We introduce conditionally clean ancilla qubits, a new quantum resource, recently explored by \cite{nie2024quantum}, that bridges the gap between traditional clean and dirty ancillae. Like dirty ancillae, they begin and end in an unknown state and can be borrowed from existing system qubits, avoiding the space overhead of explicit qubit allocation. Like clean ancillae, they can be treated as initialized in a known state within specific computations, thus avoiding the overhead of toggle detection required for dirty ancillae. We present new circuit constructions leveraging conditionally clean ancillae to achieve lower gate counts and depths, particularly with limited ancilla availability. Specifically, we provide constructions for:(a) n -controlled NOT using 2 n Toffolis and O ( log ⁡ n ) depth given 2 clean ancillae.(b) n -qubit incrementer using 3 n Toffolis given log 2 ∗ ⁡ n clean ancillae.(c) n -qubit quantum-classical comparator using 3 n Toffolis given log 2 ∗ ⁡ n clean ancillae.(d) unary iteration over [ 0 , N ) using 2.5 N Toffolis given log 2 ∗ ⁡ n clean ancillae.(e) unary iteration via skew tree over [ 0 , N ) using 1.25 N Toffolis given n dirty ancillae.We also introduce laddered toggle detection , a technique to replace clean ancillae with dirty ancillae in all our constructions, incurring a 2x Toffoli gate overhead. Our results demonstrate that conditionally clean ancillae are a valuable tool for quantum circuit design, especially in the resource-constrained early fault-tolerant era.We introduce conditionally clean ancilla qubits, a new quantum resource, recently explored by \cite{nie2024quantum}, that bridges the gap between traditional clean and dirty ancillae. Like dirty ancillae, they begin and end in an unknown state and can be borrowed from existing system qubits, avoiding the space overhead of explicit qubit allocation. Like clean ancillae, they can be treated as initialized in a known state within specific computations, thus avoiding the overhead of toggle detection required for dirty ancillae. We present new circuit constructions leveraging conditionally clean ancillae to achieve lower gate counts and depths, particularly with limited ancilla availability. Specifically, we provide constructions for:(a) n -controlled NOT using 2 n Toffolis and O ( log ⁡ n ) depth given 2 clean ancillae.(b) n -qubit incrementer using 3 n Toffolis given log 2 ∗ ⁡ n clean ancillae.(c) n -qubit quantum-classical comparator using 3 n Toffolis given log 2 ∗ ⁡ n clean ancillae.(d) unary iteration over [ 0 , N ) using 2.5 N Toffolis given log 2 ∗ ⁡ n clean ancillae.(e) unary iteration via skew tree over [ 0 , N ) using 1.25 N Toffolis given n dirty ancillae.We also introduce laddered toggle detection , a technique to replace clean ancillae with dirty ancillae in all our constructions, incurring a 2x Toffoli gate overhead. Our results demonstrate that conditionally clean ancillae are a valuable tool for quantum circuit design, especially in the resource-constrained early fault-tolerant era.

arXiv:2407.17966QuantumMay 21, 202516 citations

Correlation Functions

Peter Millington

Springer thesesOct 29, 20130 citations

Correlation Functions

Jurgen Michael Honig, Józef Spałek

Elsevier eBooksJan 1, 20180 citations

Kinetic inductance of few-layer NbSe2 in the two-dimensional limit

Sameia Zaman, Joel I-Jan Wang, Thomas Werkmeister +19 more

Abstract Van der Waals (vdW) superconductors remain superconducting down to the monolayer limit, enabling the exploration of emergent physical phenomena and functionality driven by reduced dimensionality. Here, we report the characterization of the kinetic inductance of atomically thin NbSe 2 , a two-dimensional van der Waals superconductor, using superconducting coplanar waveguides and microwave measurement techniques familiar to circuit quantum electrodynamics (cQED). The kinetic inductance scales inversely with the number of NbSe 2 layers, reaching 1.2 nH/ □ in the monolayer limit. Furthermore, the measured kinetic inductance exhibits a thickness-dependent crossover from clean- to dirty-limit behavior, with enhanced dirty-limit contributions emerging in the ultra-thin regime. These effects are likely driven by increased surface scattering, multi-band superconductivity, and geometric confinement. Additionally, the self-Kerr nonlinearity of the NbSe 2 films ranges from K/2π = −0.006 to −14.7 Hz/photon, indicating its strong potential in applications requiring compact, nearly linear, high-inductance superconducting quantum devices and detectors. The fabrication and characterization techniques demonstrated here are extensible to the investigation of other two-dimensional superconductors.Abstract Van der Waals (vdW) superconductors remain superconducting down to the monolayer limit, enabling the exploration of emergent physical phenomena and functionality driven by reduced dimensionality. Here, we report the characterization of the kinetic inductance of atomically thin NbSe 2 , a two-dimensional van der Waals superconductor, using superconducting coplanar waveguides and microwave measurement techniques familiar to circuit quantum electrodynamics (cQED). The kinetic inductance scales inversely with the number of NbSe 2 layers, reaching 1.2 nH/ □ in the monolayer limit. Furthermore, the measured kinetic inductance exhibits a thickness-dependent crossover from clean- to dirty-limit behavior, with enhanced dirty-limit contributions emerging in the ultra-thin regime. These effects are likely driven by increased surface scattering, multi-band superconductivity, and geometric confinement. Additionally, the self-Kerr nonlinearity of the NbSe 2 films ranges from K/2π = −0.006 to −14.7 Hz/photon, indicating its strong potential in applications requiring compact, nearly linear, high-inductance superconducting quantum devices and detectors. The fabrication and characterization techniques demonstrated here are extensible to the investigation of other two-dimensional superconductors.

arXiv:2511.08466Nature CommunicationsJul 23, 20261 citation

Correlation Functions

Ulrich Hohenester

Graduate texts in physicsDec 18, 20190 citations

Dirty Hubbard rings: renormalization group and exact diagonalization studies

弘之森, Minoru HAMADA

We studied mesoscopic Hubbard rings with impurities using the renormalization group (RG) technique and the exact diagonalizations. The exact diagonalization calculations showed that the charge stiffness normalized by the value of clean system has a peak as a function of electron-electron interactions. Previous RG analysis has succeeded to show the enhancement of the stiffness at weak interactions, but does not show the peak behavior. We derived RG equations with $4k_F$ impurity scattering term, which was ignored in the previous studies, and reproduced the overall behavior of the exact diagonalization results.We studied mesoscopic Hubbard rings with impurities using the renormalization group (RG) technique and the exact diagonalizations. The exact diagonalization calculations showed that the charge stiffness normalized by the value of clean system has a peak as a function of electron-electron interactions. Previous RG analysis has succeeded to show the enhancement of the stiffness at weak interactions, but does not show the peak behavior. We derived RG equations with $4k_F$ impurity scattering term, which was ignored in the previous studies, and reproduced the overall behavior of the exact diagonalization results.

arXiv:cond-mat/9509060Sep 12, 19950 citations

4k_F

impurity scattering term, which was ignored in the previous studies, and reproduced the overall behavior of the exact diagonalization results.