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 Physics A Mathematical and General

Simulation of quantum logic via collisions of vector solitons

Andrzej Janutka

Published Sep 19, 2006• 13 citations
Publisher

Abstract

The polarization of a multi-component vector soliton (of the Manakov type) can be thought of as a state vector of a system of qubits (a register of quantum information). A change of this state on demand via colliding the register pulse with other solitons is shown to be possible with arbitrary accuracy. The parameters (polarization, pulse width, velocity) of the register-switching solitons corresponding to the computationally universal set of quantum gates are found. Physical realizations of information processing using effects of the self-focusing of optical media or of the self-induced transparency are considered.

DOI
10.1088/0305-4470/39/40/015

Related papers

Error of quantum-logic simulation via vector-soliton collisions

Andrzej Janutka

In a concept of simulating the quantum logic with vector solitons by the author (Janutka 2006 J. Phys. A: Math. Gen. 39 12505 ), the soliton polarization is thought of as a state vector of a system of cebits (classical counterparts of qubits) switched via collisions with other solitons. The advantage of this method of information processing compared to schemes using linear optics is the possibility of the determination of the information-register state in a single measurement. Minimization of the information-processing error for different optical realizations of the logical systems is studied in the framework of a quantum analysis of soliton fluctuations. The problem is considered with relevance to general difficulties of the quantum error-correction schemes for the classical analogies of the quantum-information processing.

Journal of Physics A Mathematical and Theoretical•Aug 14, 2007•6 citations

Quantum-like information processing using vector solitons

Andrzej Janutka

The concept of simulating the quantum logic via collisions of vector solitons (Janutka 2006 J. Phys. A: Math. Gen. 39 12505 , 2007 J. Phys. A: Math. Theor. 40 10813 ) is developed in the direction of designing a true quantum-information processor that is based on mesoscopic objects, solitons. In this concept, quantum-like information is encoded in the vector-soliton (polarization) parameters. An exponential increase of the logical-operating speed compared to that achievable in the earlier simulation schemes is found to be possible due to a coherent conversion of a 2 n -component vector soliton that carries an n -cebit of information into an ensemble of 2 n −1 two-component and 2 n −2 four-component vector pulses. Two solid-state circuits (transmitting magnetic solitons or fluxons of long Josephson junctions) which enable such a pulse conversion are proposed.

Journal of Physics A Mathematical and Theoretical•Aug 11, 2008•7 citations

Quantum theory of Manakov solitons

Darren Rand, Ken Steiglitz, Paul R. Prucnal

A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schr\"odinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.

Physical Review A•May 11, 2005•21 citations

Calculation of SIT soliton collisions for optical computing

Willem P. Beeker, Edip Can, Chris Lee +1 more

The optical solitons that play the role of information carriers, are moving, requiring careful experimental timing to achieve the desired logic operation. In contrast, self-induced transparency (SIT) is a strong resonant nonlinear effect, supporting the propagation of optical solitons and are usually associated with a two-level system. By the appropriate application of light fields, the optical soliton, resonant with the SIT transition, can generate an excited region with ground state coherence in the medium, allowing logic operations to be performed on this coherence.

Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)•Jun 1, 2009•0 citations

Quantum Information Processing with Low-Dimensional Systems

Alexander Yu. Vlasov

A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare arbitrary entangled state of these k systems. Preparation and arbitrary transformations of states are possible with universal set of quantum gates and for any d may be suggested such gates acting only on single systems and neighbouring pairs. Here are revisited methods of construction of Hamiltonians for such universal set of gates and as a concrete new example is considered case with qutrits. Quantum tomography is also revisited briefly.

arXiv:quant-ph/0512034•Dec 5, 2005•1 citation

Quantum lattice gas representation for vector solitons

George Vahala, Linda L. Vahala, Jeffrey Yepez

Quantum lattice gas algorithms are developed for the coupled-nonlinear Schrodinger (coupled-NLS) equations, equations that describe the propagation of pulses in birefringent fibers. When the cross-phase modulation factor is unity, the coupled-NLS reduce to the Manakov equations. The quantum lattice gas algorithm yields vector solitons for the fully integrable Manakov system that are in excellent agreement with exact results. Simulations are also presented for the interaction between a turbulent 2-soliton mode and a simple NLS 2-soliton mode. The quantum algorithm requires 4 qubits for each spatial node, with quantum entanglement required only between pairs of qubits through a unitary collision operator. The coupling between the qubits is achieved through a local phase change in the absolute value of the paired qubit wave functions. On symmetrizing the unitary streaming operators, the resulting quantum algorithm, which is unconditionally stable, is accurate to O(ε2).

