Quantum Computing with Superconducting Circuits

Transcription

1 Quantum Computing with Superconducting Circuits S. Filipp, A. Fuhrer, P. Müller, N. Moll, I. Tavernelli IBM Research Zurich, Switzerland J. Chow, M. Steffen, J. Gambetta, A. Corcoles, D. McKay et al. IBM T. J. Watson Research Lab, Yorktown, USA cqom Workshop Diavolezza Feb 2, 2016 This work was partially supported by the U.S. Government

2 Quantum computing e.g. Cryptography: Shor s algorithm for exponential speed up for factoring [Shor, 1994] Database search/optimization: Grover s search algorithm for proven, sub-exponential quantum advantage [Grover, 1997] Linear equations: solving systems of linear equations with exponential speed up [Harrow, 2009] Quantum annealing: solve optimization problem by finding the ground state of an Ising spin system [D-Wave] Quantum simulation: properties and Hamiltonian dynamics of complex physical systems [Feynman, 1982] TU DELFT 2015

3 Quantum simulations Problem: limited possibilities of measurement & control of complex system exponential resources to store wave-function (2 N complex coefficients): Solution: Quantum simulator [Feynman, 1982; Lloyd,1996] system with equivalent dynamics, which can be well controlled and measured Troyer Applications: Quantum chemistry (nitrogen fixation, photosynthetic water-splitting [Kurashige (2013)], ) Materials (high-tc superconductivity, quantum magnets, )

4 Outline Error correction - Topological surface code Superconducting qubits Arbitrary error detection on a four-qubit lattice [IBM experiments: Chow, 2014; Corcoles, 2015] Future superconducting qubit development Tunable coupling mechanism 4 TU DELFT 2015

5 The quantum computing system Shor s, Grover s, Quantum simulations Quantum algorithms and user interface Magic states Braiding?? Holes in the QEC surface?? Logical gates Logical qubit construction Logical readout Still many open questions with regards to application and implementation up here! Surface code approach Classical computing, minimum weight matching algorithms Shaped microwave pulses Microwave generators and arbitrary waveforms Physical controls Quantum error correction Physical quantum processor Physical readout Quantum-limited amplifiers Microwave isolators ADCs Lattice of superconducting qubits and resonators 5 TU DELFT 2015

6 Fault-tolerant qubits Aim: build a fault tolerant system of physical qubits Path: quantum error correction for fault-tolerant qubits Qubits must have long coherence times Need high fidelity universal gates Physical controls (gates) and readout must be robust Complementary classical computer to keep up with quantum clock cycles Quantum error correction Physical controls Physical readout Physical quantum processor 6 TU DELFT 2015

7 Error Detection To detect error: encode 1 bit in 2 bits Bit-flip error parity change indicates error Quantum: no measurement without disturbance Solution: use an ancilla qubit to detect the error (but not the qubit state) data qubits ancilla qubit TU DELFT Controlled-NOT gates ZZ-measurement Ancilla qubit signals parity of data qubits

8 Error detection - Example Stabilizer state: ψψ BBBBBBBB measure ZZ: measure XX: ZZZZ = ψψ ZZZZ ψψ = ψψ ψψ = 11 XXXX = 11 Bit-flip (Z) error: ZZZZ = ψψ ( 1) 1 ψψ = 11 XXXX = = 11 Phase (X) error: ± ZZZZ = 11 XXXX = 11 Phase & bit-flip (X+Z) error: ± ZZZZ = 11 XXXX = 11

9 Fault-tolerant QC: Surface Code Make a two-dimensional lattice of qubits: code qubit Z syndrome X syndrome Measure syndrome qubits parity information about code qubits correct for errors on actual code qubits error threshold: pp 0 = 0.7% Logical qubits formed by specific states of code qubit (delocalized) [Raussendorf, Harrington, PRL (2007); Fowler et al. PRA (2009); Bravyi (1998)] TU DELFT 2015

