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

IEEE Conference on Nanotechnology (IEEE NANO)

Circuit Models for Small Signal Performance of Spin 1/2 Quantum Systems

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

Published Jan 1, 2006• 7 citations
Publisher

Abstract

Nanocircuits are composed of nanoelements interacting with external electromagnetic fields which are ultimately described in terms of voltages and currents or incident and reflected waves. Hence the necessity of describing their quantum performance in terms of circuit quantities. We present equivalent circuits for the small signal performance of a population of non-interacting spin 1/2 particles about passive and active equilibria induced by external pumping between the ground and the excited state, that describe respectively e.g. nuclear magnetic resonance and reflection amplification.

DOI
10.1109/nano.2006.1717252

Related papers

Equivalent circuits for small signal performance of spin ½ particles: Research Articles

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

A quantum system composed of a large number of non-interacting spin ½ particles, biased by a large constant magnetic field along the z-axis and excited by a small circularly polarized electromagnetic wave in the xy-plane is considered. Its small signal reflectance about the equilibrium state resulting from the biasing field and a pumping activity is calculated in the complex frequency plane. It is suggested that the equilibrium state can be locally passive or active depending on the pumping sign and level. Equivalent circuits containing imaginary resistors, i.e. frequency independent reactances, are presented for both passive and active cases. Copyright © 2006 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Mar 1, 2006•0 citations

Equivalent circuits for small signal performance of spin ½ particles

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

Abstract A quantum system composed of a large number of non‐interacting spin ½ particles, biased by a large constant magnetic field along the z‐axis and excited by a small circularly polarized electromagnetic wave in the xy‐plane is considered. Its small signal reflectance about the equilibrium state resulting from the biasing field and a pumping activity is calculated in the complex frequency plane. It is suggested that the equilibrium state can be locally passive or active depending on the pumping sign and level. Equivalent circuits containing imaginary resistors, i.e. frequency independent reactances, are presented for both passive and active cases. Copyright © 2006 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Jan 25, 2006•12 citations

Equivalent circuits for two‐state quantum systems

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

Abstract The development of nanocircuits designed to ultimately interact with classical electromagnetic environments demands a description of their performance in circuit terms, i.e. in terms of voltages and currents for incident, reflected and transmitted waves. A class of quantum systems which are particularly promising for applications (e.g. in spintronics) and at the same time easy to analyse and to understand physically are the two‐state systems. Here, we present equivalent circuits for a generic two‐state quantum system imbedded in a one‐port or two‐port structure guiding a linearly polarized electromagnetic wave. For the sake of concreteness we explicitly refer to a system of spin ½ particles whose magnetic moments are aligned with the axis of the guiding structure by a strong constant magnetic field; but the formalism can be easily extended to particles endowed with electric dipole moments or any other system with two degrees of freedom. Copyright © 2007 John Wiley & Sons, Ltd.

International Journal of Circuit Theory and Applications•Apr 12, 2007•9 citations

Spatially Extended Spinning Quantum Systems

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

An open quantum system composed of identical particles spinning in a constant longitudinal magnetic field and excited by a transverse electromagnetic wave is considered as a model for a typical nanocircuit component. The electromagnetic wave is carried by a microstrip transmission line terminated on a box, wherein the particles are introduced at an upper energy level and wherefrom they are extracted at a lower one; the released energy is partly surrendered to the electromagnetic wave yielding reflection amplification, and partly dissipated in a thermal bath. The state of the particles is described in terms of the spin and of the momentum (or position) coordinates. The interaction between the electromagnetic field and the momentum variables is neglected. The LlNDBLAD equations for the system in either representation are derived.

IEEE Conference on Nanotechnology (IEEE NANO)•Aug 1, 2008•1 citation

Equivalent circuits for two-fermion four-state quantum systems

Pier Paolo Civalleri, Marco Gilli, Michele Bonnin

An equivalent circuit is presented for a quantum system composed of two spin 1/2 particles. Such a circuit shows that the entire dynamics of the system, including single-particle and two-particle annihilation and creation, as well as the single particle transitions between ground and excited states, can be described as the superposition of the variables of two uncoupled resonant circuits.

IEEE International Symposium on Circuits and Systems proceedings•May 1, 2009•1 citation

Circuit models for the co-simulation of superconducting quantum computing systems

Rohith Acharya, Fahd A. Mohiyaddin, Anton Potočnik +5 more

Quantum computers based on superconducting qubits have emerged as a leading candidate for a scalable quantum processor architecture. The core of a quantum processor consists of quantum devices that are manipulated using classical electronic circuits, which need to be co-designed for optimal performance and operation. As the principles governing the behavior of the classical circuits and the quantum devices are different, this presents a unique challenge in terms of the simulation, design and optimization of the joint system. A methodology is presented to transform the behavior of small-scale quantum processors to equivalent circuit models that are usable with classical circuits in a generic electrical simulator, enabling the detailed analysis of the impact of many important non-idealities. The methodology has specifically been employed to derive a circuit model of a superconducting qubit interacting with the quantized electromagnetic field of a superconducting resonator. Based on this technique, a comprehensive analysis of the qubit operation is performed, including the coherent control and readout of the qubit using electrical signals. Furthermore, the effect of several non-idealities in the system such as qubit relaxation, decoherence and leakage out of the computational subspace are captured, in contrast to previous works. As the presented method enables the co-simulation of the control electronics with the quantum system, it facilitates the design and optimization of near-term superconducting quantum processors.

