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Bulletin of the American Physical Society

Effect of Two Level System Saturation on Charge Noise in Josephson Junction Qubits

M. Constantin, Clare C. Yu, John M. Martinis

Published Mar 11, 2008• 1 citation
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Abstract

Author(s): Yu, Clare C; Constantin, Magdalena; Martinis, John M | Abstract: We show that charge noise $S_Q$ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio $J/J_c$ of the electromagnetic flux $J$ to the critical flux $J_c$. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with $J/J_c\gg 1$. Our results are consistent with experimental conclusions that $S_Q\sim 1/f$ at low frequencies and $S_Q\sim f$ at high frequencies.

Related papers

Effect of Two Level System Saturation on Charge Noise in Josephson Junction Qubits

Clare C. Yu, Constantin, Magdalena, John M. Martinis

We show that charge noise $S_Q$ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio $J/J_c$ of the electromagnetic flux $J$ to the critical flux $J_c$. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with $J/J_c\gg 1$. Our results are consistent with experimental conclusions that $S_Q\sim 1/f$ at low frequencies and $S_Q\sim f$ at high frequencies.

arXiv:0707.1514•Jul 10, 2007•1 citation

Effect of Two Level System Saturation on Charge Noise in Josephson\n Junction Qubits

Clare C. Yu, Magdalena Constantin, John M. Martinis

We show that charge noise $S_Q$ in Josephson qubits can be produced by\nfluctuating two level systems (TLS) with electric dipole moments in the\nsubstrate using a flat density of states. At high frequencies the frequency and\ntemperature dependence of the charge noise depends on the ratio $J/J_c$ of the\nelectromagnetic flux $J$ to the critical flux $J_c$. It is not widely\nappreciated that TLS in small qubits can easily be strongly saturated with\n$J/J_c\\gg 1$. Our results are consistent with experimental conclusions that\n$S_Q\\sim 1/f$ at low frequencies and $S_Q\\sim f$ at high frequencies.

•Apr 3, 2018•0 citations

Saturation of two-level systems and charge noise in Josephson junction qubits

Magdalena Constantin, Clare C. Yu, John M. Martinis

We study the charge noise ${S}_{Q}$ in Josephson qubits produced by fluctuating two-level systems (TLSs) with electric-dipole moments in the substrate. The TLSs are driven by an alternating electric field of angular frequency $\ensuremath{\Omega}$ and electric field intensity $I$. It is not widely appreciated that TLS in small qubits can easily be strongly saturated if $I⪢{I}_{c}$, where ${I}_{c}$ is the critical electric field intensity. To investigate the effect of saturation on the charge noise, we express the noise spectral density in terms of density-matrix elements. To determine the dependence of the density-matrix elements on the ratio $I/{I}_{c}$, we find the steady-state solution for the density matrix using the Bloch-Redfield differential equations. We then obtain an expression for the spectral density of charge fluctuations as a function of frequency $f$ and the ratio $I/{I}_{c}$. We find $1/f$ charge noise at low frequencies, and that the charge noise is white (constant) at high frequencies. Using a flat density of states, we find that TLS saturation has no effect on the charge noise at either high or low frequencies.

arXiv:0810.1334•Physical Review B•Mar 20, 2009•35 citations

Decoherence in Josephson-junction qubits due to critical-current fluctuations

Dale J. Van Harlingen, Timothy L. Robertson, B. L. T. Plourde +3 more

We compute the decoherence caused by $1∕f$ fluctuations at low frequency $f$ in the critical current ${I}_{0}$ of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ scales as ${I}_{0}∕\ensuremath{\Omega}\ensuremath{\Lambda}{S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$, where $\ensuremath{\Omega}∕2\ensuremath{\pi}$ is the energy-level splitting frequency, ${S}_{{I}_{0}}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$ is the spectral density of the critical-current noise at $1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}$, and $\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{\mid}{I}_{0}d\ensuremath{\Omega}∕\ensuremath{\Omega}d{I}_{0}\ensuremath{\mid}$ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time $t$ scales as $\mathrm{exp}(\ensuremath{-}{t}^{2}∕2{\ensuremath{\tau}}_{\ensuremath{\phi}}^{2})$ when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in ${I}_{0}$ and area $\mathcal{A}$, and show that their values of ${S}_{{I}_{0}}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$ scale to within a factor of 3 of $[144{({I}_{0}∕\ensuremath{\mu}\mathrm{A})}^{2}∕(\mathcal{A}∕\ensuremath{\mu}{\mathrm{m}}^{2})]{(\mathrm{pA})}^{2}∕\mathrm{Hz}$ at $4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. We empirically extrapolate ${S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$ to lower temperatures using a scaling $T(\mathrm{K})∕4.2$. Using this result, we find that the predicted values of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ at $100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}$ range from $0.8\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, and are usually substantially longer than values measured experimentally at lower temperatures.

