TITOLO!!!!!

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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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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

• 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...
fails for 1/f noise, where
Golden Rule
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 to1/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 gt100 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!!
Fast processes
Slow 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
73x10-6 0 SQUID2500-160000 mm2
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.