Abraham Asfaw Princeton University

1. Three-qubit quantum error correction with superconducting circuits Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature482, 382 (2012) Abraham Asfaw Princeton University

2. Three-qubit quantum error correction with superconducting circuits Outline • Quantum Error Correction • Bit-flip QEC • Phase-flip QEC • QEC Codes • Circuit QED • Relevant energy level transitions • Implementation of a CCPHASE gate • QEC experimental results • Alternate scheme(s)

3. Three-qubit quantum error correction with superconducting circuits Quantum Error Correction Nielsen & Chuang, Kaye, Laflamme & Mosca

4. Three-qubit quantum error correction with superconducting circuits Bit-Flip Quantum Error Correction • Encoding scheme produces entangled GHZ-like states • Codewords are +1 eigenstates of the ZiZj operators Nielsen & Chuang, Kaye, Laflamme & Mosca

5. Three-qubit quantum error correction with superconducting circuits Bit-Flip Quantum Error Correction Without decoding Nielsen & Chuang, Kaye, Laflamme & Mosca

6. Three-qubit quantum error correction with superconducting circuits Bit-Flip Errors in GHZ-Like States Measured observable-pair is unique for each error – SYNDROME CHECK Nielsen & Chuang, Kaye, Laflamme & Mosca

7. Three-qubit quantum error correction with superconducting circuits Phase-Flip Quantum Error Correction • Phase flips are equivalent to bit flips in the Hadamard basis • Codewords are +1 eigenstates of the XiXj operators Nielsen & Chuang, Kaye, Laflamme & Mosca

8. Three-qubit quantum error correction with superconducting circuits Roadmap

9. Three-qubit quantum error correction with superconducting circuits Circuit QED Architecture ~8 GHz ~7 GHz ~6 GHz Strauch et al., PRL91, 167005 (2003) Wallraff et al., Nature431, 162 (2004) DiCarlo et al., Nature460, 240 (2009) Reed et al., PRL 105, 173601 (2010) DiCarlo et al., Nature467, 574 (2010) Strauch et al., PRL91, 167005 (2003)

10. Three-qubit quantum error correction with superconducting circuits Roadmap

11. Three-qubit quantum error correction with superconducting circuits CPHASE Gate – Energy Levels Experimental detuning parameter ϵ relates the normalized currents of two capacitively coupled Josephson junctions Strauch et al., PRL91, 167005 (2003)

12. Three-qubit quantum error correction with superconducting circuits CPHASE Gate – Sudden Dynamics Suddenly move to and allow phase accumulation ; After CPHASE! Strauch et al., PRL91, 167005 (2003)

13. Three-qubit quantum error correction with superconducting circuits CPHASE Gate – Experimental Results Go back and measure 11 – Black 02 – White12 ns Suddenly move to resonance Wait some time to accumulate phase 12 ns! DiCarlo et al., Nature467, 574 (2010)

14. Three-qubit quantum error correction with superconducting circuits CPHASE Gate – Adiabatic Interaction Single excitation manifold Two excitation manifold CPHASE! DiCarlo et al., Nature460, 240 (2009)

15. Three-qubit quantum error correction with superconducting circuits Roadmap

16. Three-qubit quantum error correction with superconducting circuits Preparing GHZ States Stabilizers are being used as entanglement witnesses! 88% Fidelity DiCarlo et al., Nature467, 574 (2010)

17. Three-qubit quantum error correction with superconducting circuits Roadmap

18. Three-qubit quantum error correction with superconducting circuits Sudden Transfer Adiabatic Interaction Three excitation manifold Same as with a 6 GHz offset  3-QUBIT PHASE! M. Reed et al. Nature482, 382 (2012)

19. Three-qubit quantum error correction with superconducting circuits Move to site Move to cancel phase between and Return population to Move to site Move back to M. Reed et al. Nature482, 382 (2012)

20. Three-qubit quantum error correction with superconducting circuits State Tomography – Classical Action M. Reed et al. Nature482, 382 (2012)

21. Three-qubit quantum error correction with superconducting circuits Roadmap

22. Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature482, 382 (2012) Bit-Flip Error Correction Error causes rotation by angle Step 1: encoding Step 2: error channel; Step 3: recovery Result

23. Three-qubit quantum error correction with superconducting circuits Phase-Flip Error Correction Single qubit error rate Probability of more than one error Fidelity of error correction = Fidelity = Single qubit error rate Probability of more than one error Fidelity of error correction = Fidelity = M. Reed et al. Nature482, 382 (2012)

24. Three-qubit quantum error correction with superconducting circuits Future Directions Shor’s 9-Qubit Code Fault-tolerant error correction Introducing measurement-based error correction

25. Three-qubit quantum error correction with superconducting circuits Summary Questions? Implemented encoding into GHZ-like states using two CNOT gates CNOT gates from sudden excitations of 11 to 02 and waiting for phase accumulation in the two-excitation manifold (Strauch, Reed) Characterized error channel with at most one bit-flip and at most one phase-flip Implemented recovery using three-qubit CCPHASE from adiabatic interaction between 102 and 003 in the three-excitation manifold (Reed, also Federov) Used the circuit QED architecture with transmonqubits

26. Three-qubit quantum error correction with superconducting circuits Thank you for your attention! http://goo.gl/f2n7f Thanks to Matt Reed for helpful discussions.