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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 State of the field**

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 Motivation Problem Novel ideas on charge noise

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**Josephson junction qubits**

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

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**Characterization of the noise**

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

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**Sources of noise A strategy to identify the 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) Zorin et al. 1996 A strategy to identify the sources of noise Level I : Complete Phenomenological model of the noise. Proper model of dephasing [fluctuator model] Non-Markovian bath, non gaussian noise. Level II : Fingerprint experiments in order to infer spectral proprieties of the charge noise (correlated or uncorrelated noise? Use of dynamical decoupling schemes?) Analysis of error threshold for fault-tolerant QC. Level III : Novel ideas on microscopic origin of 1/f charge noise Experiments in progress at NEC, NIST, UIUC, MD

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**Phenomenological model of decoherence**

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

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**But 1/f noise is special... Golden Rule fails for 1/f noise, where**

Non-exponential decay of coherence Cottet et al. (01)

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**Robustness of G. Ithier et al. PRB 05 Saclay, Charge – Flux Qubit**

Y. Nakamura et al. 2006 NEC, Flux Qubit K. Kakuyanagi et al. 2006 NTT, Flux Qubit

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**From Random Telegraph Signals to 1/f Noise: the role of classical fluctuators**

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

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**Interplay of several energy scales**

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

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**Noise in superconducting qubits**

Small Josephson charge qubits Critical current fluctuations for all other qubits F. C. Wellstood et al. 2004 D. Van Harlingen et a. 2004 Same origin of the noise at low and high frequency? O. Astafiev et al. 2004 A. Shnirman et al. 2005

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**Dephasing by TLSs Faoro & Ioffe, 2006**

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

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

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**Dephasing rates for the dipoles**

The weak interaction between dipoles causes: a width in each TLS at low frequency some of the TLSs become classical Effective electric field pure dephasing: 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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**Theory of TLSs NEC Experiments For substrate volume**

Because of the qualitatively disagreement: search for fluctuators of different nature !!

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**In the barrier... The density of TLSs ~ too low! Strongly coupled TLS**

Astafiev et al. 2004 Relaxation in phase qubit, NIST UCSB

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**… and the solutions? Faoro, Bergli, Altshuler and Galperin, 2005**

Andreev fluctuators qubit - dependence at low frequency

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

Kondo Temperature

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**Properties of the ground state and the localized excited state**

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**“Physics” of the Kondo-like traps**

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

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**at low and high frequency**

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

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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-Al2O3-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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**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? Impressive universality: 7±3x10-6 [ 0] SQUID~ mm F.C.Wellstood et al. APL50, 772 (1987) 1.5x10-6 [ 0] phase qubit ~10000? mm2 (UCSB) ~ 1x10-6 [ 0] flux qubit ~1000 mm2 (Berkeley) ~ 1x10-6 [ 0] flux qubit ~ 100 mm2 (NTT) ~ 1x10-6 [ 0] flux qubit ~ 3 mm2 (NEC) (2006) Loop size independent ?? Slope of the noise 2/3 ?? There are no RTSs! * in collaboration with Fred Wellstood, MD.

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