10 Surface Code Single code state Stabilizers: XX and ZZ Z X 4 qubits, 4 buses, 4 readout resonators stepping stone towards full plaquette with 8 qubits Chow et al. Nat. Comm. 5, 4015(2014) S. Filipp - cqom Diavolezza, Feb 2016

11 SUPERCONDUCTING QUBITS TU DELFT 2015

12 Circuit Quantum Electrodynamics (QED) superconducting qubits (transmon) + microwave photons transmission line resonator transmon-type superconducting qubit 1 mm

13 Transmission line resonator 1 mm Nb on silicon Resonator is used as: read-out of qubit states multi-qubit quantum bus noise filter

14 The qubit a non-linear quantum circuit qubit: an-harmonic oscillator with non-linear energy spectrum Josephson junction (non-dissipative, non-linear element) JJ SEM image: qubit S. Filipp - cqom Diavolezza, Feb 2016

15 The transmon a noise resilient qubit φ JJ [Koch et al. PRA 2007] E SEM micrograph of artificial atom (transmon) Characteristic features Strong coupling to microwaves Multi-level structure Control: Magnetic flux: modulates frequencies (not at IBM) Microwaves: induces transition between levels f e g f e g

16 Dilution refrigerator chip hosting superconducting circuits sample holder (PCB) mounted at 10 mk stage of dilution fridge S. Filipp - cqom Diavolezza, Feb 2016

17 Circuit QED Applications: e.g. Quantum Hybrid Systems Spin Ensembles: e.g. NV centers D. Schuster et al., PRL 105, (2010) Y. Kubo et al., PRL 105, (2010) Nano-Mechanics J. Teufel et al., Nature 475, 359 (2011) X. Zhou et al., Nat. Phys. 9, 179(2013) Rydberg Atoms S. Hogan et al., PRL 108 (2012) Quantum Computing & Simulation Deutsch, Grover Algorithms L. DiCarlo et al., Nature 460, 240 (2009); ibid.nature 467, 574 (2010) Simulation Y. Salathe et al., PRX (2015); R. Barends et al, Nat. Comm. (2015) Error Correction M. Mariantoni et al., Sciene 334, 61 (2011) A. Fedorov et al., Nature 481, 170 (2012); M. Reed et al., Nature 481, 382 (2012); D. Risté et al., Nature Comm. 6 (2015); Kelly et al, Nature 519 (2015); Chow et al., Nat. Comm 5, (2013); A. Corcoles, Nat. Comm 6 (2015) Quantum effects e.g. geometric phases and topological phases Schroer et al., PRL 113, (2014) Roushan et al., Nature 515, 241 (2014) Abdumalikov et al., Nature 496, 482 (2013) Berger et al., Nature Comm. 6, 8757 (2015)

18 COHERENCE TU DELFT 2015

19 COHERENCE OF SUPERCONDUCTING QUBITS [1] Best T 2 Reproducible T 2 3D 2D Developments to extend coherence times Materials e.g. [2] Design and geometries e.g. [3] 3D transmon [4] IR Shielding [5,6] etc T 2 Remarkable progress over the past decade! [2] J. Martinis et al., PRL (2005) [3] K. Geerlings et al., APL (2012) [4] H. Paik et al., PRL 107, (2011) [5] R. Barends et al., APL 99, (2011) [6] A. Corcoles et al., APL 99, (2011) Year [1] Noise threshold for surface code QEC assuming ns gate time TU DELFT 2015

20 SURFACE LOSS Strategy: minimizing E-field density on the surface 2012: metal-substrate 11057t* substrate-air t QQ TT : metal-substrate 44399t substrate-air 66920t QQ TT μμμμ Metal-substrate or substrate-air interfaces as current dominant loss mechanisms *t is thickness of junk layer [Wenner et al., APL 99, 2011]

