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/9912047 · Journal of Experimental and Theoretical Physics Letters

Multiqubit spin

A. R. Kessel, Vladimir L. Ermakov

Published Jul 1, 1999• 59 citations
arXivHTMLPDF

Abstract

It is proposed that the state space of quantum objects with a complicated discrete spectrum be used as a basis for multiqubit recording and processing of information in a quantum computer. As an example, nuclear spin 3/2 is considered. The possibilities of writing and reading two quantum bits of information, preparation of the initial state, and the implementation of the operations “rotation” and “controlled negation,” which are sufficient for constructing complex algorithms, are demonstrated.

DOI
10.1134/1.568130

Related papers

Coding of the quantum information on virtual qubits

A. R. Kessel, Vladimir L. Ermakov

One qubit is mapped to two level system in the standard model of quantum computation: a typical example is a spin-1/2 system. Further progress requires the use of network of multilevel quantum systems of different physical origin in solids: optical levels, large or strong interacting spins etc. We propose virtual qubit formalism and show how the quantum objects state space can be used as a basis for multiqubit information recording and processing in a quantum computer. It is suggested to map the qubits into solid state NMR spin system collective states instead of the state of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to obtain the universal set of quantum gates, which operation time is determined only by the RF pulses.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Nov 15, 2001•1 citation

Quantum information processing

Stephen Mark Barnett

We have seen how information can be encoded onto a quantum system by selecting the state in which it is prepared. Retrieving the information is achieved by performing a measurement, and the optimal measurement in any given situation is usually a generalized measurement. In between preparation and measurement, the information resides in the quantum state of the system, which evolves in a manner determined by the Hamiltonian. The associated unitary transformation may usefully be viewed as quantum information processing; if we can engineer an appropriate Hamiltonian then we can use the quantum evolution to assist in performing computational tasks. Our objective in quantum information processing is to implement a desired unitary transformation. Typically this will mean coupling together a number, perhaps a large number, of qubits and thereby generating highly entangled states. It is fortunate, although by no means obvious, that we can realize any desired multiqubit unitary transformation as a product of a small selection of simple transformations and, moreover, that each of these need only act on a single qubit or on a pair of qubits. The situation is reminiscent of digital electronics, in which logic operations are decomposed into actions on a small number of bits. If we can realize and control a very large number of such operations in a single device then we have a computer. Similar control of a large number of qubits will constitute a quantum computer. It is the revolutionary potential of quantum computers, more than any other single factor, that has fuelled the recent explosion of interest in our subject. We shall examine the remarkable properties of quantum computers in the next chapter. In digital electronics, we represent bit values by voltages: the logical value 1 is a high voltage (typically +5 V) and 0 is the ground voltage (0 V). The voltage bits are coupled and manipulated by transistor-based devices, or gates. The simplest gates act on only one bit or combine two bits to generate a single new bit, the value of which is determined by the two input bits. For a single bit, with value 0 or 1, the only possible operations are the identity (which does not require a gate) and the bit flip.

Oxford University Press eBooks•May 28, 2009•7 citations

Quantum information processing by nuclear magnetic resonance on quadrupolar nuclei

B Y J Oão, T Eles, E Duardo +6 more

Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover’s algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 and quadrupolar spin 3 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.

•Jan 1, 2015•2 citations

Virtual qubits: Multilevels instead of multiparticles

A. R. Kesel’, Vladimir L. Ermakov

The possibility of using multilevel quantum systems with a discrete nonequidistant spectrum for the physical implementation of a universal collection of quantum gates, which is required for constructing an arbitrary algorithm for a quantum computer, is studied on the basis of the proposed virtual-spin formalism. It is shown that such a set of gates, including two-qubit gates, can be constructed on a single spin-3/2 nucleus. The assertion that three-qubit gates can also be realized on a single spin-7/2 quantum particle is substantiated.

Journal of Experimental and Theoretical Physics•Mar 1, 2000•3 citations

Multiqubit logic gates in NMR quantum computing

Mark D. Price, Timothy F. Havel, David G. Cory

Much of the current understanding of logic gates for quantum computation relies on the application of one- and two-qubit gates in order to implement a universal set of logic gates, as well as other gates. Such ideas stem from the notion that the Hamiltonians available for quantum computation are one or two-body processes. However, present day NMR implementations of quantum information processing (QIP) rely on the internal Hamiltonian of a liquid state system in which there are many two-body processes that occur simultaneously. Such use of the internal Hamiltonian allows for the creation of `multiqubit' logic gates, i.e. logic gates that operate on many qubits simultaneously and are more efficient than a sequence of one- and two-qubit rotations that effect the same operation. Such larger qubit operations offer a universal set of gates (even when not all couplings within the internal Hamiltonian are readily accessible) as well as more convenient and efficient implementations of the Hadamard transform, the controlled-NOT gate, and a quantum Fourier transform that scales linearly (assuming all couplings can be turned on and off at will).

New Journal of Physics•May 31, 2000•26 citations

Experimental implementation of a quantum algorithm in a multiqubit NMR system formed by an oriented 7∕2 spin

Ranabir Das, Anil Kumar

A growing appreciation among researchers is the use of quadrupolar nuclei with spin >1∕2 as a suitable candidate for quantum information processing. Such systems have multiple qubits per nuclei and large quadrupolar couplings, resulting in well separated lines in the spectrum. Preparation of pseudopure states and implementation of logic gates have been demonstrated in these systems. Two-qubit quantum algorithms have also been implemented in spin-3∕2 systems. In this letter we report implementation of three-qubit Deutsch-Jozsa algorithm [Proc. R. Soc. London, Ser. A 693, 553 (1992)] in a spin-7∕2 system of Cs133 nucleus oriented in a liquid crystalline matrix.