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Aug 5, 2003•3 citations
The polarization of a multi-component vector soliton (of the Manakov type) can be thought of as a state vector of a system of qubits (a register of quantum information). A change of this state on demand via colliding the register pulse with other solitons is shown to be possible with arbitrary accuracy. The parameters (polarization, pulse width, velocity) of the register-switching solitons corresponding to the computationally universal set of quantum gates are found. Physical realizations of information processing using effects of the self-focusing of optical media or of the self-induced transparency are considered.
In a concept of simulating the quantum logic with vector solitons by the author (Janutka 2006 J. Phys. A: Math. Gen. 39 12505 ), the soliton polarization is thought of as a state vector of a system of cebits (classical counterparts of qubits) switched via collisions with other solitons. The advantage of this method of information processing compared to schemes using linear optics is the possibility of the determination of the information-register state in a single measurement. Minimization of the information-processing error for different optical realizations of the logical systems is studied in the framework of a quantum analysis of soliton fluctuations. The problem is considered with relevance to general difficulties of the quantum error-correction schemes for the classical analogies of the quantum-information processing.
The concept of simulating the quantum logic via collisions of vector solitons (Janutka 2006 J. Phys. A: Math. Gen. 39 12505 , 2007 J. Phys. A: Math. Theor. 40 10813 ) is developed in the direction of designing a true quantum-information processor that is based on mesoscopic objects, solitons. In this concept, quantum-like information is encoded in the vector-soliton (polarization) parameters. An exponential increase of the logical-operating speed compared to that achievable in the earlier simulation schemes is found to be possible due to a coherent conversion of a 2 n -component vector soliton that carries an n -cebit of information into an ensemble of 2 n −1 two-component and 2 n −2 four-component vector pulses. Two solid-state circuits (transmitting magnetic solitons or fluxons of long Josephson junctions) which enable such a pulse conversion are proposed.
A fully quantum mechanical model of two-component Manakov solitons is developed in both the Heisenberg and Schr\"odinger representations, followed by an analytical, linearized quantum theory of Manakov solitons in the Heisenberg picture. This theory is used to analyze the vacuum-induced fluctuations of Manakov soliton propagation and collision. The vacuum fluctuations induce phase diffusion and dispersion in Manakov soliton propagation. Calculations of the position, polarization angle, and polarization state fluctuations show an increase in collision-induced noise with a decrease in the relative velocity between the two solitons, as expected because of an increase in the interaction length. Fluctuations in both the polarization angle and state are shown to be independent of propagation distance, opening up possibilities for communications, switching, and logic, exploiting these properties of Manakov solitons. Calculations of the phase noise reveal, surprisingly, that the collision-induced fluctuations can be reduced slightly below the level of fluctuations in the absence of collision, due to cross-correlation effects between the collision-induced phase and amplitude fluctuations of the soliton. The squeezing effect of Manakov solitons is also studied and proven, unexpectedly, to have the same theoretical optimum as scalar solitons.
The optical solitons that play the role of information carriers, are moving, requiring careful experimental timing to achieve the desired logic operation. In contrast, self-induced transparency (SIT) is a strong resonant nonlinear effect, supporting the propagation of optical solitons and are usually associated with a two-level system. By the appropriate application of light fields, the optical soliton, resonant with the SIT transition, can generate an excited region with ground state coherence in the medium, allowing logic operations to be performed on this coherence.
A `register' in quantum information processing -- is composition of k quantum systems, `qudits'. The dimensions of Hilbert spaces for one qudit and whole quantum register are d and d^k respectively, but we should have possibility to prepare arbitrary entangled state of these k systems. Preparation and arbitrary transformations of states are possible with universal set of quantum gates and for any d may be suggested such gates acting only on single systems and neighbouring pairs. Here are revisited methods of construction of Hamiltonians for such universal set of gates and as a concrete new example is considered case with qutrits. Quantum tomography is also revisited briefly.
Quantum lattice gas algorithms are developed for the coupled-nonlinear Schrodinger (coupled-NLS) equations, equations that describe the propagation of pulses in birefringent fibers. When the cross-phase modulation factor is unity, the coupled-NLS reduce to the Manakov equations. The quantum lattice gas algorithm yields vector solitons for the fully integrable Manakov system that are in excellent agreement with exact results. Simulations are also presented for the interaction between a turbulent 2-soliton mode and a simple NLS 2-soliton mode. The quantum algorithm requires 4 qubits for each spatial node, with quantum entanglement required only between pairs of qubits through a unitary collision operator. The coupling between the qubits is achieved through a local phase change in the absolute value of the paired qubit wave functions. On symmetrizing the unitary streaming operators, the resulting quantum algorithm, which is unconditionally stable, is accurate to O(ε2).