Design, Automation, and Test in Europe•Feb 1, 2021•7 citations
Nanocircuits are composed of nanoelements interacting with external electromagnetic fields which are ultimately described in terms of voltages and currents or incident and reflected waves. Hence the necessity of describing their quantum performance in terms of circuit quantities. We present equivalent circuits for the small signal performance of a population of non-interacting spin 1/2 particles about passive and active equilibria induced by external pumping between the ground and the excited state, that describe respectively e.g. nuclear magnetic resonance and reflection amplification.
A quantum system composed of a large number of non-interacting spin ½ particles, biased by a large constant magnetic field along the z-axis and excited by a small circularly polarized electromagnetic wave in the xy-plane is considered. Its small signal reflectance about the equilibrium state resulting from the biasing field and a pumping activity is calculated in the complex frequency plane. It is suggested that the equilibrium state can be locally passive or active depending on the pumping sign and level. Equivalent circuits containing imaginary resistors, i.e. frequency independent reactances, are presented for both passive and active cases. Copyright © 2006 John Wiley & Sons, Ltd.
Abstract A quantum system composed of a large number of non‐interacting spin ½ particles, biased by a large constant magnetic field along the z‐axis and excited by a small circularly polarized electromagnetic wave in the xy‐plane is considered. Its small signal reflectance about the equilibrium state resulting from the biasing field and a pumping activity is calculated in the complex frequency plane. It is suggested that the equilibrium state can be locally passive or active depending on the pumping sign and level. Equivalent circuits containing imaginary resistors, i.e. frequency independent reactances, are presented for both passive and active cases. Copyright © 2006 John Wiley & Sons, Ltd.
Abstract The development of nanocircuits designed to ultimately interact with classical electromagnetic environments demands a description of their performance in circuit terms, i.e. in terms of voltages and currents for incident, reflected and transmitted waves. A class of quantum systems which are particularly promising for applications (e.g. in spintronics) and at the same time easy to analyse and to understand physically are the two‐state systems. Here, we present equivalent circuits for a generic two‐state quantum system imbedded in a one‐port or two‐port structure guiding a linearly polarized electromagnetic wave. For the sake of concreteness we explicitly refer to a system of spin ½ particles whose magnetic moments are aligned with the axis of the guiding structure by a strong constant magnetic field; but the formalism can be easily extended to particles endowed with electric dipole moments or any other system with two degrees of freedom. Copyright © 2007 John Wiley & Sons, Ltd.
An open quantum system composed of identical particles spinning in a constant longitudinal magnetic field and excited by a transverse electromagnetic wave is considered as a model for a typical nanocircuit component. The electromagnetic wave is carried by a microstrip transmission line terminated on a box, wherein the particles are introduced at an upper energy level and wherefrom they are extracted at a lower one; the released energy is partly surrendered to the electromagnetic wave yielding reflection amplification, and partly dissipated in a thermal bath. The state of the particles is described in terms of the spin and of the momentum (or position) coordinates. The interaction between the electromagnetic field and the momentum variables is neglected. The LlNDBLAD equations for the system in either representation are derived.
Quantum computers based on superconducting qubits have emerged as a leading candidate for a scalable quantum processor architecture. The core of a quantum processor consists of quantum devices that are manipulated using classical electronic circuits, which need to be co-designed for optimal performance and operation. As the principles governing the behavior of the classical circuits and the quantum devices are different, this presents a unique challenge in terms of the simulation, design and optimization of the joint system. A methodology is presented to transform the behavior of small-scale quantum processors to equivalent circuit models that are usable with classical circuits in a generic electrical simulator, enabling the detailed analysis of the impact of many important non-idealities. The methodology has specifically been employed to derive a circuit model of a superconducting qubit interacting with the quantized electromagnetic field of a superconducting resonator. Based on this technique, a comprehensive analysis of the qubit operation is performed, including the coherent control and readout of the qubit using electrical signals. Furthermore, the effect of several non-idealities in the system such as qubit relaxation, decoherence and leakage out of the computational subspace are captured, in contrast to previous works. As the presented method enables the co-simulation of the control electronics with the quantum system, it facilitates the design and optimization of near-term superconducting quantum processors.