Andreev Readout of Superconducting Qubits

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Andreev Read-out of Superconducting Qubits

• V T Petrashov
• Royal Holloway, University of London,
• Egham, Surrey TW20 0EX, UK
• In collaboration with
• K G Chua, K M Marshall, C Checkley, R
  Shaikhaidarov and J T Nicholls

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Superconducting Josephson-junction qubits
PERSISTENT CURRENT (FLUX) QUBIT
Quantum states with clockwise and anticlockwise
persistent current circulation in
superconducting loops interrupted by Josephson
junctions
Mooij et al. Science 285, 1036 (1999)
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Persistent current qubit (continued)
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Read-out using switching-to-voltage-state
probability measurements
(a)
(b)
(c)
(a), (b) Delft University of Technology , (b)
NEC, (a) NTT, (c) Quantronics Group CEA-Saclay
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Non-destructive read-out of persistent current
states using SQUID rf inductance measurements
Lupascu, A., Verwijs, C. J. M., Schouten, R. N.,
Harmans, C. J. P. M. Mooij, J. E.. Phys. Rev.
Lett. 93 177006 (2004)
The qubit is biased with a static magnetic flux
and with a small flux oscillating in the MW
frequency range. A coaxial line is used to apply
the RF and DC bias current (for the inductance
method and switching current measurements,
respectively).
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Non-destructive read-out of persistent current
states The impedance measurement technique
Ilichev, E. et al. Appl. Phys. Lett. 80, 4184
(2002)
Photographs of the design. The superconducting
coil with an inner hole 50 mm has 15 windings of
Nb wire of the width of 5 mm. The distance
between the wires is 5 mm. Inset the circuit
diagram of the design
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SQUID-based read-out methods Summary

• To produce a read-out the SQUID is switched into
  a voltage state, a process that strongly disturbs
  both the qubit circuit and the SQUID itself.
  Bursts of non-equilibrium quasiparticles are
  created with energies exceeding the
  superconductor gap, thus poisoning the qubit
  circuit.
• Due to the AC Josephson effect the voltage
  across the SQUID produces a microwave voltage
  pulse that can drive neighbouring qubits into
  their excited states. This makes switching
  methods unsuitable for simultaneous measurements
  of multiple qubits,
• Switching is a probabilistic process and high
  fidelity measurements require up to 105 switching
  events.
• Switching methods are unsuitable for experiments
  in which the preservation of the qubit state
  after the measurement is required (e.g., quantum
  non-demolition measurements)
• Alternative methods using dispersive read-out
  schemes have also been explored, but these are
  slow and there is a strong back-action on the
  qubit.

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Read-out of persistent current states with
Andreev interferometers
Andreev reflection no quasiparticle poisoning
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Superconducting phase-periodic transport in
normal mesoscopic conductors(Andreev
interferometers)V T Petrashov, V N Antonov, P
Delsing, and T Claeson Phys Rev Letters, 74,
5268 (1995) JETP Letters 59, 551 (1994).
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The resistance-phase relationship

• The oscillating part of the resistance between a
  and b, depends on the superconducting phase
  difference between c and d, which can be
  described by
• 
  
• The phase difference between points e and f is
  given by
• and does not depend on measurement details.
• In the absence of the screening current,
  IsA,
  
• is the external
  flux through the area enclosed by c-d-e-f .

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The layout of superconducting Josephson circuit
with attached Andreev interferometerV. T.
Petrashov, K. G. Chua, K. M. Marshall, R. Sh.
Shaikhaidarov and J. T. Nicholls Phys. Rev.
Lett. 95 147001 (2005)
Figure a, General view. b, Andreev
interferometer. The resistance R between a and b
is measured using current (I1, I2) and voltage
probes (U1, U2). c, Superconducting quantum loop
interrupted by Josephson junctions. The
superconducting phase difference between e and f
is measured with the Andreev interferometer.romete
r.
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Read-out of persistent current stateswith
Andreev interferometers experiment
V. T. Petrashov, K. G. Chua, K. M. Marshall, R.
Sh. Shaikhaidarov and J. T. Nicholls (PRL (2005))
a, Normalised oscillating resistance, , between
a and b of the Andreev interferometer as a
function of the normalised exteral flux . b,
The phase difference between e and f , black
are experimental data, the solid line is
theoretical. c, Hysteresis in the resistance
of an Andreev interferometer attached to a
classical Josephson circuit white and black
dots are the data taken with increasing and
decreasing magnetic field, respectively. d,
Close-up of the Andreev interferometer
oscillations in Fig. a near the degeneracy point.
The transition between different circulations of
persistent current show no evidence of
hysteresis white and black dots are the data
taken as in c. The dashed line corresponds to .
.
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The energy spectrum construction using Andreev
probe data