Applied Physics Letters•Jul 10, 2006•10 citations
It is proposed that the state space of quantum objects with a complicated discrete spectrum be used as a basis for multiqubit recording and processing of information in a quantum computer. As an example, nuclear spin 3/2 is considered. The possibilities of writing and reading two quantum bits of information, preparation of the initial state, and the implementation of the operations “rotation” and “controlled negation,” which are sufficient for constructing complex algorithms, are demonstrated.
One qubit is mapped to two level system in the standard model of quantum computation: a typical example is a spin-1/2 system. Further progress requires the use of network of multilevel quantum systems of different physical origin in solids: optical levels, large or strong interacting spins etc. We propose virtual qubit formalism and show how the quantum objects state space can be used as a basis for multiqubit information recording and processing in a quantum computer. It is suggested to map the qubits into solid state NMR spin system collective states instead of the state of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to obtain the universal set of quantum gates, which operation time is determined only by the RF pulses.
We have seen how information can be encoded onto a quantum system by selecting the state in which it is prepared. Retrieving the information is achieved by performing a measurement, and the optimal measurement in any given situation is usually a generalized measurement. In between preparation and measurement, the information resides in the quantum state of the system, which evolves in a manner determined by the Hamiltonian. The associated unitary transformation may usefully be viewed as quantum information processing; if we can engineer an appropriate Hamiltonian then we can use the quantum evolution to assist in performing computational tasks. Our objective in quantum information processing is to implement a desired unitary transformation. Typically this will mean coupling together a number, perhaps a large number, of qubits and thereby generating highly entangled states. It is fortunate, although by no means obvious, that we can realize any desired multiqubit unitary transformation as a product of a small selection of simple transformations and, moreover, that each of these need only act on a single qubit or on a pair of qubits. The situation is reminiscent of digital electronics, in which logic operations are decomposed into actions on a small number of bits. If we can realize and control a very large number of such operations in a single device then we have a computer. Similar control of a large number of qubits will constitute a quantum computer. It is the revolutionary potential of quantum computers, more than any other single factor, that has fuelled the recent explosion of interest in our subject. We shall examine the remarkable properties of quantum computers in the next chapter. In digital electronics, we represent bit values by voltages: the logical value 1 is a high voltage (typically +5 V) and 0 is the ground voltage (0 V). The voltage bits are coupled and manipulated by transistor-based devices, or gates. The simplest gates act on only one bit or combine two bits to generate a single new bit, the value of which is determined by the two input bits. For a single bit, with value 0 or 1, the only possible operations are the identity (which does not require a gate) and the bit flip.
Nuclear magnetic resonance is viewed as an important technique for the implementation of many quantum information algorithms and protocols. Although the most straightforward approach is to use the two-level system composed of spin 1 nuclei as qubits, quadrupolar nuclei, which possess a spin greater than 1 , are being used as an alternative. In this study, we show some unique features of quadrupolar systems for quantum information processing, with an emphasis on the ability to execute efficient quantum state tomography (QST) using only global rotations of the spin system, whose performance is shown in detail. By preparing suitable states and implementing logical operations by numerically optimized pulses together with the QST method, we follow the stepwise execution of Grover’s algorithm. We also review some work in the literature concerning the relaxation of pseudo-pure states in spin 3 systems as well as its modelling in both the Redfield and Kraus formalisms. These data are used to discuss differences in the behaviour of the quantum correlations observed for two-qubit systems implemented by spin 1 and quadrupolar spin 3 systems, also presented in the literature. The possibilities and advantages of using nuclear quadrupole resonance experiments for quantum information processing are also discussed.
The possibility of using multilevel quantum systems with a discrete nonequidistant spectrum for the physical implementation of a universal collection of quantum gates, which is required for constructing an arbitrary algorithm for a quantum computer, is studied on the basis of the proposed virtual-spin formalism. It is shown that such a set of gates, including two-qubit gates, can be constructed on a single spin-3/2 nucleus. The assertion that three-qubit gates can also be realized on a single spin-7/2 quantum particle is substantiated.
Much of the current understanding of logic gates for quantum computation relies on the application of one- and two-qubit gates in order to implement a universal set of logic gates, as well as other gates. Such ideas stem from the notion that the Hamiltonians available for quantum computation are one or two-body processes. However, present day NMR implementations of quantum information processing (QIP) rely on the internal Hamiltonian of a liquid state system in which there are many two-body processes that occur simultaneously. Such use of the internal Hamiltonian allows for the creation of `multiqubit' logic gates, i.e. logic gates that operate on many qubits simultaneously and are more efficient than a sequence of one- and two-qubit rotations that effect the same operation. Such larger qubit operations offer a universal set of gates (even when not all couplings within the internal Hamiltonian are readily accessible) as well as more convenient and efficient implementations of the Hadamard transform, the controlled-NOT gate, and a quantum Fourier transform that scales linearly (assuming all couplings can be turned on and off at will).
A growing appreciation among researchers is the use of quadrupolar nuclei with spin >1∕2 as a suitable candidate for quantum information processing. Such systems have multiple qubits per nuclei and large quadrupolar couplings, resulting in well separated lines in the spectrum. Preparation of pseudopure states and implementation of logic gates have been demonstrated in these systems. Two-qubit quantum algorithms have also been implemented in spin-3∕2 systems. In this letter we report implementation of three-qubit Deutsch-Jozsa algorithm [Proc. R. Soc. London, Ser. A 693, 553 (1992)] in a spin-7∕2 system of Cs133 nucleus oriented in a liquid crystalline matrix.