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:2208.03738

Experimental verification of the treatment of time-dependent flux in circuit quantization

Jacob Bryon, D. K. Weiss, Xinyuan You, Sara Sussman, Xanthe Croot, Ziwen Huang, Jens Koch, Andrew Houck

Published Aug 7, 2022• 1 citation
arXivHTMLPDF

Abstract

Recent theoretical work has highlighted that quantizing a superconducting circuit in the presence of time-dependent flux $Φ(t)$ generally produces Hamiltonian terms proportional to $dΦ/dt$ unless a special allocation of the flux across inductive terms is chosen. Here, we present an experiment probing the effects of a fast flux ramp applied to a heavy-fluxonium circuit. The experiment confirms that naïve omission of the $dΦ/dt$ term leads to theoretical predictions inconsistent with experimental data. Experimental data are fully consistent with recent theory that includes the derivative term or equivalently uses "irrotational variables" that uniquely allocate the flux to properly eliminate the $dΦ/dt$ term.

DOI
10.48550/arxiv.2208.03738

Related papers

Time-Dependent Magnetic Flux in Devices for Circuit Quantum Electrodynamics

Jacob Bryon, Daniel Weiss, Xinyuan You +5 more

Time-dependent external flux is ubiquitous across circuit quantum electrodynamics and calls for accurate modeling. Contrary to long-held belief, it is recently predicted---but not yet verified---that the allocation of time-dependent flux cannot be arbitrary in the Hamiltonian. This study provides an experimental verification of this prediction by applying fast flux pulses to a fluxonium qubit and taking measurements of the quantum state following the pulses. Given the widespread use of time-dependent flux in experiments with superconducting qubits, verification of this theory is critical to our understanding of circuit quantum electrodynamics.

Physical Review Applied•Mar 9, 2023•24 citations

Circuit quantization in the presence of time-dependent external flux

Xinyuan You, James A. Sauls, Jens Koch

Circuit quantization links a physical circuit to its corresponding quantum Hamiltonian. The standard quantization procedure generally assumes any external magnetic flux to be static. Time dependence naturally arises, however, when flux is modulated or when flux noise is considered. In this case, application of the existing quantization procedure can lead to inconsistencies. To resolve these, we generalize circuit quantization to incorporate time-dependent external flux.

arXiv:1902.04734•Physical review. B./Physical review. B•May 21, 2019•87 citations

Compact description of quantum phase slip junctions

Christina Koliofoti, Roman-Pascal Riwar

Abstract Quantum circuit theory is a powerful tool to describe superconducting circuits. In its language, quantum phase slips (QPSs) are considered to be the exact dual to the Josephson effect. This duality renders the integration of QPS junctions into a unified theoretical framework challenging. As we argue, different existing formalisms may be inconsistent, and the correct inclusion of time-dependent flux driving requires introducing a large number of auxiliary, nonphysical degrees of freedom. We resolve these issues by describing QPS junctions as inductive rather than capacitive elements, and reducing the Hilbert space to account for a compact superconducting phase. Our treatment provides an approach to circuit quantization exclusively in terms of node-flux-node variables, and eliminates spurious degrees of freedom. Finally, the inductive treatment reveals the possibility of a voltage-dependent renormalization of the QPS amplitude, by accounting for spatial variations of the electric field built up across the junction.

npj Quantum Information•Dec 19, 2023•10 citations

Inherent flux crosstalk and coupler-driven single-qubit gates in superconducting circuits

Balázs Gulácsi, Guido Burkard

Crosstalk refers to unwanted qubit addressing. This is particularly detrimental when scaling up quantum information systems because unintended interactions limit their overall performance. For superconducting qubits, tunable couplings and frequency tunability achieved through externally applied magnetic fluxes enable high-fidelity entangling gates; however, they also introduce crosstalk through unintended flux coupling. In this work, we investigate the impact of time-dependent external magnetic fluxes in quantized circuits on superconducting qubit couplings. We find that non-trivial cross-voltage driving emerges between capacitively linked qubits when the magnetic flux threading the SQUID loop of a qubit varies in time, in a manner analogous to Faraday's law of induction. Crucially, we show that this effect enables fast single qubit control through the coupler element in standard tunable-coupler architectures, potentially eliminating the need for individual microwave $XY$ control lines.

quant-pharXiv:2606.10970•Jun 10, 2026•0 citations

Flux-charge symmetric theory of superconducting circuits

Andrew Osborne, Andrew Lucas

The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to circuit quantization treat fluxes and charges, which end up as the canonically conjugate degrees of freedom on phase space, asymmetrically. By combining intuition from topological graph theory with a recent symplectic geometry approach to circuit quantization, we present a theory of circuit quantization that treats charges and fluxes on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to nonplanar circuits.

arXiv:2401.08549•Physical review. B./Physical review. B•May 23, 2024•4 citations

The quantization of mesoscopic LC-circuits. Basic ideas and applications

Erhardt Papp, Codruta Micu, Dania Racolta

In this paper one deals with the quantization of mesoscopic LC-circuits under the influence of an external time dependent voltage. The canonically conjugated variables, such as given by the electric charge and the magnetic flux get established by resorting to the hamiltonian equations of motion. This time the discretization of the electric charge is accounted for by working in combination with both right-hand and left-hand discrete derivatives. This results in the onset of related magnetic flux operators. Besides the discrete Schrödinger equation with nearest-neighbor hoppings, a nontrivial next nearest neighbor generalization has also been established. Handling the time dependent voltage within the nearest neighbor description opens the way to the derivation of dynamic localization effects in terms of the approach discussed before by Dunlap and Kenkre, L-ring configurations included.