arXiv:cond-mat/0404307•Physical Review B•Aug 30, 2004•171 citations

Decoherence of a Josephson qubit due to coupling to two-level systems

Li-Chung Ku, Clare C. Yu

Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and $1∕f$ noise in the Josephson junction critical current ${I}_{0}$. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.

arXiv:cond-mat/0409006•Physical Review B•Jul 18, 2005•55 citations

Stabilizing and Improving Qubit Coherence by Engineering the Noise Spectrum of Two-Level Systems

Xinyuan You, Ziwen Huang, Uğur Alyanak +3 more

Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material defects that can be well described as an ensemble of two-level systems (TLSs). Among them, charge fluctuators inside amorphous oxide layers contribute to both low-frequency $1/f$ charge noise and high-frequency dielectric loss, causing fast qubit dephasing and relaxation. Moreover, spectral diffusion from mutual TLS interactions varies the noise amplitude over time, fluctuating the qubit lifetime. Here, we propose to mitigate those harmful effects by engineering the relevant TLS noise spectral densities. Specifically, our protocols smooth the high-frequency noise spectrum and suppress the low-frequency noise amplitude via depolarizing and dephasing the TLSs, respectively. As a result, we predict a drastic stabilization in qubit lifetime and an increase in qubit pure dephasing time. Our detailed analysis of feasible experimental implementations shows that the improvement is not compromised by spurious coupling from the applied noise to the qubit.

