error-correcting the IBM error-correcting the IBM qubitqubit

panos aliferis IBM

the IBM qubit- three Josephson junctions

- three loops

- high-Q superconducting transmission line

- three Josephson junctions

- three loops

- high-Q superconducting transmission line

- three side transmission lines for

- two SQUIDs for measurement

flux control

- Q~104 ( but 106 @ 4K possible)

- T1~3μs @ IBM

- T1~15ns @ IBM ( but ~μs elsewhere)

the IBM qubit

parameter space

1) flux difference in two big loops,

2) control flux, (mostly in small loop)

for , symmetry

adjusts the potential barrier

- three Josephson junctions

- three loops

- high-Q superconducting transmission line

- three side transmission lines for

- two SQUIDs for measurement

flux control

- Q~104 ( but 106 @ 4K possible)

- T1~3μs @ IBM

- T1~15ns @ IBM ( but ~μs elsewhere)

the IBM qubit

the IBM qubit

basis forpersistentcurrents

the IBM qubit

the problem

- in arXiv:0709.1478, 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.

so, Panos, are we below

threshold?

for most qubits, .

the problem

- in fact, dephasing is much stronger than de-excitation in many systems―

the obvious question is, can we exploit this noise asymmetry

to improve the threshold for quantum computation?

- they estimated gate fidelities of the order of 99%, and they observed noise is biased with bias ~10.

- in arXiv:0709.1478, the IBM team, Brito , DiVincenzo, Koch, and Steffen ,

discussed pulsed gates for their qubit.

so, Panos, are we below

threshold?

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

cluster- state computation.

the idea

- our quantum computer will execute

biased noise more balanced effective noise with str. below

effective noise witharbitrarily small str.

- we will encode the ideal quantum circuit by using .

concatenated CSS codelength-n repetition code

where

the idea

- our quantum computer will execute

- but, how biased is noise for operations in ?

biased noise more balanced effective noise with str. below

effective noise witharbitrarily small str.

- we will encode the ideal quantum circuit by using .

concatenated CSS codelength-n repetition code

mostly operate

here; the “S line”

the IBM qubit

qubit “parked”

- resting qubits are parked

the IBM qubit

qubit “parked”

measurement point

- resting qubits are parked

- to measure, we completely unpark and move to flux-qubit region

the IBM qubit

qubit “parked”

measurement point

“portal”

- for diagonal one-qubit gates, we unpark, approach the portal, and park again

- resting qubits are parked

- to measure, we completely unpark and move to flux-qubit region

the IBM qubit

always on

the IBM qubit

- 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

always on

the IBM qubit

- to apply a between qubits A and D

- both qubits start from parking

- apply the adiabatic flux pulses

the IBM qubit

error sources in the model

- flux low-frequency noise (due to bath spins)

- Johnson noise (due to resistances)

& pulse synchronization (due to pulse generator)

- truncation of Hilbert space (~10%, systematic )

flux/time shifts constant in each

“shot”, taken from Gaussian with

use a model with 2 flux and 2 transmission-line states per qubit

limits coherence time to

estimates

we will only

usethis set

estimates

we will only

usethis set

- indirect implementations use 3 CPHASE

gates, or 1 CPHASE and 2 Hadamards.

estimates

we will only

usethis set

- indirect implementations use 3 CPHASE

gates, or 1 CPHASE and 2 Hadamards.

estimates

we will only

usethis 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.)

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.

- should we celebrate ?

!

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.)

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.

- should we celebrate ?

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.)

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.

- should we celebrate ?

!

- The message for experiments is that CPHASE can effectively replace the

CNOT, and that the more biased the noise the more useful the qubit.

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.

threshold theorem & level reductionPA, Gottesman, and Preskill, quant-ph/0504218,

Knill, quant-ph/0410199 &

references

& my thesis, quant-ph/0703230

PA, quant-ph/0709:3603

Fibonacci scheme

quantum computing against biased noisePA and Preskill, arXiv:0710.1301

PA, Brito, DiVincenzo, Steffen, Preskill, and Terhal; soon.