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Abraham Asfaw Princeton University Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature 482, 382 (2012) Three-qubit quantum error correction with superconducting circuits

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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) Three-qubit quantum error correction with superconducting circuits

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Quantum Error Correction Three-qubit quantum error correction with superconducting circuits Condition for the existence of a recovery operator In other words, Nielsen & Chuang, Kaye, Laflamme & Mosca

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

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

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

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

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

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Roadmap Three-qubit quantum error correction with superconducting circuits

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Circuit QED Architecture Three-qubit quantum error correction with superconducting circuits DiCarlo et al., Nature 467, 574 (2010) Wallraff et al., Nature 431, 162 (2004) Reed et al., PRL 105, 173601 (2010) Strauch et al., PRL 91, 167005 (2003) DiCarlo et al., Nature 460, 240 (2009) ~8 GHz ~7 GHz ~6 GHz

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Roadmap Three-qubit quantum error correction with superconducting circuits

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CPHASE Gate – Energy Levels Three-qubit quantum error correction with superconducting circuits Experimental detuning parameter relates the normalized currents of two capacitively coupled Josephson junctions Strauch et al., PRL 91, 167005 (2003)

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CPHASE Gate – Sudden Dynamics Three-qubit quantum error correction with superconducting circuits Suddenly move to and allow phase accumulation CPHASE! Strauch et al., PRL 91, 167005 (2003)

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CPHASE Gate – Experimental Results Three-qubit quantum error correction with superconducting circuits 12 ns! DiCarlo et al., Nature 467, 574 (2010) Suddenly move to resonance Wait some time to accumulate phase Go back and measure 11 – Black 02 – White 12 ns

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CPHASE Gate – Adiabatic Interaction Three-qubit quantum error correction with superconducting circuits Single excitation manifoldTwo excitation manifold DiCarlo et al., Nature 460, 240 (2009) CPHASE!

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Roadmap Three-qubit quantum error correction with superconducting circuits

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Preparing GHZ States Three-qubit quantum error correction with superconducting circuits DiCarlo et al., Nature 467, 574 (2010) Stabilizers are being used as entanglement witnesses! 88% Fidelity

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Roadmap Three-qubit quantum error correction with superconducting circuits

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Bit-Flip Quantum Error Correction Three-qubit quantum error correction with superconducting circuits Encoding scheme produces entangled GHZ-like states Codewords are +1 eigenstates of the Z i Z j operators We have all the ingredients except a CCNOT gate Can make CCNOT gate from five two-qubit gates, six CNOTs Nielsen & Chuang T.C. Ralph et al., PRA 75, 022313 (2007)

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Three-qubit quantum error correction with superconducting circuits Sudden TransferAdiabatic Interaction Same as with a 6 GHz offset 3-QUBIT PHASE! M. Reed et al. Nature 482, 382 (2012)

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Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature 482, 382 (2012)

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State Tomography – Theory Three-qubit quantum error correction with superconducting circuits J.M. Chow, Thesis (2010)

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State Tomography – Classical Action Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature 482, 382 (2012)

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Roadmap Three-qubit quantum error correction with superconducting circuits

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Process Tomography – State Evolution Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature 482, 382 (2012)

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Alternate Toffoli Gate Three-qubit quantum error correction with superconducting circuits 76%, 69% 90 ns vs 85%, 78% 63 ns Federov et al., Nature 481, 170 (2012)

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Bit-Flip Error Correction Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature 482, 382 (2012)

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Phase-Flip Error Correction Three-qubit quantum error correction with superconducting circuits M. Reed et al. Nature 482, 382 (2012)

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Future Directions Three-qubit quantum error correction with superconducting circuits Shors 9-Qubit Code Fault-tolerant error correction Introducing measurement-based error correction

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Three-qubit quantum error correction with superconducting circuits 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 transmon qubits Summary Questions?

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

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