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

Journal of Engineering Science

QUANTUM COMPUTING FOR MULTI-QUBIT SYSTEMS USING SCHWINGER REPRESENTATION OF ANGULAR MOMENTUM

Ion Geru

Published Jul 15, 2025• 0 citations
Publisher

Abstract

This paper deals with the features of quantum computing for a system containing a relatively large number of qubits n, which is characterized by a half-integer effective spin S in the Schwinger representation of paired bosons. It was shown that for n = 70, the number of boson states corresponding to lowest 2S + 1 excited energy levels of each of the two harmonic oscillators implementing the two-boson representation of the effective spin S is N = 1070 = 1.18 x 1021. Under such conditions, it can be assumed with great precision that for n ≥ 70 all boson states of both harmonic oscillators participate in the implementation of the two-boson representation of the effective spin S. This allows one to apply the quantum field theory methods when performing quantum computations for multi-qubit systems. Another advantage of the Schwinger representation of paired bosons compared to the spinor representation when performing quantum computations for multi-qubit systems is that in the first case the form of the spin projection operators of the effective spin S does not depend on the number of qubits n.

DOI
10.52326/jes.utm.2025.32(2).06

Related papers

Superdense Coding of Information in Quantum Computer in the Paired Bosons Representation

Ion I. Geru

An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger’s two-boson representation of angular momentum. Since the effective spin S = 2n-1 - ½ corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.

International Conference on Electronics, Communications and Computing (IC|ECCO)•Apr 1, 2022•0 citations

Oscillator Model of Spin

Yitian Ding, Miaomiao Xu

The Schwinger's representation of angular momentum(AM) relates two important fundamental models, that of AM and that of harmonic oscillator(HO). However, the representation offers only the relations of operators but not states. Here, by developing a graphic method to calculate the states, we show that the Schwinger's model is valid only with certain spin. With the relation of states, we also demonstrate how the superposition states in AM map to entangled states in HO. This study has promising applications in quantum computation, and may cast light on the relation between superposition and entanglement.

arXiv:1405.4614•May 19, 2014•0 citations

Schwinger's oscillator method, supersymmetric quantum mechanics and massless particles

F. M. Mejía, V. Pleitez

We consider Schwinger's method of angular momentum addition using the SU(2) algebra with both a fermionic and a bosonic oscillator. We show that the total spin states obtained are: one boson singlet state and an arbitrary number of spin-1/2 states, the later ones are energy degenerate. It means that we have in this case supersymmetric quantum mechanics and also the addition of angular momentum for massless particles. We review too the cases of two bosonic and two fermionic oscillators.

Revista Brasileira de Ensino de Física•Mar 1, 2002•2 citations

A Bosonic Coherent State Path Integral Representation for Spin Systems based on a Projection Operator Implementation of the Schwinger boson number constraint

Seong Jae Kim

The path integral single spin partition function in the basis of boson coherent states, for a general normal ordered two-mode Schwinger boson Hamiltonian, has been computed. Within the initial phase of the calculational process, by a specific approach, the Schwinger boson constraint by means of the projection operator has been implemented.\nAfter, the case of the Zeeman Hamiltonian has been taken on. Using the expression for the partition function obtained for the general case, the appropriate single spin partition function has been produced. Additionally, partition functions have been computed for a few specific spin quantum numbers and then compared with those calculated by the straightforward means, which brought about great confidence in the projection operator implementation; both results match perfectly. \nFinally, the Heisenberg Model has been tackled, and the appropriate expressions for the partition functions have been computed. Their validity has not been verified for any specific cases, but the Zeeman Hamiltonian case dealt with earlier appears to be a strong indicator that these are indeed the correct expressions. \nMany open questions remain, however, for future research to address. All in all, it has been discovered that using the projection operator as a means to enforce the Schwinger boson constraint, veritably works for a Zeeman Hamiltonian problem for specific spin quantum numbers.

•Jan 1, 2018•0 citations

Accidental Symmetry in the Tavis-Cummings Model via the Schwinger Boson Representation

Plato Deliyannis, Iman Marvian

The Jaynes-Cummings (JC) Hamiltonian is a paradigmatic model of light-matter interaction and, more generally, qubit-boson interactions, widely used across atomic, optical, and superconducting qubit platforms. In the multi-qubit setting, where n qubits are identically coupled to a single boson mode, this interaction is known as the Tavis-Cummings (TC) Hamiltonian. The structure of the TC model is usually understood in terms of two standard symmetries: permutation invariance of the qubits and a U(1) symmetry associated with conservation of the total excitation number. Here we identify an additional, independent "accidental" symmetry of the TC Hamiltonian and construct the corresponding conserved observable. We show that, for n>2 qubits, this symmetry imposes strong constraints on the realizable unitary transformations. These constraints persist in the presence of the global $J_z$ Hamiltonian, but are removed by adding $J_z^2$, even though $J_z^2$ preserves both permutation invariance and the U(1) symmetry. Finally, we explain the origin of this previously unnoticed symmetry using Schwinger's boson representation of angular momentum. These restrictions have important implications for controllability of the TC system and for its applications to quantum computing, which are investigated further in a companion paper.

