logic gate operations will be presented. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40: 25–37, 2012.

Concepts in Magnetic Resonance Part A•Jan 1, 2012•7 citations

Fast preparation method of effective pure states for NMR‐quantum computer with controlled‐not gates

Minaru Kawamura, Ryuichi Sawae, Takashi Kumaya +3 more

Abstract A fast method to prepare effective pure states for NMR‐quantum computer in homo‐nuclear spin system is proposed. The temporal averaging method has been introduced to prepare an effective pure state in NMR‐quantum computer, but the method requires many experiments, whose number increases exponentially with the number of quantum bits (qubits), and it seems that a huge number of logical gates are required. The proposed method avoids this problem by eliminating a part of elements in the density matrices. This method requires only one ancillary qubit and two different experiments; the steps have been confirmed to be proportional to the number of qubits up to four‐qubit. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

International Journal of Quantum Chemistry•Aug 30, 2004•7 citations

Use of pairs of pseudopure states for NMR quantum computing

B. M. Fung

The premise of nuclear magnetic resonance (NMR) quantum computing is that pseudopure quantum states, for which the populations of all energy levels but one are equal, can be used instead of pure quantum states. However, for systems with a large number of quantum bits (qubits), it would require elaborate pulse sequences with many steps to prepare these pseudopure states. To overcome this problem, a method using pairs of pseudopure states (POPS) instead of individual pseudopure states as the basis for NMR quantum computing is introduced here. The POPS approach has a significant advantage over the existing methods that, regardless of the number of qubits, only a single step is needed to prepare each pair of pseudopure states. A detailed analysis of a 16-level spin system is given, and the results of applying a ${c}^{2}$-NOT quantum logic gate (a controlled-NOT gate conditional upon the state of two other qubits) to all the POPS in the system are presented.

Physical Review A•Jan 12, 2001•27 citations

Preparation of pseudopure state in nuclear spin ensemble using CNOT gates combination

Xiaodong, Yang, Daxiu +5 more

Nuclear magnetic resonance (NMR) is one of the experimental schemes for quantum computation. Most initial state of quantum algorithm in NMR computation is the pseudopure state. Until now, there are several methods to prepare pseudopure state. This note, based on the idea of controlled-not (CNOT) gates combination, has analyzed the characteristics of this method in the odd- and even-qubit system. Also, we have designed the pulse sequence for a 4-qubit sample to obtain pseudopure state, and realized it in the experiment. This method reduces the complexity of experiment and gives a high signal-to-noise (S/N) ratio.

中国科学通报：英文版•Jan 1, 2002•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
Abstract The initialization of states is of importance in nuclear magnetic resonance quantum computing systems. In this article it is shown that the initialization ofn‐qubits states can be realized via a sequence of controlled‐not quantum gates from any mixed state. We present a general algorithm and its optimization to construct a circuit of controlled‐not quantum gates that realizes the initialization using the concept of Gray Codes. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003
Abstract In nuclear magnetic resonance (NMR) quantum computing systems, it is very important to prepare an effective pure state rather than a true pure state. Our main objective is to present a general algorithm that provides quantum circuits for preparing an effective pure state from any mixed state, consisting only of controlled‐not (CNOT) quantum gates for homonuclear spin systems. Our algorithm is based on the product operator approach and could be applicable to NMR quantum computing systems with more than eight qubits. Optimization of the number of controlled‐not quantum gates is discussed. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005
Abstract The field of quantum computing has grown rapidly in the last years. Most realizations of quantum computers were done on liquid‐state NMR quantum computers so far. We present in a didactic approach how to build small NMR quantum computers with two and three qubits. The two‐qubit quantum computer was implemented on α‐D‐methylglucose using 13C spins, whereas the three‐qubit quantum computer was implemented on 4‐bromo‐1,1,2‐trifluoro‐1‐butene using 19F spins. We describe in detail how to initialize these systems by generating pseudo‐pure states. For initialization, we used the spatial averaging method, which has the advantage that it can be easily understood by product operators. Furthermore, the implementation of quantum logic gate operations will be presented. © 2012 Wiley Periodicals, Inc. Concepts Magn Reson Part A 40: 25–37, 2012.
Abstract A fast method to prepare effective pure states for NMR‐quantum computer in homo‐nuclear spin system is proposed. The temporal averaging method has been introduced to prepare an effective pure state in NMR‐quantum computer, but the method requires many experiments, whose number increases exponentially with the number of quantum bits (qubits), and it seems that a huge number of logical gates are required. The proposed method avoids this problem by eliminating a part of elements in the density matrices. This method requires only one ancillary qubit and two different experiments; the steps have been confirmed to be proportional to the number of qubits up to four‐qubit. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004
The premise of nuclear magnetic resonance (NMR) quantum computing is that pseudopure quantum states, for which the populations of all energy levels but one are equal, can be used instead of pure quantum states. However, for systems with a large number of quantum bits (qubits), it would require elaborate pulse sequences with many steps to prepare these pseudopure states. To overcome this problem, a method using pairs of pseudopure states (POPS) instead of individual pseudopure states as the basis for NMR quantum computing is introduced here. The POPS approach has a significant advantage over the existing methods that, regardless of the number of qubits, only a single step is needed to prepare each pair of pseudopure states. A detailed analysis of a 16-level spin system is given, and the results of applying a c2{c}^{2}c2-NOT quantum logic gate (a controlled-NOT gate conditional upon the state of two other qubits) to all the POPS in the system are presented.
Nuclear magnetic resonance (NMR) is one of the experimental schemes for quantum computation. Most initial state of quantum algorithm in NMR computation is the pseudopure state. Until now, there are several methods to prepare pseudopure state. This note, based on the idea of controlled-not (CNOT) gates combination, has analyzed the characteristics of this method in the odd- and even-qubit system. Also, we have designed the pulse sequence for a 4-qubit sample to obtain pseudopure state, and realized it in the experiment. This method reduces the complexity of experiment and gives a high signal-to-noise (S/N) ratio.
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.