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arXiv:0909.4321 · Physical Review B

Experimental demonstration of a robust and scalable flux qubit

R. Harris, J. Johansson, A. J. Berkley, Mark W. Johnson, Trevor M. Lanting, Siyuan Han, P. Bunyk, E. Ladizinsky, T. Oh, I. Perminov, E. Tolkacheva, Sergey V. Uchaikin, E. M. Chapple, Colin Enderud, C. Rich, M. C. Thom, J. Wang, B. Wilson, Geordie Rose

Published Apr 7, 2010• 180 citations
arXivHTMLPDF

Abstract

A rf--superconducting quantum interference device (SQUID) flux qubit that is robust against fabrication variations in Josephson-junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest-lying states, both in the coherent and incoherent regimes, are presented. These experimental results are shown to be in agreement with predictions of a quantum-mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf SQUIDs reported in the literature thus far, with a $1/f$ flux noise spectral density at 1 Hz of ${1.3}_{\ensuremath{-}0.5}^{+0.7}\text{ }\ensuremath{\mu}{\ensuremath{\Phi}}_{0}/\sqrt{\text{Hz}}$. An explicit formula for converting the observed flux noise spectral density into a free-induction-decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented.

DOI
10.1103/physrevb.81.134510

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It is well known that that superconducting qubits based on Josephson junctions have the advantages of scalability and the qubit states are easy to prepare and control. In addition, demonstration of Rabi oscillations in various superconducting circuits shows that superconducting qubits are promising for scalable quantum information processing. However, despite flexibility of design and fabrication, easier to scale up, and fast gate speed, superconducting qubits usually have much shorter decoherence time than trapped ions, NMR etc. due to the relatively strong interactions between qubits and environment. Recent experiments show that low frequency flux noise is the dominant mechanism of decoherence in superconducting flux qubits. However, despite extensive effort the origin of flux noise is still not well understood. The goal of this work is to identify the source and characterize the property of flux noisein rf SQUID flux qubit through various spectroscopy and time-resolved measurements. Our result show that one can determine all circuit parameters needed for reconstructing qubit Hamiltonian with high accuracy via measurement of macroscopic resonant tunneling (MRT) and photon assisted tunneling (PAT) and that the amount of flux noise in rf SQUID qubits scales linearly with self inductance of the qubits. In addition, we have investigated the dynamics of a three-level flux qubit in incoherent regime. The result demonstrates that treating a multi-level physical qubit, such as the superconducting flux qubit, as an ideal two-level quantum system may be inadequate under certain circumstances.

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Abstract The detailed characteristics of classical states in a radio-frequency superconducting quantum interference device (rf-SQUID) with well-designed energy-potential shape are investigated at 4.2 K. Using Nb/AlO x standard process which enables precise circuit-parameter implementation, the rf-SQUID is designed in its energy potential. Directions of persistent current can be distinguished in the rf-SQUID we have fabricated. Analyses in circuit simulations indicate the device design based on enough high critical current provides available parameters to construct the device for 10 mK measurement by circuit-parameter scaling. This knowledge may contribute to the precise design of the rf-SQUID for superconducting qubit through device process with lower critical current density.