AIP conference proceedings•Jan 1, 2015•3 citations
Recent theoretical work has highlighted that quantizing a superconducting circuit in the presence of time-dependent flux Φ(t)Φ(t)Φ(t) generally produces Hamiltonian terms proportional to dΦ/dtdΦ/dtdΦ/dt unless a special allocation of the flux across inductive terms is chosen. Here, we present an experiment probing the effects of a fast flux ramp applied to a heavy-fluxonium circuit. The experiment confirms that naïve omission of the dΦ/dtdΦ/dtdΦ/dt term leads to theoretical predictions inconsistent with experimental data. Experimental data are fully consistent with recent theory that includes the derivative term or equivalently uses "irrotational variables" that uniquely allocate the flux to properly eliminate the dΦ/dtdΦ/dtdΦ/dt term.
Time-dependent external flux is ubiquitous across circuit quantum electrodynamics and calls for accurate modeling. Contrary to long-held belief, it is recently predicted---but not yet verified---that the allocation of time-dependent flux cannot be arbitrary in the Hamiltonian. This study provides an experimental verification of this prediction by applying fast flux pulses to a fluxonium qubit and taking measurements of the quantum state following the pulses. Given the widespread use of time-dependent flux in experiments with superconducting qubits, verification of this theory is critical to our understanding of circuit quantum electrodynamics.
Abstract Quantum circuit theory is a powerful tool to describe superconducting circuits. In its language, quantum phase slips (QPSs) are considered to be the exact dual to the Josephson effect. This duality renders the integration of QPS junctions into a unified theoretical framework challenging. As we argue, different existing formalisms may be inconsistent, and the correct inclusion of time-dependent flux driving requires introducing a large number of auxiliary, nonphysical degrees of freedom. We resolve these issues by describing QPS junctions as inductive rather than capacitive elements, and reducing the Hilbert space to account for a compact superconducting phase. Our treatment provides an approach to circuit quantization exclusively in terms of node-flux-node variables, and eliminates spurious degrees of freedom. Finally, the inductive treatment reveals the possibility of a voltage-dependent renormalization of the QPS amplitude, by accounting for spatial variations of the electric field built up across the junction.
Crosstalk refers to unwanted qubit addressing. This is particularly detrimental when scaling up quantum information systems because unintended interactions limit their overall performance. For superconducting qubits, tunable couplings and frequency tunability achieved through externally applied magnetic fluxes enable high-fidelity entangling gates; however, they also introduce crosstalk through unintended flux coupling. In this work, we investigate the impact of time-dependent external magnetic fluxes in quantized circuits on superconducting qubit couplings. We find that non-trivial cross-voltage driving emerges between capacitively linked qubits when the magnetic flux threading the SQUID loop of a qubit varies in time, in a manner analogous to Faraday's law of induction. Crucially, we show that this effect enables fast single qubit control through the coupler element in standard tunable-coupler architectures, potentially eliminating the need for individual microwave XYXYXY control lines.
The quantum mechanics of superconducting circuits is derived by starting from a classical Hamiltonian dynamical system describing a dissipationless circuit, usually made of capacitive and inductive elements. However, standard approaches to circuit quantization treat fluxes and charges, which end up as the canonically conjugate degrees of freedom on phase space, asymmetrically. By combining intuition from topological graph theory with a recent symplectic geometry approach to circuit quantization, we present a theory of circuit quantization that treats charges and fluxes on a manifestly symmetric footing. For planar circuits, known circuit dualities are a natural canonical transformation on the classical phase space. We discuss the extent to which such circuit dualities generalize to nonplanar circuits.
In this paper one deals with the quantization of mesoscopic LC-circuits under the influence of an external time dependent voltage. The canonically conjugated variables, such as given by the electric charge and the magnetic flux get established by resorting to the hamiltonian equations of motion. This time the discretization of the electric charge is accounted for by working in combination with both right-hand and left-hand discrete derivatives. This results in the onset of related magnetic flux operators. Besides the discrete Schrödinger equation with nearest-neighbor hoppings, a nontrivial next nearest neighbor generalization has also been established. Handling the time dependent voltage within the nearest neighbor description opens the way to the derivation of dynamic localization effects in terms of the approach discussed before by Dunlap and Kenkre, L-ring configurations included.