1. error-correcting the IBM qubit error-correcting the IBM qubit panos aliferis IBM

2. the IBM qubit - three Josephson junctions - three loops - high-Q superconducting transmission line

3. - three Josephson junctions - three loops - high-Q superconducting transmission line - three side transmission lines for - two SQUIDs for measurement flux control - Q~10 4 ( but 10 6 @ 4K possible) - T 1 ~3μs @ IBM - T 1 ~15ns @ IBM ( but ~μs elsewhere) the IBM qubit

4. 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~10 4 ( but 10 6 @ 4K possible) - T 1 ~3μs @ IBM - T 1 ~15ns @ IBM ( but ~μs elsewhere) the IBM qubit

6. basis for persistent currents the IBM qubit

7. 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?

8. 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?

9. 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.

10. 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.

11. 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.

12. the idea - our quantum computer will execute biased noisemore balanced effective noise with str. below effective noise with arbitrarily small str. - we will encode the ideal quantum circuit by using. concatenated CSS code length-n repetition code where

13. the idea - our quantum computer will execute - but, how biased is noise for operations in ? biased noisemore balanced effective noise with str. below effective noise with arbitrarily small str. - we will encode the ideal quantum circuit by using. concatenated CSS code length-n repetition code

14. mostly operate here; the “S line” the IBM qubit

15. qubit “parked” - resting qubits are parked the IBM qubit

16. qubit “parked”measurement point - resting qubits are parked - to measure, we completely unpark and move to flux-qubit region the IBM qubit

17. 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

18. always on the IBM qubit

19. - 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

20. - to apply a between qubits A and D - both qubits start from parking - apply the adiabatic flux pulses the IBM qubit

21. 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

22. estimates we will only use this set

23. estimates we will only use this set - indirect implementations use 3 CPHASE gates, or 1 CPHASE and 2 Hadamards.

24. estimates we will only use this set - indirect implementations use 3 CPHASE gates, or 1 CPHASE and 2 Hadamards.

25. estimates we will only use this set - indirect implementations use 3 CPHASE gates, or 1 CPHASE and 2 Hadamards.

26. the scheme

27. the problem with leakage

29. - 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.

30. the problem with leakage repeat - and now note that there is no way for a single leakage error to propagate to both output blocks.

31. 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.) !

32. 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 ? !

33. 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. !

34. 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.

35. threshold theorem & level reduction PA, 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 noise PA and Preskill, arXiv:0710.1301 PA, Brito, DiVincenzo, Steffen, Preskill, and Terhal; soon.