errorcorrecting the IBM qubit

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error-correcting the IBM qubit
panos aliferis
IBM
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the IBM qubit
- three Josephson junctions
- three loops
- high-Q superconducting transmission line
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the IBM qubit
- three Josephson junctions
- three loops
- three side transmission lines for
flux control
- two SQUIDs for measurement
- T115ns _at_ IBM ( but µs elsewhere)
- high-Q superconducting transmission line
- Q104 ( but 106 _at_ 4K possible)
- T13µs _at_ IBM
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the IBM qubit
- three Josephson junctions
- three loops
- three side transmission lines for
flux control
- two SQUIDs for measurement
- T115ns _at_ IBM ( but µs elsewhere)
- high-Q superconducting transmission line
- Q104 ( but 106 _at_ 4K possible)
- T13µs _at_ IBM
parameter space
1) flux difference in two big loops,
for ,
symmetry
2) control flux, (mostly in small loop)
adjusts the potential barrier
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the IBM qubit
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the IBM qubit
basis for persistent currents
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so, Panos, are we below threshold?
the problem
- in arXiv0709.1478, the IBM team, Brito
, DiVincenzo, Koch, and Steffen ,
discussed pulsed gates for their qubit.
- they estimated gate fidelities of the order of
99, and they observed noise is biased with
bias 10.
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so, Panos, are we below threshold?
the problem
- in arXiv0709.1478, the IBM team, Brito
, DiVincenzo, Koch, and Steffen ,
discussed pulsed gates for their qubit.
- they estimated gate fidelities of the order of
99, and they observed noise is biased with
bias 10.
- in fact, dephasing is much stronger than
de-excitation in many systems?
for most qubits, .
the obvious question is, can we exploit this
noise asymmetry to improve the threshold
for quantum computation?
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the problem
- but this is tricky. why?
1) the gates that we apply can destroy this
asymmetry e.g., Hadamard gates will
propagate errors to errors.
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the problem
- but this is tricky. why?
1) the gates that we apply can destroy this
asymmetry e.g., Hadamard gates will
propagate errors to errors.
2) and even if we restrict to gates that
propagate phase errors to phase errors
alone?e.g., the CNOT?, noise in the gates may not
be biased e.g., to describe noise in a
CNOT, you need operators that contain .
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the problem
- but this is tricky. why?
1) the gates that we apply can destroy this
asymmetry e.g., Hadamard gates will
propagate errors to errors.
2) and even if we restrict to gates that
propagate phase errors to phase errors
alone?e.g., the CNOT?, noise in the gates may not
be biased e.g., to describe noise in a
CNOT, you need operators that contain .
3) and even if we restrict to diagonal gates
to avoid (1) (2), errors can propage
to errors via measurements
e.g., think of teleportation and cluster-
state computation.
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the idea
- we will encode the ideal quantum circuit by
using .
concatenated CSS code
length-n repetition code
biased noise
more balanced effective noise with str. below
effective noise with arbitrarily small str.
- our quantum computer will execute
where
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the idea
- we will encode the ideal quantum circuit by
using .
concatenated CSS code
length-n repetition code
biased noise
more balanced effective noise with str. below
effective noise with arbitrarily small str.
- our quantum computer will execute
- but, how biased is noise for operations in
?
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the IBM qubit
mostly operate here the S line
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the IBM qubit
qubit parked
- resting qubits are parked
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the IBM qubit
qubit parked
measurement point
- resting qubits are parked
- to measure, we completely unpark and move to
flux-qubit region
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the IBM qubit
qubit parked
measurement point
portal
- resting qubits are parked
- to measure, we completely unpark and move to
flux-qubit region
- for diagonal one-qubit gates, we unpark,
approach the portal, and park again
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the IBM qubit
always on
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the IBM qubit
always on
- two qubit species, A and D, s.t.