Japanese Journal of Applied Physics•May 13, 2021•6 citations

Magnetic flux noise in SQUIDs and qubits

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For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as $S_Phi(f) propto 1/f^alpha$, where $alpha lesssim 1$, has been known to limit the low-frequency performance of dc superconducting quantum interference devices (SQUIDs). In recent years, experiments indicate that this same noise persists to frequencies up to 1~GHz and is a dominant source of dephasing in flux-sensitive superconducting quantum bits (qubits). Thus, the reduction of flux noise presents a major hurdle towards the successful realization of scalable quantum computers that are based on flux-based qubits. In this thesis, we present experimental measurements, theoretical analyses, and numerical simulations that support a more detailed understanding of both the microscopic and macroscopic properties of flux noise.Our experimental work begins with flux noise measurements of a large number of SQUIDs in the temperature range from 0.1~K to 4~K. We report on measurements of ten SQUIDs with systematically varied geometries and show that $alpha$ increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID washer. We show that these results are incompatible with a model based on the random reversal of independent, spins that are located at the surface of the SQUID washer.In the course of our flux noise measurements, we became aware of a spurious contribution to low-frequency critical current noise in Josephson junctions---normally attributed to charge trapping in the barrier---arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. By computing cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions, we show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, because $1/f$ critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.Next, we introduce a numerical method of calculating the mean square flux noise $Phisq$ from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, $Phisq$ is proportional to $langleBbf(rbf)^2rangle$, where $Bbf(rbf)$ is the magnetic field generated by a circulating current around the loop and $rbf$ varies over the loop surface. By discretizing the loop nonuniformly, we efficiently and accurately compute the current distribution and resulting magnetic field, which may vary rapidly across the loop. We use this method to compute $Phisq$ in a number of scenarios in which we systematically vary physical parameters of the loop. We compare our simulations to an earlier analytic result predicting that $Phisq propto R/W$ in the limit where the loop radius $R$ is much greater than the linewidth $W$. We further show that the previously neglected contribution of edge spins to $Phisq$ is significant---even dominant---in narrow-linewidth loops.To calculate theoretical dephasing rates in qubits, we consider flux noise with a spectral density $S_Phi(f) = A^2/(f/1~hbox{Hz})^alpha$, where $A$ is of the order of 1~$muPhi_0 , hbox{Hz}^{-1/2}$ and $0.6 leq alpha leq 1.2$; $Phi_{0}$ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, our calculations of the dependence of the pure dephasing time $tau_phi$ of Ramsey and echo pulse sequences on $alpha$ for fixed $A$ show that $tau_phi$ decreases rapidly as $alpha$ is reduced. We find that $tau_phi$ is relatively insensitive to the noise bandwidth, $f_1 leq f leq f_2$, for all $alpha$ provided the ultraviolet cutoff frequency $f_2 > 1/tau_phi$. We calculate the ratio $tau_{phi,E} / tau_{phi,R}$ of the echo ($E$) and Ramsey ($R$) sequences, and the dependence of the decay function on $alpha$ and $f_2$. We investigate the case in which $S_Phi(f_0)$ is fixed at the ``pivot frequency'' $f_0 neq 1$~Hz while $alpha$ is varied, and find that the choice of $f_0$ can greatly influence the sensitivity of $tau_{phi,E}$ and $tau_{phi,R}$ to the value of $alpha$.Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research.

•Jan 1, 2013•0 citations

Studies of Quantum Transitions of Magnetic Flux in a RF Squid Qubit

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R Harris, F Brito, A J Berkley +10 more

A practical strategy for synchronizing the properties of compound Josephson junction (CJJ) radio frequency monitored superconducting quantum interference device (rf-SQUID) qubits on a multi-qubit chip has been demonstrated. The impact of small (∼1%) fabrication variations in qubit inductance and critical current can be minimized by the application of a custom-tuned flux offset to the CJJ structure of each qubit. This strategy allows for a simultaneous synchronization of the qubit persistent current and tunnel splitting over a range of external bias parameters that is relevant for the implementation of an adiabatic quantum processor.

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R. Harris, Trevor M. Lanting, A. J. Berkley +7 more

An improved tunable coupling element for building networks of coupled rf-superconducting quantum interference device (rf-SQUID) flux qubits has been experimentally demonstrated. This new form of coupler, based on the compound Josephson-junction rf-SQUID, provides a sign and magnitude tunable mutual inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility.

