Prospects for Superconducting Qubits. David DiVincenzo Varenna Course CLXXXIII

Transcription

1 Prospects for Superconducting ubits David DiVincenzo Varenna Course CLXXXIII

2 uantum error correction and the future of solid state qubits David DiVincenzo Varenna Course CLXXXIII

3 The uantum Computer Roadmap, and going off road David DiVincenzo Varenna Course CLXXXIII

4 Basic Science to the Threshold of Technology History: Prospects: Macroscopic quantum coherence The Josephson junction Making superconducting qubits Theory and experiment progress on coherence Moore s law for quantum coherence Metrics for a quantum computer Architecture and the requirements of quantum error correction An integrated-circuit quantum computer

5 Interesting claim: Go direct from lumped electric circuit To Schrodinger equation V I

6 Current controlled by! " V dt

7 Some other history: Current controlled by! " V dt IBM had a large project ( ) to make a Josephson junction digital computer. 0 was the zero-voltage state, 1 was the finite-voltage state. Very different from a quantum computer.

8 (Al or Nb) ϕ 2 ϕ 1 (Al 2 O 3 ) I = I c sin ( ϕ ϕ ) 1 2

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10 Coherent control of macroscopic quantum states in a single-cooper-pair box Y. Nakamura, Yu. A. Pashkin and J. S. Tsai Nature 398, (29 April 1999) Feeble signs of quantum coherence

11 Saclay Josephson junction qubit Science 296, 886 (2002) Oscillations show rotation of qubit at constant rate, with noise.

12 Simple electric circuit s m a l l L C harmonic oscillator with resonant frequency ω 0 =1/ LC uantum mechanically, like a kind of atom (with harmonic potential): x is any circuit variable (capacitor charge/current/voltage, Inductor flux/current/voltage) That is to say, it is a macroscopic variable that is being quantized.

13 small Textbook (classical) SUID characteristic: the washboard Energy φ Φ 1. Loop: inductance L, energy φ 2 /L 2. Josephson junction: critical current I c, energy I c cos φ 3. External bias energy (flux quantization effect): φφ/l Josephson phase φ Junction capacitance C, plays role of particle mass

14 uantum SUID characteristic: small Energy φ Φ 1. Loop: inductance L, energy φ 2 /L 2. Josephson junction: critical current I c, energy I c cos φ 3. External bias energy (flux quantization effect): φφ/l uantum energy levels: 0>, 1>, 2>, etc. Josephson phase φ Junction capacitance C, plays role of particle mass

15 Burkard, Koch, DiVincenzo, Phys. Rev. B (2004) DiVincenzo, Brito, and Koch, Phys. Rev. B (2006). Effective potential is generally multidimensional, complex interplay between anharmonic and harmonic parts

16 Yale Josephson junction qubit Nature, 2004 Coherence time again c. 0.5 ls (in Ramsey fringe experiment) But fringe visibility > 90%!

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18 UCSB Josephson junction qubit ( phase )

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20 Recent IBM Experiments Capacitively Shunted Flux ubit (CSF) I 0 I 0 αi 0 C s T 1 =2.2µs 50µm C s /2 C s /2 [1] Signal [arb. units] Rabi oscillations T 2* = µs Time [µs] Ramsey fringes Nine out of ten samples measured gave T1>1µs No device failure observed yet Energy loss likely dominated by dielectric surface loss [1] M.Steffen et al., PRL, 105, (2010)

21 Prospects: a Moore s law for coherence NB: anticipated gate time approximately 30 nsec t gate /T 2 5 x10-3 = noise threshold of 2D surface code scheme 1µsec T 2 Reproducible T 2 1nsec

22 Prospects: a Moore s law for coherence 100µsec NB: anticipated gate time approximately 30 nsec t gate /T 2 5 x10-3 = noise threshold of 2D surface code scheme 1µsec T 2 >75µsec reported, L. DiCarlo, Oct T 2 >95µsec reported, Rigetti et al., Mar T 2 150µsec rep. Schoelkopf et al., June nsec T 2 Reproducible T 2

23 Nature 460, (2009) Fidelity well above 90% for two qubit gates Like early NMR experiments, but in scalable system!

24 Device Performance Metrics: Key Milestones and Projection Threshold for fault tolerant quantum computation On-off ratio R R 99.9% Measurement fidelity M Gate fidelity F 99.7% F 99% M R F R 96.8% F M M 90% F R F R M 68% Aggressive program could push all metrics in coordination towards fault tolerant operation

25 Device Performance Metrics: Key Milestones and Projection Threshold for fault tolerant quantum computation On-off ratio R R 99.9% Measurement fidelity M Gate fidelity F 99.7% F 99% M R F R 96.8% F M M 90% F R F R M 68% Aggressive program could push all metrics in coordination towards fault tolerant operation

26 Five criteria for physical implementation of a quantum computer & quantum communications 1. Well defined extendible qubit array -stable memory 2. Preparable in the 000 state 3. Long decoherence time (>10 4 operation time) 4. Universal set of gate operations 5. Single-quantum measurements 6. Interconvert stationary and flying qubits 7. Transmit flying qubits from place to place D. P. DiVincenzo, in Mesoscopic Electron Transport, eds. Sohn, Kowenhoven, Schoen (Kluwer 1997), p. 657, cond-mat/ ; The Physical Implementation of uantum Computation, Fort. der Physik 48, 771 (2000), quant-ph/

27 Approach to fault tolerant quantum computation: qubits (abstract) in fixed 2D square arrangement ( sea of qubits ), only nearest-neighbor coupling are possible

28 Fault tolerant algorithms with surface code Do repetitive pattern in large patches, except for holes where nothing is done Holes define qubits; algorithm performed by braiding holes measurements give error correction info theoretical threshold is 0.75%

29 Regular square lattice of coupled qubits make an effective architecture for fault tolerance ubits (green) coupled via high- superconducting resonators (gray) skew-square layout of qubits and resonators is one way to achieve abstract square Every qubit has a number of controller and sensor lines to be connected to the outside world (gold pads)

30 Nature 460, (2009) Fidelity well above 90% for two qubit gates Like early NMR experiments, but in scalable system!

31 IBM (February 2012) 3 qubit structure, start of scalability?

32 Vision: 2D integrated-circuit array Known components, qubits & coupling resonators Can implement surface code Concept (IBM) of surface code fabric with Superconducting qubits and coupling resonators

33 Final thoughts uantum computers are coming It will be as much a matter of business, policy, politics, etc. as of science Is there a further role for scientists? Example: semiconductors physics We should get ready to build the second, third, etc., quantum computer they will be a lot better than the first one We ve come a long way with quantum coherence!

34 FIN