- qubits of same species cannot interact, but
it is ok with our schemethink of A as ancilla
and D as data
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the IBM qubit
- to apply a between qubits A and
D
- both qubits start from parking
- apply the adiabatic flux pulses
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error sources in the model
- truncation of Hilbert space (10, systematic )

use a model with 2 flux and 2 transmission-line
states per qubit
- flux low-frequency noise (due to bath spins)
pulse synchronization (due to pulse
generator)
flux/time shifts constant in each shot, taken
from Gaussian with
- Johnson noise (due to resistances)
limits coherence time to
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estimates
we will only use this set
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estimates
we will only use this set
- indirect implementations use 3 CPHASE
gates, or 1 CPHASE and 2 Hadamards.
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estimates
we will only use this set
- indirect implementations use 3 CPHASE
gates, or 1 CPHASE and 2 Hadamards.
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estimates
we will only use this set
- indirect implementations use 3 CPHASE
gates, or 1 CPHASE and 2 Hadamards.
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the scheme
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the problem with leakage
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the problem with leakage
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the problem with leakage
- if a qubit leaks, then leakage can propagate
(with probability 10-3) to every other qubit
that interacts with it.
- although this is a rare effect, it is useful to
have a simple way to block leakage from
spreading.
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the problem with leakage
repeat
- and now note that there is no way for a single
leakage error to propagate to both output
blocks.
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comments
- by taking to be the concatenated 4-qubit
code, and using a Fibonacci decoding scheme,
we find our error rates are below threshold
!
(we can use the 3-bit repetition code, and 3
measurement repetitions.)
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comments
- by taking to be the concatenated 4-qubit
code, and using a Fibonacci decoding scheme,
we find our error rates are below threshold
!
(we can use the 3-bit repetition code, and 3
measurement repetitions.)
- should we celebrate ?
NEY 1) our analysis shows we are just below
thresholdoverhead is large, 2) the scheme
is not geometrically local, 3) we have
assumed noise is described by superoperatorsno
memory.
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comments
- by taking to be the concatenated 4-qubit
code, and using a Fibonacci decoding scheme,
we find our error rates are below threshold
!
(we can use the 3-bit repetition code, and 3
measurement repetitions.)
- should we celebrate ?
NEY 1) our analysis shows we are just below
thresholdoverhead is large, 2) the scheme
is not geometrically local, 3) we have
assumed noise is described by superoperatorsno
memory.
YEY 1) our analysis is rigorous but not
tightbelieving Knill, we may be
significantly below threshold, and the overhead
will be moderate, 2) we use very small
codes, so the penalty for enforcing locality may
only be a small factor, 3) since
1/f noise is primarily due to bath spins in the
proximity of each qubit, correlated
errors will mainly occur on already erroneous
qubits.
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comments
- by taking to be the concatenated 4-qubit
code, and using a Fibonacci decoding scheme,
we find our error rates are below threshold
!
(we can use the 3-bit repetition code, and 3
measurement repetitions.)
- should we celebrate ?
NEY 1) our analysis shows we are just below
thresholdoverhead is large, 2) the scheme
is not geometrically local, 3) we have
assumed noise is described by superoperatorsno
memory.
YEY 1) our analysis is rigorous but not
tightbelieving Knill, we may be
significantly below threshold, and the overhead
will be moderate, 2) we use very small
codes, so the penalty for enforcing locality may
only be a small factor, 3) since
1/f noise is primarily due to bath spins in the
proximity of each qubit, correlated
errors will mainly occur on already erroneous
qubits.
- The message for experiments is that CPHASE can
effectively replace the CNOT, and that the
more biased the noise the more useful the qubit.
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references
threshold theorem level reduction
PA, Gottesman, and Preskill, quant-ph/0504218,
my thesis, quant-ph/0703230
Fibonacci scheme
Knill, quant-ph/0410199
PA, quant-ph/07093603
quantum computing against biased noise
PA and Preskill, arXiv0710.1301
PA, Brito, DiVincenzo, Steffen, Preskill, and
Terhal soon.