21 Thermal radiation induced dephasing attenuation configuration: residual thermal photons reduce TT φφ = TT 2 2 TT 1 bus 10mK: TT φφ > 1ss (calc) readout resonator (exposed to thermal radiation): 300K ~44K 3K in 10dB 10dB 20dB out HEMT TT φφ = 3333 μμμμ / 65 μμμμ (meas/calc) T φ wanted: > 1.5 ms (nn ttt = 10 4 ; TT eeeeee = 43 mmmm) (TT 1 = 41 μμμμ; TT 2 = 65μμμμ) 700mK 100mK 6dB 20dB 12 GHZ LP filter add (+16dB) + reconfigure attenuators TT φφ = 330 μμμμ 9mK Eccosorb117 filter 6 db 26 db 20 db 6 db DUT Eccosorb117 filter S. Filipp - cqom Diavolezza, Feb 2016

22 GATE FIDELITIES TU DELFT 2015

23 FOUR QUBIT LATTICE: PROPERTIES 4 qubits, 4 bus resonators, 4 independent readouts GHz readout frequencies GHz bus frequencies Cavity (GHz) Qubit f 01 (GHz) T1 (ms) T2 (ms) Gate fidelity Q Q Q Q (S1) Q2 (C1) Q1 (C2) Q3 (S2) Q4 [Corcoles et al., Nature Communications (2015)] TU DELFT 2015

24 2-qubit gate: Cross resonance gate Cross resonance gate: HH CCCC /ħ = Ω XXXX + νννννν + μμμμμμ + αααααα + ββββββ coupling-induced Rabi-rate Ω ± JJ/Δ of target transition Depends on state of control qubit) ωω 1 ωω 2 CCCC R1 Q1 control bus J R2 Q2 target ωω 2 [Rigetti, Devoret PRB (2010); JMC et al. PRL (2011); P. de Groot et al., Nat. Phys. (2010)] echo pulse to eliminate IX, ZZ, and ZI components [Corcoles (2013)] Typical gate times: nnnn (ZZZZ ππ gate) 2 Typical gate fidelities: 94%

25 READOUT TU DELFT 2015

26 Dispersive single-shot readout HH DD = ħ ωω rr + χχσσ zz aa + aa + ħ 2 ωω qq + χχ σσ zz qubit-state dependent resonance shift 95.9% ground excited M1 94.7% M2 94.1% M3 96.5% M4 measured with parametric amplifiers TU DELFT 2015

27 Correlated histograms of syndromes Q 2 excited 2 M2 (Arbitrary Voltage) Q 2 ground -1 0 M4 (Arbitrary Voltage) Q 4 ground Q 4 excited 1 TU DELFT 2015

28 ARBITRARY ERROR DETECTION TU DELFT 2015

29 Bit-flip and phase-flip error detection No error Phase flip error Bit flip error Y flip error State tomography of code qubits State Fidelity State Fidelity State Fidelity State Fidelity TU DELFT 2015 [Corcoles, Magesan, Srinivasan et al. Nature Comm (2015)]

30 Tracking X (phase)-errors TU DELFT 2015

31 Tracking Z(flip) & Y(combined) errors Z-errors -> {0,-} quadrant Y-errors -> {1,-} quadrant TU DELFT 2015

32 ONWARDS FROM A 4-QUBIT LATTICE Next steps: extend size of lattice while preserving quantum control Z X 8Q: Z + X plaquette X Z Z X 13Q: [[9,1,3]] code would demonstrate the Smallest FT logical qubit in our architecture TU DELFT 2015

33 Technology roadmap Reliable, robust cross-overs UCSB Delft ETH Microwave mode suppression (through-vias, multi-chips) Vertical signal delivery (to address/couple all qubits in 2D array) Improved material/fabrication methods Quintana (2014) Verification/characterization of qubits Two-qubit gates

