1. 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)

2. 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

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

4. 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

5. 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

6. 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

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

8. 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

9. 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

10. 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

11. 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

12. 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.

13. 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:

14. 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...)

15. 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

16. Charge noise power spectrum
Rotated basis:
Low frequency
High frequency

17. Theory of TLSs NEC Experiments For substrate volume
Because of the qualitatively disagreement: search for fluctuators of different nature !!

18. In the barrier... The density of TLSs ~ too low! Strongly coupled TLS
Astafiev et al. 2004
Relaxation in phase qubit, NIST UCSB

19. … and the solutions? Faoro, Bergli, Altshuler and Galperin, 2005
Andreev fluctuators
qubit
- dependence at low
frequency

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

21. Properties of the ground state and the localized excited state

22. “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

23. 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:

24. 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)

25. with the Kondo-like traps model
Nb-Al2O3-Nb
At higher frequency:

26. 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

27. 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.