Transcript Slide 1

error-correcting the IBM qubit
panos aliferis
IBM
the IBM qubit
- three Josephson junctions
- three loops
- high-Q superconducting transmission line
the IBM qubit
- three Josephson junctions
- three loops
- three side transmission lines for
flux control
- two SQUIDs for measurement
- T1~15ns @ IBM (but ~μs elsewhere)
- high-Q superconducting transmission line
- Q~104 (but 106 @ 4K possible)
- T1~3μs @ IBM
the IBM qubit
- three Josephson junctions
- three loops
- three side transmission lines for
flux control
- two SQUIDs for measurement
- T1~15ns @ IBM (but ~μs elsewhere)
- high-Q superconducting transmission line
- Q~104 (but 106 @ 4K possible)
- T1~3μs @ IBM
parameter space
1) flux difference in two big loops,
for
2) control flux,
, symmetry
(mostly in small loop)
adjusts the potential barrier
the IBM qubit
the IBM qubit
basis for
persistent
currents
so, Panos,
are we below threshold?
the problem
- in arXiv:0709.1478, the IBM team,
Brito
discussed pulsed gates for their qubit.
, DiVincenzo, Koch, and
- they estimated gate fidelities of the order of 99%,
and they observed noise is biased with bias ~10.
Steffen ,
so, Panos,
are we below threshold?
the problem
- in arXiv:0709.1478, the IBM team,
Brito
discussed pulsed gates for their qubit.
, DiVincenzo, Koch, and
Steffen ,
- 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?
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.
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
.
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 clusterstate computation.
the idea
- we will encode the ideal quantum circuit by using
length-n repetition code
biased noise
more balanced effective
noise with str. below
- our quantum computer will execute
where
.
concatenated CSS code
effective noise with
arbitrarily small str.
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
?
the IBM qubit
mostly operate
here; the “S line”
the IBM qubit
qubit “parked”
- resting qubits are parked
the IBM qubit
measurement point
qubit “parked”
- resting qubits are parked
- to measure, we completely unpark and move to flux-qubit region
the IBM qubit
measurement point
qubit “parked”
“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
the IBM qubit
always on
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 scheme—think of “A” as ancilla and “D” as data
the IBM qubit
- to apply a
between qubits A and D
- both qubits start from parking
- apply the adiabatic flux pulses
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
estimates
we will
only use
this set
estimates
we will
only use
this set
- indirect implementations use 3 CPHASE
gates, or 1 CPHASE and 2 Hadamards.
estimates
we will
only use
this set
- indirect implementations use 3 CPHASE
gates, or 1 CPHASE and 2 Hadamards.
estimates
we will
only use
this set
- indirect implementations use 3 CPHASE
gates, or 1 CPHASE and 2 Hadamards.
the scheme
the problem with leakage
the problem with leakage
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.
the problem with leakage
repeat
- and now note that there is no way for a single leakage error to
propagate to both output blocks.
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.)
!
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 threshold—overhead is large,
2) the scheme is not geometrically local,
3) we have assumed noise is described by superoperators—no memory.
!
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 threshold—overhead is large,
2) the scheme is not geometrically local,
3) we have assumed noise is described by superoperators—no memory.
YEY 1) our analysis is rigorous but not tight—believing 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.
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 threshold—overhead is large,
2) the scheme is not geometrically local,
3) we have assumed noise is described by superoperators—no memory.
YEY 1) our analysis is rigorous but not tight—believing 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 .
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/0709:3603
quantum computing against biased noise
PA and Preskill, arXiv:0710.1301
PA, Brito, DiVincenzo, Steffen, Preskill, and Terhal; soon.