• The phase difference is related to the
  persistent current in the qubit
• is itself related to the energy of
  the Josephson loop through the derivative
• . Therefore, there is a
  formula
• that can be used to find the energy spectrum .
  To demonstrate the technique, we use a generic
  form for the spectrum
• where 2D is the energy gap at between the
  excited ( ) and ground ( ) states.
• For energy far away from the point we model with
  the two-junction energy
  
  
  

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The energy spectrum construction
1)
1)
2)
2)
3)
3)
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Comparison of experimental results with model
calculations
V. T. Petrashov, K. G. Chua, K. M. Marshall, R.
Sh. Shaikhaidarov and J. T. Nicholls Phys. Rev.
Letters, (2005)
Model calculations
Experiment
Model calculations a, Oscillations of the
normalised resistance in the ground energy state
as a function of the normalised external flux .
The insets show detail of oscillations in the
ground (solid lines) and excited states (dashed
lines) for different values of b, Phase
shifts in the ground and excited states the
insets show greater detail. c, The energy
spectrum.
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Temperature dependence of persistent currents

• The peak-to-peak amplitude of change in qq
  during transition between persistent current
  states of different circulation at different
  temperatures. Experimental (black symbols) and
  calculated (dashed lines for D 0.035Ej () and
  D 0.025Ej ()). The decrease in D qq is a
  result of reduction in Isq due to thermal
  fluctuations given by
• ISq (T) ISq (0) tanh(Eq - Eq-)/2kBT,

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Time domain experiments

• The next stage is the measurement of the excited
  states using high frequency techniques. When the
  circuit is irradiated at resonant frequency , the
  measured resistance is expected to oscillate in
  time at Rabi frequency with amplitude
  with corresponding
  difference in the voltages
  between the two states, an easily measurable
  difference providing the basis for read-out of
  the quantum states.

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• The Andreev read-out timescalesThe following
  calculated timescales are attractive compared to
  other read-out techniques
• The response time tr 10-10 s, which is
  determined by the quasiparticles time of
  flight.
• The discrimination time tD characterizes the
  sensitivity of the read-out, and is the time
  taken to reach a signal-to-noise ratio of 1 when
  measuring a quantum state. For the reflection
  measurements tD, SV /(DVR)2, where DVR is the
  reflected signal and SV is spectral density of
  the voltage noise. We estimate tD3.110-8 s, for
  the amplifier noise temperature TN2K, which is
  more than two orders of magnitude shorter than
  state-of-art.
• The measurement time tm is the actual time taken
  to measure a state. The fidelity F of a
  measurement with negligible back-action follows
  the functional form Ferf (tm/2tD)1/2.
• For a single-shot measurement the fidelity F of
  the probe should be close to unity and the
  measuring time tm must be smaller than the energy
  relaxation time T1. Our estimate of the
  single-shot time tS110-7 s.
• The dead time td is the time needed to reset both
  the read-out and the qubit after a measurement.
  During read-out the qubit stays in thermal
  equilibrium, and td is expected to be negligible.

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Back action in the ON and OFF states
Ideally a read-out should have an ON and an
OFF state. During reset and gate operations the
read-out should be completely decoupled from the
qubit (OFF), and during read-out the probe should
be coupled to the qubit (ON), however the
back-action in the ON state should be weak enough
not to relax the qubit.
The read-out is OFF when the measurement current
Im is zero. The superconducting gap is induced in
the interferometer by the proximity effect that
is less than or equal to Thouless energy and the
qubit is decoupled from the measurement circuit
the back-action is expected to be negligible. A
measuring current passed through a-b turns the
probe ON, generating quasiparticles that couple
the read-out circuit to the qubit and performing
phase probing. The back-action in the ON state is
expected to be caused by the Nyquist-Johnson
noise, which will be minimized in a number of
ways.
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Summary

• Simple resistance measurements of an Andreev
  interferometer provide direct read-out of the
  local superconducting phase difference in a wide
  range of superconducting circuits
• from the phase difference the qubit energy
  spectrum can be constructed
• the probe is estimated to be more precise and
  faster than previous methods it can be
  fabricated to be impedance matched to standard
  high frequency setups
• the probe measures the local phase difference
  enabling direct determination of the quantum
  entanglement between different elements of
  complicated Josephson circuits that is
  unattainable with previous methods
• an increase in the operation speed can be
  achieved using ballistic Andreev interferometers
  made of high mobility two dimensional electron
  gas, which will also allow gate-controlled
  Andreev probes.
• Theory of the dynamic and thermal noise
  back-action is on order