arXiv:0904.3784•Physical Review B•Aug 20, 2009•95 citations
A rf--superconducting quantum interference device (SQUID) flux qubit that is robust against fabrication variations in Josephson-junction critical currents and device inductance has been implemented. Measurements of the persistent current and of the tunneling energy between the two lowest-lying states, both in the coherent and incoherent regimes, are presented. These experimental results are shown to be in agreement with predictions of a quantum-mechanical Hamiltonian whose parameters were independently calibrated, thus justifying the identification of this device as a flux qubit. In addition, measurements of the flux and critical current noise spectral densities are presented that indicate that these devices with Nb wiring are comparable to the best Al wiring rf SQUIDs reported in the literature thus far, with a 1/f1/f1/f flux noise spectral density at 1 Hz of 1.3\ensuremath−0.5+0.7 \ensuremathμ\ensuremathΦ0/Hz{1.3}_{\ensuremath{-}0.5}^{+0.7}\text{ }\ensuremath{\mu}{\ensuremath{\Phi}}_{0}/\sqrt{\text{Hz}}1.3\ensuremath−0.5+0.7​ \ensuremathμ\ensuremathΦ0​/Hz​. An explicit formula for converting the observed flux noise spectral density into a free-induction-decay time for a flux qubit biased to its optimal point and operated in the energy eigenbasis is presented.
It is well known that that superconducting qubits based on Josephson junctions have the advantages of scalability and the qubit states are easy to prepare and control. In addition, demonstration of Rabi oscillations in various superconducting circuits shows that superconducting qubits are promising for scalable quantum information processing. However, despite flexibility of design and fabrication, easier to scale up, and fast gate speed, superconducting qubits usually have much shorter decoherence time than trapped ions, NMR etc. due to the relatively strong interactions between qubits and environment. Recent experiments show that low frequency flux noise is the dominant mechanism of decoherence in superconducting flux qubits. However, despite extensive effort the origin of flux noise is still not well understood. The goal of this work is to identify the source and characterize the property of flux noisein rf SQUID flux qubit through various spectroscopy and time-resolved measurements. Our result show that one can determine all circuit parameters needed for reconstructing qubit Hamiltonian with high accuracy via measurement of macroscopic resonant tunneling (MRT) and photon assisted tunneling (PAT) and that the amount of flux noise in rf SQUID qubits scales linearly with self inductance of the qubits. In addition, we have investigated the dynamics of a three-level flux qubit in incoherent regime. The result demonstrates that treating a multi-level physical qubit, such as the superconducting flux qubit, as an ideal two-level quantum system may be inadequate under certain circumstances.
Abstract The detailed characteristics of classical states in a radio-frequency superconducting quantum interference device (rf-SQUID) with well-designed energy-potential shape are investigated at 4.2 K. Using Nb/AlO x standard process which enables precise circuit-parameter implementation, the rf-SQUID is designed in its energy potential. Directions of persistent current can be distinguished in the rf-SQUID we have fabricated. Analyses in circuit simulations indicate the device design based on enough high critical current provides available parameters to construct the device for 10 mK measurement by circuit-parameter scaling. This knowledge may contribute to the precise design of the rf-SQUID for superconducting qubit through device process with lower critical current density.
For over three decades, the presence of magnetic flux noise with a power spectral density scaling roughly as SPhi(f)propto1/falphaS_Phi(f) propto 1/f^alphaSP​hi(f)propto1/falpha, where alphalesssim1alpha lesssim 1alphalesssim1, has been known to limit the low-frequency performance of dc superconducting quantum interference devices (SQUIDs). In recent years, experiments indicate that this same noise persists to frequencies up to 1~GHz and is a dominant source of dephasing in flux-sensitive superconducting quantum bits (qubits). Thus, the reduction of flux noise presents a major hurdle towards the successful realization of scalable quantum computers that are based on flux-based qubits. In this thesis, we present experimental measurements, theoretical analyses, and numerical simulations that support a more detailed understanding of both the microscopic and macroscopic properties of flux noise.Our experimental work begins with flux noise measurements of a large number of SQUIDs in the temperature range from 0.1~K to 4~K. We report on measurements of ten SQUIDs with systematically varied geometries and show that alphaalphaalpha increases as the temperature is lowered; in so doing, each spectrum pivots about a nearly constant frequency. The mean square flux noise, inferred by integrating the power spectra, grows rapidly with temperature and at a given temperature is approximately independent of the outer dimension of a given SQUID washer. We show that these results are incompatible with a model based on the random reversal of independent, spins that are located at the surface of the SQUID washer.In the course of our flux noise measurements, we became aware of a spurious contribution to low-frequency critical current noise in Josephson junctions---normally attributed to charge trapping in the barrier---arising from temperature instabilities inherent in cryogenic systems. These temperature fluctuations modify the critical current via its temperature dependence. By computing cross-correlations between measured temperature and critical current noise in Al-AlOx-Al junctions, we show that, despite excellent temperature stability, temperature fluctuations induce observable critical current