arXiv:2206.10669•Physical Review Applied•Oct 11, 2022•16 citations
Author(s): Yu, Clare C; Constantin, Magdalena; Martinis, John M | Abstract: We show that charge noise SQS_QSQ​ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio J/JcJ/J_cJ/Jc​ of the electromagnetic flux JJJ to the critical flux JcJ_cJc​. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with J/Jc≫1J/J_c\gg 1J/Jc​≫1. Our results are consistent with experimental conclusions that SQ∼1/fS_Q\sim 1/fSQ​∼1/f at low frequencies and SQ∼fS_Q\sim fSQ​∼f at high frequencies.
We show that charge noise SQS_QSQ​ in Josephson qubits can be produced by fluctuating two level systems (TLS) with electric dipole moments in the substrate using a flat density of states. At high frequencies the frequency and temperature dependence of the charge noise depends on the ratio J/JcJ/J_cJ/Jc​ of the electromagnetic flux JJJ to the critical flux JcJ_cJc​. It is not widely appreciated that TLS in small qubits can easily be strongly saturated with J/Jc≫1J/J_c\gg 1J/Jc​≫1. Our results are consistent with experimental conclusions that SQ∼1/fS_Q\sim 1/fSQ​∼1/f at low frequencies and SQ∼fS_Q\sim fSQ​∼f at high frequencies.
We show that charge noise SQS_QSQ​ in Josephson qubits can be produced by\nfluctuating two level systems (TLS) with electric dipole moments in the\nsubstrate using a flat density of states. At high frequencies the frequency and\ntemperature dependence of the charge noise depends on the ratio J/JcJ/J_cJ/Jc​ of the\nelectromagnetic flux JJJ to the critical flux JcJ_cJc​. It is not widely\nappreciated that TLS in small qubits can easily be strongly saturated with\nJ/Jcgg1J/J_c\\gg 1J/Jc​gg1. Our results are consistent with experimental conclusions that\nSQsim1/fS_Q\\sim 1/fSQ​sim1/f at low frequencies and SQsimfS_Q\\sim fSQ​simf at high frequencies.
We study the charge noise SQ{S}_{Q}SQ​ in Josephson qubits produced by fluctuating two-level systems (TLSs) with electric-dipole moments in the substrate. The TLSs are driven by an alternating electric field of angular frequency $\ensuremath{\Omega}$ and electric field intensity III. It is not widely appreciated that TLS in small qubits can easily be strongly saturated if I⪢IcI⪢{I}_{c}I⪢Ic​, where Ic{I}_{c}Ic​ is the critical electric field intensity. To investigate the effect of saturation on the charge noise, we express the noise spectral density in terms of density-matrix elements. To determine the dependence of the density-matrix elements on the ratio I/IcI/{I}_{c}I/Ic​, we find the steady-state solution for the density matrix using the Bloch-Redfield differential equations. We then obtain an expression for the spectral density of charge fluctuations as a function of frequency fff and the ratio I/IcI/{I}_{c}I/Ic​. We find 1/f1/f1/f charge noise at low frequencies, and that the charge noise is white (constant) at high frequencies. Using a flat density of states, we find that TLS saturation has no effect on the charge noise at either high or low frequencies.
We compute the decoherence caused by 1∕f1∕f1∕f fluctuations at low frequency fff in the critical current I0{I}_{0}I0​ of Josephson junctions incorporated into flux, phase, charge, and hybrid flux-charge superconducting quantum bits (qubits). The dephasing time ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ scales as ${I}_{0}∕\ensuremath{\Omega}\ensuremath{\Lambda}{S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})$, where $\ensuremath{\Omega}∕2\ensuremath{\pi}$ is the energy-level splitting frequency, SI0(1Hz){S}_{{I}_{0}}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})SI0​​(1Hz) is the spectral density of the critical-current noise at 1Hz1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz}1Hz, and $\ensuremath{\Lambda}\ensuremath{\equiv}\ensuremath{\mid}{I}_{0}d\ensuremath{\Omega}∕\ensuremath{\Omega}d{I}_{0}\ensuremath{\mid}$ is a parameter computed for given parameters for each type of qubit that specifies the sensitivity of the level splitting to critical-current fluctuations. Computer simulations show that the envelope of the coherent oscillations of any qubit after time ttt scales as $\mathrm{exp}(\ensuremath{-}{t}^{2}∕2{\ensuremath{\tau}}_{\ensuremath{\phi}}^{2})$ when the dephasing due to critical-current noise dominates the dephasing from all sources of dissipation. We compile published results for fluctuations in the critical current of Josephson tunnel junctions fabricated with different technologies and a wide range in I0{I}_{0}I0​ and area A\mathcal{A}A, and show that their values of SI0(1Hz){S}_{{I}_{0}}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})SI0​​(1Hz) scale to within a factor of 3 of $[144{({I}_{0}∕\ensuremath{\mu}\mathrm{A})}^{2}∕(\mathcal{A}∕\ensuremath{\mu}{\mathrm{m}}^{2})]{(\mathrm{pA})}^{2}∕\mathrm{Hz}$ at 4.2K4.2\phantom{\rule{0.3em}{0ex}}\mathrm{K}4.2K. We empirically extrapolate SI01∕2(1Hz){S}_{{I}_{0}}^{1∕2}(1\phantom{\rule{0.3em}{0ex}}\mathrm{Hz})SI0​1∕2​(1Hz) to lower temperatures using a scaling T(K)∕4.2T(\mathrm{K})∕4.2T(K)∕4.2. Using this result, we find that the predicted values of ${\ensuremath{\tau}}_{\ensuremath{\phi}}$ at 100mK100\phantom{\rule{0.3em}{0ex}}\mathrm{mK}100mK range from $0.8\phantom{\rule{0.5em}{0ex}}\text{to}\phantom{\rule{0.5em}{0ex}}12\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{s}$, and are usually substantially longer than values measured experimentally at lower temperatures.
Noise and decoherence are major obstacles to the implementation of Josephson junction qubits in quantum computing. Recent experiments suggest that two-level systems (TLS) in the oxide tunnel barrier are a source of decoherence. We explore two decoherence mechanisms in which these two-level systems lead to the decay of Rabi oscillations that result when Josephson junction qubits are subjected to strong microwave driving. (A) We consider a Josephson qubit coupled resonantly to a two-level system, i.e., the qubit and TLS have equal energy splittings. As a result of this resonant interaction, the occupation probability of the excited state of the qubit exhibits beating. Decoherence of the qubit results when the two-level system decays from its excited state by emitting a phonon. (B) Fluctuations of the two-level systems in the oxide barrier produce fluctuations and 1∕f1∕f1∕f noise in the Josephson junction critical current I0{I}_{0}I0​. This in turn leads to fluctuations in the qubit energy splitting that degrade the qubit coherence. We compare our results with experiments on Josephson junction phase qubits.
Superconducting circuits are a leading platform for quantum computing. However, their coherence times are still limited and exhibit temporal fluctuations. Those phenomena are often attributed to the coupling between qubits and material defects that can be well described as an ensemble of two-level systems (TLSs). Among them, charge fluctuators inside amorphous oxide layers contribute to both low-frequency 1/f1/f1/f charge noise and high-frequency dielectric loss, causing fast qubit dephasing and relaxation. Moreover, spectral diffusion from mutual TLS interactions varies the noise amplitude over time, fluctuating the qubit lifetime. Here, we propose to mitigate those harmful effects by engineering the relevant TLS noise spectral densities. Specifically, our protocols smooth the high-frequency noise spectrum and suppress the low-frequency noise amplitude via depolarizing and dephasing the TLSs, respectively. As a result, we predict a drastic stabilization in qubit lifetime and an increase in qubit pure dephasing time. Our detailed analysis of feasible experimental implementations shows that the improvement is not compromised by spurious coupling from the applied noise to the qubit.