error-correcting the IBM qubit

1. error-correcting the IBM qubit panos aliferis IBM

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

3. 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

4. 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 , symmetry 2) control flux, (mostly in small loop) adjusts the potential barrier

5. the IBM qubit

6. the IBM qubit basis for persistent currents

7. so, Panos, are we below threshold? 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.

8. so, Panos, are we below threshold? 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. - 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?

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 - 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

13. 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 ?

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

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

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

17. 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

18. the IBM qubit always on

19. 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

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

21. 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

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

28. the problem with leakage

29. 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.

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.) - 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.

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.) - 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.

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.) - 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.

35. 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.