quant-pharXiv:2606.12813•Jun 12, 2026•0 citations

Coupling Schemes for an n su(2) Spin System

Masatoshi Yamamura, Constança Providência, João Da Providência +2 more

In the framework of the Schwinger boson representation for the su(2)-algebra, the closed form is derived for the total spin eigenstates which result from the coupling of n su(2)-spins. In order to demonstrate its usefulness, the orthogonal set for the so(5)-algebra, which is reduced to four su(2)-spin systems, is obtained. 1 typeset using PTPTEX.sty <ver.1.0>§1. Introduction and preliminaries The boson realization of the su(2)-algebra due to Schwinger 1) and named after him plays a crucial role in the Theory of Angular Momentum, for instance in the derivation of the irreducible representations of the rotation operators. The Schwinger representation of the su(2)-algebra also proved to be most useful in the study of various many-body systems,

•Jan 1, 2004•0 citations
This paper deals with the features of quantum computing for a system containing a relatively large number of qubits n, which is characterized by a half-integer effective spin S in the Schwinger representation of paired bosons. It was shown that for n = 70, the number of boson states corresponding to lowest 2S + 1 excited energy levels of each of the two harmonic oscillators implementing the two-boson representation of the effective spin S is N = 1070 = 1.18 x 1021. Under such conditions, it can be assumed with great precision that for n ≥ 70 all boson states of both harmonic oscillators participate in the implementation of the two-boson representation of the effective spin S. This allows one to apply the quantum field theory methods when performing quantum computations for multi-qubit systems. Another advantage of the Schwinger representation of paired bosons compared to the spinor representation when performing quantum computations for multi-qubit systems is that in the first case the form of the spin projection operators of the effective spin S does not depend on the number of qubits n.
An alternative approach to superdense coding of information in quantum computing is proposed on the basis of Schwinger’s two-boson representation of angular momentum. Since the effective spin S = 2n-1 - ½ corresponds to the n-qubit system, this representation can be used in the quantum computing. Operators of the logical elements of the quantum circuit were found, performing superdense coding of information in the paired bosons representation. It is shown that for superdense coding of information, the results obtained in the spinor representation and in the representation of paired bosons coincide. For one-qubit systems, one of the two representations cannot be favored. In the case of n-qubit systems for n >> 1, the representation of paired bosons is probably more convenient for applications, since in this representation the explicit form of the Pauli operators X, Y, and Z does not depend on n.
The Schwinger's representation of angular momentum(AM) relates two important fundamental models, that of AM and that of harmonic oscillator(HO). However, the representation offers only the relations of operators but not states. Here, by developing a graphic method to calculate the states, we show that the Schwinger's model is valid only with certain spin. With the relation of states, we also demonstrate how the superposition states in AM map to entangled states in HO. This study has promising applications in quantum computation, and may cast light on the relation between superposition and entanglement.
The path integral single spin partition function in the basis of boson coherent states, for a general normal ordered two-mode Schwinger boson Hamiltonian, has been computed. Within the initial phase of the calculational process, by a specific approach, the Schwinger boson constraint by means of the projection operator has been implemented.\nAfter, the case of the Zeeman Hamiltonian has been taken on. Using the expression for the partition function obtained for the general case, the appropriate single spin partition function has been produced. Additionally, partition functions have been computed for a few specific spin quantum numbers and then compared with those calculated by the straightforward means, which brought about great confidence in the projection operator implementation; both results match perfectly. \nFinally, the Heisenberg Model has been tackled, and the appropriate expressions for the partition functions have been computed. Their validity has not been verified for any specific cases, but the Zeeman Hamiltonian case dealt with earlier appears to be a strong indicator that these are indeed the correct expressions. \nMany open questions remain, however, for future research to address. All in all, it has been discovered that using the projection operator as a means to enforce the Schwinger boson constraint, veritably works for a Zeeman Hamiltonian problem for specific spin quantum numbers.
The Jaynes-Cummings (JC) Hamiltonian is a paradigmatic model of light-matter interaction and, more generally, qubit-boson interactions, widely used across atomic, optical, and superconducting qubit platforms. In the multi-qubit setting, where n qubits are identically coupled to a single boson mode, this interaction is known as the Tavis-Cummings (TC) Hamiltonian. The structure of the TC model is usually understood in terms of two standard symmetries: permutation invariance of the qubits and a U(1) symmetry associated with conservation of the total excitation number. Here we identify an additional, independent "accidental" symmetry of the TC Hamiltonian and construct the corresponding conserved observable. We show that, for n>2 qubits, this symmetry imposes strong constraints on the realizable unitary transformations. These constraints persist in the presence of the global JzJ_zJz​ Hamiltonian, but are removed by adding Jz2J_z^2Jz2​, even though Jz2J_z^2Jz2​ preserves both permutation invariance and the U(1) symmetry. Finally, we explain the origin of this previously unnoticed symmetry using Schwinger's boson representation of angular momentum. These restrictions have important implications for controllability of the TC system and for its applications to quantum computing, which are investigated further in a companion paper.
In the framework of the Schwinger boson representation for the su(2)-algebra, the closed form is derived for the total spin eigenstates which result from the coupling of n su(2)-spins. In order to demonstrate its usefulness, the orthogonal set for the so(5)-algebra, which is reduced to four su(2)-spin systems, is obtained. 1 typeset using PTPTEX.sty <ver.1.0>§1. Introduction and preliminaries The boson realization of the su(2)-algebra due to Schwinger 1) and named after him plays a crucial role in the Theory of Angular Momentum, for instance in the derivation of the irreducible representations of the rotation operators. The Schwinger representation of the su(2)-algebra also proved to be most useful in the study of various many-body systems,