34 Limitations to cross-resonance gate ωω 1 ωω 2 CCCC R1 Q1 J control bus R2 Q2 target ωω 2 [Rigetti and Devoret PRB 81, (2010) Chow et al. PRL 107, (2011)] Qubits must be closely spaced: Target qubit between 01 and 12 of control Good qubit limit Leakage regime CR works but slow Issue for large circuits: keep qubits close in frequency (for effective CR) minimize crosstalk given current fabrication constraints (frequency ±5%) Alternative: (flux-) tunable qubits, but these suffer from flux noise and cross-talk issues 2 nd alternative: tunable coupler, fixed qubits

35 Tunable coupler gate Idea: modulate coupling, keep qubits at fixed frequency [Bertet, PRA (2006)]. JJ JJ tt = JJ 0 + JJ 1 cos δδδδ HH/ħ = ωω 1 2 σσ 1 zz + ωω 2 2 σσ (2) (1) (2) zz + JJ tt σσxx σσxx high speed ( JJ 5 10MMMMMM), large qubit-qubit detunings (avoid qubit cross-coupling) maintain coherence (TT 1 /TT μμμμ) frequency of coupler modulated via external flux φφ tt : modulates qubit-coupler detunings modulates J-coupling δδ 1rr, δδ 2rr = ωω rr ωω 1,2 φφ tt JJ(tt) = gg 1gg δ 1rr (tt) + 1 δ 2rr (tt)

36 Tunable coupler gate Time-dependent Hamiltonian (neglecting DC term) In rotating frame of qubits: HH/ħ = ωω 1 2 σσ 1 zz + ωω 2 2 σσ (2) (1) (2) zz + JJ1 cos ωω dd tt σσ xx σσxx σσ xx = σσ + + σσ HH RRRR ħ JJ 1 2 eeiiωω ddtt + ee iiωω ddtt ee iiδδ 12tt σσ + 1 σσ 2 + ee iiδδ 12tt σσ 1 σσ ee iiσ 12tt σσ + 1 σσ ee iiσ 12tt σσ 1 σσ 2 ωω dd = δδ 12 (qubits difference frequency): iswap operation between states 10> and 01> JJ 1 σσ (1) 2 + (2) σσ + σσ (1) (2) σσ + ωω dd = Σ 12 = ωω 1 + ωω 2 (qubits sum frequency): blue sideband transition JJ 1 σσ (1) (2) 2 + σσ+ + (1) (2) σσ σσ ωω dd = δδ 12 + αα (difference + anharmonicity): shift of 1111 (mind leakage!) XX-YY δδ 12 Σ 12 Tunable quantum gate to create XX, YY & ZZ interactions simultaneously

37 Microwave activated swap interaction ωω 1 /ωω 2 (GHz) Q1 Q2 TC max Δ (MHz) TT 1 (us) TT 2 (us) oscillations in 01/10 state (XX+YY): 25x25um SQUID SSSSSSSS-gate

38 XX-90 gate 2 SWAP gates with echo pulse: echo pulse flips the sign of Y and Z YY and ZZ are cancelled 90 degree rotation around the XX axis Q1 Q2 TC 450ns UU XXXX 90 = ii 0 1 ii 0 0 ii 1 0 ii e.g. 10 ( 10 ii 01 )/ 2 95% process fidelity 98% entangled state fidelity

39 Quantum IBM Zurich Fermionic systems, e.g. Fermi Hubbard model or molecules (H 2 ) Required: Realization of hopping Hamiltonian HH = tt (cc + ii cc jj + cc + jj cc ii ) 2 Mapping to spins: ii,jj 1 3 HH JJJJ = 1 2 tt XX 1XX 2 + YY 1 YY 2 + XX 2 XX 3 + YY 2 YY 3 + XX 1 ZZ 2 XX 3 + YY 1 ZZ 2 YY 3 Ancilla qubits to generate 2-local terms HH JJJJ = HH 2 Δtt 12 ZZ rrzz 5 + ZZ 4 ZZ 6 + {XXXX, ZZZZ, }

40 Quantum IBM Zurich work in progress Postdoc position available!