fluctuations. Particularly, because 1/f1/f1/f critical current noise has decreased with improved fabrication techniques in recent years, it is important to understand and eliminate this additional noise source.Next, we introduce a numerical method of calculating the mean square flux noise PhisqPhisqPhisq from independently fluctuating spins on the surface of thin-film loops of arbitrary geometry. By reciprocity, PhisqPhisqPhisq is proportional to langleBbf(rbf)2ranglelangleBbf(rbf)^2ranglelangleBbf(rbf)2rangle, where Bbf(rbf)Bbf(rbf)Bbf(rbf) is the magnetic field generated by a circulating current around the loop and rbfrbfrbf varies over the loop surface. By discretizing the loop nonuniformly, we efficiently and accurately compute the current distribution and resulting magnetic field, which may vary rapidly across the loop. We use this method to compute PhisqPhisqPhisq in a number of scenarios in which we systematically vary physical parameters of the loop. We compare our simulations to an earlier analytic result predicting that PhisqproptoR/WPhisq propto R/WPhisqproptoR/W in the limit where the loop radius RRR is much greater than the linewidth WWW. We further show that the previously neglected contribution of edge spins to PhisqPhisqPhisq is significant---even dominant---in narrow-linewidth loops.To calculate theoretical dephasing rates in qubits, we consider flux noise with a spectral density SPhi(f)=A2/(f/1 hboxHz)alphaS_Phi(f) = A^2/(f/1~hbox{Hz})^alphaSP​hi(f)=A2/(f/1 hboxHz)alpha, where AAA is of the order of 1~muPhi0,hboxHz−1/2muPhi_0 , hbox{Hz}^{-1/2}muPhi0​,hboxHz−1/2 and 0.6leqalphaleq1.20.6 leq alpha leq 1.20.6leqalphaleq1.2; Phi0Phi_{0}Phi0​ is the flux quantum. For a qubit with an energy level splitting linearly coupled to the applied flux, our calculations of the dependence of the pure dephasing time tauphitau_phitaup​hi of Ramsey and echo pulse sequences on alphaalphaalpha for fixed AAA show that tauphitau_phitaup​hi decreases rapidly as alphaalphaalpha is reduced. We find that tauphitau_phitaup​hi is relatively insensitive to the noise bandwidth, f1leqfleqf2f_1 leq f leq f_2f1​leqfleqf2​, for all alphaalphaalpha provided the ultraviolet cutoff frequency f2>1/tauphif_2 > 1/tau_phif2​>1/taup​hi. We calculate the ratio tauphi,E/tauphi,Rtau_{phi,E} / tau_{phi,R}tauphi,E​/tauphi,R​ of the echo (EEE) and Ramsey (RRR) sequences, and the dependence of the decay function on alphaalphaalpha and f2f_2f2​. We investigate the case in which SPhi(f0)S_Phi(f_0)SP​hi(f0​) is fixed at the ``pivot frequency'' f0neq1f_0 neq 1f0​neq1~Hz while alphaalphaalpha is varied, and find that the choice of f0f_0f0​ can greatly influence the sensitivity of tauphi,Etau_{phi,E}tauphi,E​ and tauphi,Rtau_{phi,R}tauphi,R​ to the value of alphaalphaalpha.Finally, we conclude with a brief review of our principal results and conclusions. We also comment on promising avenues of future research.
At low temperature and low damping, the magnetic flux of a rf Superconducting QUantum Interference Device (SQUID) acts as a macroscopic quantum variable whose dynamic is described by a double well potential. A rf SQUID consists of a superconducting loop interrupted by a thin insulating barrier, known as a Josephson junction. The modified rf SQUID design discussed in this thesis has independent, in situ, controls that allow varying the barrier height between the potential wells and their relative tilt. This high level of control of the potential together with the capability to implement an experimental setup optimized to reduce coupling to external sources of noise, made this system ideal not only for tests of quantum transition at a macroscopic level, but also as a scalable solid state device for quantum computation. A variety of measurements of quantum phenomena are reported in this thesis, including microwave level spectroscopy, coherent oscillations, and macroscopic resonant tunneling (MRT). These measurements are compared with theoretical models to study the possible sources of decoherence in a rf SQUID qubit. The analysis confirmed that the main source of decoherence is not due to coupling to the external environment, but it can be linked to intrinsic low frequency flux noise. Work from many groups over the last several years has shown that the performance of a superconductive qubit is limited by coupling to spurious defects in the materials used for the device fabrication. In this work we analyze the possibility of using the MRT as a tool for future studies of effects of materials and fabrication process in the realization of improved qubits, and we also explore the feasibility for measurements of quantum phenomena that involve fast pulsing of the potential barrier height.
A practical strategy for synchronizing the properties of compound Josephson junction (CJJ) radio frequency monitored superconducting quantum interference device (rf-SQUID) qubits on a multi-qubit chip has been demonstrated. The impact of small (∼1%) fabrication variations in qubit inductance and critical current can be minimized by the application of a custom-tuned flux offset to the CJJ structure of each qubit. This strategy allows for a simultaneous synchronization of the qubit persistent current and tunnel splitting over a range of external bias parameters that is relevant for the implementation of an adiabatic quantum processor.
An improved tunable coupling element for building networks of coupled rf-superconducting quantum interference device (rf-SQUID) flux qubits has been experimentally demonstrated. This new form of coupler, based on the compound Josephson-junction rf-SQUID, provides a sign and magnitude tunable mutual inductance between qubits with minimal nonlinear crosstalk from the coupler tuning parameter into the qubits. Quantitative agreement is shown between an effective one-dimensional model of the coupler's potential and measurements of the coupler persistent current and susceptibility.