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Low frequency noise in superconducting qubits Lara Faoro and Lev Ioffe Rutgers University (USA) Exp. Collaborators: Oleg Astafiev (NEC, Tsukuba), Ray Simmonds (NIST, Boulder), Dale Van Harlingen (UIUC, Urbana Champaign) and Fred Wellstood (MD)

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Outline Studies of decoherence in superconducting qubits (almost complete phenomenology of the noise) : low frequency noise (1/f noise in charge, critical currents, flux) high frequency noise ( f noise for charge qubits but... for the other devices ??) Recent developments in Fault-Tolerant QEC show that proofs and estimates of the error thresholds strongly depend on the physical characteristics of the noise: i.e. temporal (memory effects) and spatial (inter-qubits) correlations. It is essential to achieve the complete phenomenological characterization of the noise in superconducting qubit in order to design “realistic” strategies for QEC. We need to understand the microscopic origin of the charge/flux sources of noise : weakly interacting quantum Two Level Systems (TLSs) environment made by Kondo-like traps Novel ideas on charge noise State of the field Motivation Problem

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Josephson junction qubits phaseflux charge - flux charge Electrostatic Josephson energy CPB in a cavity NEC IBM Josephson junction

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Where are we? Relaxation timeDephasing time Error Per Gate Characterization of the noise Too short due to 1/f noise

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Sources of noise external circuit, quasi particle measurement motion of trapped vortices in superconductor motion of charges in associated dielectrics and oxides (responsible for 1/f noise in metallic junction) A strategy to identify the sources of noise Level II : Fingerprint experiments in order to infer spectral proprieties of the charge noise (correlated or uncorrelated noise? Use of dynamical decoupling schemes?) Zorin et al Level I : Complete Phenomenological model of the noise. Proper model of dephasing [fluctuator model] Non-Markovian bath, non gaussian noise. Level III : Novel ideas on microscopic origin of 1/f charge noise Experiments in progress at NEC, NIST, UIUC, MD Analysis of error threshold for fault-tolerant QC.

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Phenomenological model of decoherence Relaxation rate Dephasing rate Charged defects in barrier, substrate or surface lead to fluctuating induced charge Longitudinal coupling to the charge degree of freedom Golden Rule: Noise power spectrum Pure dephasing

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But 1/f noise is special... Golden Rule fails for 1/f noise, where Cottet et al. (01) Non-exponential decay of coherence

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G. Ithier et al. PRB 05 Saclay, Charge – Flux Qubit Y. Nakamura et al NEC, Flux Qubit K. Kakuyanagi et al NTT, Flux Qubit Robustness of

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From Random Telegraph Signals to 1/f Noise: the role of classical fluctuators A superposition of many RTSs with a distribution of switching rates exponentially broad gives a 1/f noise spectrum Random Telegraph Signal (RTS) Switching rate: Noise power spectrum: Number of fluctuators/decade Average coupling to the qubit

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Falci et al., PRL 2005 Interplay of several energy scales Non gaussian effects are relevant for initial decoherence (inhomogeneous broadening) and crucial for error correction! ??? MHz (indirect echo) ???

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Noise in superconducting qubits Small Josephson charge qubitsCritical current fluctuations for all other qubits Same origin of the noise at low and high frequency? O. Astafiev et al A. Shnirman et al F. C. Wellstood et al D. Van Harlingen et a. 2004

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Dephasing by TLSs Mechanisms of relaxation for TLSs A common belief: charged impurities are TLSs in the surrounding insulators J. L. Black and B. I. Halperin, (1977) L. Levitov (1991) A. L. Burin (1995) interaction with low energy phonons T >100 mK many TLSs interact via dipole-dipole interactions: Fundamental Problem!! Faoro & Ioffe, 2006 The effective strength of the interactions is controlled by and it is always very weak. Quantum coherent TLS Each TLS is coupled weakly to a dissipative bath ?

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Some notations. Each dipole induces a change in the island potential or in the gate charge i.e. barrier substrate Charge Noise Power Spectrum: Rotated basis:

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Dephasing rates for the dipoles pure dephasing: The weak interaction between dipoles causes: a width in each TLS at low frequency some of the TLSs become classical Effective electric field N.B: density of thermally activated TLSs enough (Continuum) An important limit of this analysis: we neglect the interaction with the qubit, but it might be important ! (future research work...)

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Relaxation rates for the dipoles From Fermi Golden Rule we can calculate the relaxation rates: But in presence of large disorder, some of TLSs: These dipoles become classical and will be responsible for 1/f noise: i.e. how classical fluctuators emerge from an ensemble of quantum TLSs

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Charge noise power spectrum Rotated basis: Low frequency High frequency

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Because of the qualitatively disagreement: search for fluctuators of different nature !! Theory of TLSsNEC Experiments For substrate volume

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In the barrier... The density of TLSs ~ too low! Astafiev et al Strongly coupled TLS Relaxation in phase qubit, NIST UCSB

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… and the solutions? qubit Faoro, Bergli, Altshuler and Galperin, dependence at low frequency Andreev fluctuators

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Kondo Temperature … and the solutions? Faoro & Ioffe, 2006 Kondo-like traps

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Properties of the ground state and the localized excited state

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“Physics” of the Kondo-like traps Slow processes Fast processes barrier superconductor Superconductor coherence lenght Density of states close to the Fermi energy bare density weight of the Kondo resonance Transition amplitude: So far only numerics... Linear density!!

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at low and high frequency NB: Andreev fluctuators have the same but … and Agreement with experimental value: estimates : In the barrier High frequency - fast processes Low frequency - slow processes

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1/f noise due to critical current fluctuations: Fred Wellstood, Ph. D thesis 1988 Wellstood et al, APL 85, 5296 (2004) Van Harlingen et al. PRB (2004)

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with the Kondo-like traps model Nb-Al 2 O 3 -Nb At higher frequency:

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Testing our theoretical ideas... In collaboration with NEC, Tsukuba: * is superconductivity crucial for 1/f noise in Josephson charge qubits? [magnetic field, SET with very high charging energy] * are the charged fluctuators in the barrier? Is charge noise non-Markovian but local? In collaboration with NIST, Boulder and UIUC, Urbana-Champaign * is the noise in the phase qubit due to TLSs in the substrate and barrier? * Test T-dependence of the 1/f noise [Van Harlingen, Illinois] * Measurement high frequency critical current fluctuations. [Van Harlingen, Illinois] Measurement of second spectrum both in charge noise and critical current fluctuations Supported by LPS, NSA and ARO

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7±3x10 -6 [ 0 ] SQUID~ m 2 F.C.Wellstood et al. APL50, 772 (1987) 1.5x10 -6 [ 0 ] phase qubit ~10000? m 2 (UCSB) ~ 1x10 -6 [ 0 ] flux qubit ~1000 m 2 (Berkeley) ~ 1x10 -6 [ 0 ] flux qubit ~ 100 m 2 (NTT) ~ 1x10 -6 [ 0 ] flux qubit ~ 3 m 2 (NEC) A re-discovered low frequency noise Microscopic origin of the excess low frequency noise in dc-SQUIDs above 1K (due to critical current fluctuations and/or apparent flux noise) below 1K (always due to apparent flux noise) - An “old problem”: is it the ultimate limitation for all superconducting qubit? Loop size independent ?? Slope of the noise 2/3 ?? There are no RTSs! Impressive universality: (2006) * in collaboration with Fred Wellstood, MD.

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