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Experimental quantum information processing - the  of the art

Experimental quantum information processing - the  of the art. Quantum computation workshop, Jan. 2015. Nadav Katz A biased progress report. What is a quantum information and why do we want to process it? Different models – gates, cluster, adiabatic, topological.

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Experimental quantum information processing - the  of the art

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  1. Experimental quantum information processing - the  of the art Quantum computation workshop, Jan. 2015 Nadav Katz A biased progress report • What is a quantum information and why do we want to process it? • Different models – gates, cluster, adiabatic, topological. • Different realizations – photons, atoms, ions, semi-conductors and superconductors. • Outlook and future directions Contact: katzn@phys.huji.ac.il 02-6584133

  2. Motivation Wait for one half-life Single atom decays – cat dies! We NEVER see such macroscopic superpositions – why? Schrödinger: coherence Aristotle: Nature abhors a vacuum Dual/related problem (Feynman): exponential computational overhead for simulating many-body quantum systems • Quantum Information Processing – • Practical advantages over classical info. ($$) • Relates to quantum phase transitions and computation complexity • How big a Schrödinger kitten can we build?

  3. Some comments about QC It is mainstream physics to assume it is possible with established error-correction codes (is nature malicious/ingenious?) Failure actually implies fundamentally new physics regarding decoherence (no evidence for this in known physics) QC is not magic: General/Generic unitary evolution of a many-body is still exponentially hard to simulate In the presence of symmetry and structure, sometimes dramatic speedup is predicted

  4. 0 1 Storage of Information: Bits • Classical bit: definite 0 or 1 + 5V Transistor Logic: 0 = 0 volts 1 = 5 volts Vout • Quantum bits: superpose 0 or 1 H atom wavefunctions: Example:

  5. Bloch representation Geometrical picture: Useful for any two-level system Control: resonant (or close to resonant) pulses can be visualized as a rotation!

  6. x lifetime time Qubit Characterization 1 Rabi Meas. time 0 1 1 T1 ~450ns 0 1 x/2 x/2 T~100ns P1 Ramsey time 0 1 T2~350ns y x/2 x/2 Echo time 0 0 100 200 300 400 500 600 Data from 2007… time [ns]

  7. Entanglement Qubit 1 Qubit 2 Qubit 3 Qubit 4 • Require 2N complex numbers to specify a general N-qubit state! • Many (most actually) such states are not separable = entangled Classic 2-qubit example: Bell state Resource for secure communication (not discussed) Such (anti-)correlations are normally generated by interactions (gates).

  8. Classical Computation: Gate model(DiVincenzo criteria) Quantum Computation: • Initialize state Yi = |000..0> • Logic via series of operations: • State • Manipulation • (1 qubit) • Controlled not • (2 qubit) • Final state measurement • Measure qubits of state Yf • Coherence: • tcoherence / tlogic ~ number logic operations • > 102 for error correction • Initialize state • Logic • Output result • Logic errors: • Error correction possible |0>->|1> |1>->|0> 0->1 1->0 not |0>->(|0>+|1>)/21/2 } 00->0 01->0 10->0 11->1 |00>->|00> |10>->|10> |01>->|11> |11>->|01> + linear superposition and bit control

  9. Need to be clever When we measure – we want to see something interesting (and not some random, useless state out of 2N)… Well-known quantum computing algorithms: • Deutsch-Josza’s algorithm – find the parity of a function (exponentially fast!) • Shore’s algorithm – find the prime factors of a number (exponentially fast!) • Grover’s algorithm – check if a database contains an element (poly-faster) • These are famous, but there are some more • (Eigenvalue estimation, random walk, Boson sampling hidden subgroup)… IMPORTANT: Error correction can make it work even if gates are not perfect! (Shor+many others…)

  10. Qubit progress From Devoret and Schoelkopf, Science (2013) Remarkable progress of the past 15 years Already passed the fault tolerant threshold

  11. Alternative computational models Cluster states Single photons Adiabatic Topological Briegel & Raussendorf (2001) Generate a massively entangled initial state (c-not gates between nodes in graph, compute by measuring in a specific order) Knill, Leflamme, Milburn (2001) Using single photons (if you have them!) and linear optics – Scalable QIP is possible! Farhi (2001) Slowly evolve the Hamiltonian to remain in the ground state D-wave (??) Kitaev(1997) Exponentially degenerate ground state (phases) with large gap. Braiding particles evolves the state. All are theoretically equivalent – but experimentally VERY different…

  12. a perplexing flora and fauna of different systems Experimental Quantum Information Processing (QIP) Quantum dots Neutral atoms ?? Quantum optics Josephson superconducting qubits Trapped ions NMR

  13. Experimental QIP – a guide for the perplexed Smaller Bigger Easier to isolate Harder to couple Easier to couple & construct Harder to isolate photons Ions Neutral Atoms NMR Semiconductor Spins Quantum Dots and defects Superconducting Circuits • Excellent single qubit • coupling hard… • Sinlge photon/graph states • Dots: LONG T1 and T2 • Coherent Oscillations • Coupling? • Little dissipation • Reasonable coherence • Coupling • 9 qubits demonstrated • NMR: 2 to 7 qubits; • scalability? • Ions: up to 14 qubits + scalable • Many technical issues still unsolved Goal - reach the fault tolerant threshold – F  99 %

  14. Recent results Photons – 8 photon cluster states (2012) (Jian-Wei Pan group) Ions –99.93% fidelity of 1-qubit and 2-qubit gate demonstrated (Lucas group 2014): Coherent 14 and 6 ion states demonstated (Blatt/Wineland)

  15. Recent results – cont. Atoms – Mott insulator + controlled collisons + site addressing (Bloch group) Semiconductors – even denominator fractional Hall states demonstrated A possible model system for topological QIP. Heiblum group (2010)

  16. Recent results – cont (2). Superconductors – (1) surface code fault tolerance demonstrated (Martinis, 2013) (2) errors suppressed by logical qubits – for the first time! (Martinis 2014)

  17. Recent results – cont (2b). Superconductors – (2) errors suppressed by logical qubits – for the first time! (Martinis 2014)

  18. Recent results – cont (3). Superconductors – Circuit cavity electrodynamics Schoelkopf (2010) Simmonds (2007) Generation of Fock states up to N=16, with full state tomography Martinis (2010-2013), Katz (2013-2014)

  19. Outlook - hybrids Cavity – qubit interfaces will improve Yamamoto (2006-2008) Mechanical – qubit interfaces Kimbel (2008), Dayan (2014) Can we make a mechanical S-cat? Yes we can! Lehnert (2008-2013)

  20. Summary Exciting new computational models – better suited for implementation Experimental control/coherence of quantum systems is steadily growing Expect very exciting advances in the next decade…

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